U.S. patent application number 11/987628 was filed with the patent office on 2008-08-28 for apparatus, method and computer program product for weapon flyout modeling and target damage assessment.
This patent application is currently assigned to AAI Corporation. Invention is credited to Daniel H. Bass, Adam Fletcher Ehart, James Joseph Jaklitsch.
Application Number | 20080206718 11/987628 |
Document ID | / |
Family ID | 39716303 |
Filed Date | 2008-08-28 |
United States Patent
Application |
20080206718 |
Kind Code |
A1 |
Jaklitsch; James Joseph ; et
al. |
August 28, 2008 |
Apparatus, method and computer program product for weapon flyout
modeling and target damage assessment
Abstract
A weapon flyout simulation method, system, and computer program
product, includes modeling a target as a plurality of ellipsoidal
zones corresponding to a plurality of zones on the target, and
performing hit/miss assessment on the target by determining if said
trajectory of the weapon interferes with at least one of said
plurality of ellipsoids.
Inventors: |
Jaklitsch; James Joseph;
(Parkton, MD) ; Ehart; Adam Fletcher; (Baltimore,
MD) ; Bass; Daniel H.; (Pikesville, MD) |
Correspondence
Address: |
VENABLE LLP
P.O. BOX 34385
WASHINGTON
DC
20043-9998
US
|
Assignee: |
AAI Corporation
Hunt Valley
MD
|
Family ID: |
39716303 |
Appl. No.: |
11/987628 |
Filed: |
December 3, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60872064 |
Dec 1, 2006 |
|
|
|
Current U.S.
Class: |
434/12 |
Current CPC
Class: |
F41A 31/00 20130101;
G06F 30/15 20200101; G06T 13/20 20130101; F41G 7/006 20130101 |
Class at
Publication: |
434/12 |
International
Class: |
F41A 31/00 20060101
F41A031/00 |
Claims
1. A weapon flyout simulation method, comprising: modeling a target
as a plurality of ellipsoidal zones corresponding to a plurality of
zones on the target; and determining whether a trajectory of a
weapon interferes with at least one of said plurality of
ellipsoids.
2. The weapon flyout simulation method of claim 1, further
comprising: determining whether a the weapon has reached a closest
point of approach of the target.
3. The weapon flyout simulation method of claim 2, wherein said
step of determining whether a the weapon has reached a closest
point of approach of the target comprises: determining a relative
position of the target with respect to the weapon; calculating an
engagement closure state for the weapon based on said relative
position; comparing said engagement closure state to a previous
engagement closure state; and denoting that said closest point of
approach has been reached based on a change in said engagement
closure state.
4. The weapon flyout simulation method of claim 2, wherein said
step of determining if said trajectory of the weapon interferes
with at least one of said plurality of ellipsoidal zones comprises:
computing an elliptical magnitude at said point of closest approach
based on parameters relating to said at least one ellipsoidal zone;
and determining whether said trajectory of the weapon interferes
with said at least one ellipsoidal zone based on said elliptical
magnitude.
5. The weapon flyout simulation method of claim 1, further
comprising: transforming a trajectory of the weapon to a target
zone coordinate frame for each of said plurality of ellipsoidal
zones; wherein said step of determining whether a trajectory of a
weapon interferes with at least one of said plurality of ellipsoids
is performed using said trajectory of the weapon in said target
zone coordinate frame.
6. The weapon flyout simulation method of claim 5, wherein said
step of transforming a trajectory of the weapon comprises:
determining coordinates of the weapon and the target in an
engagement coordinate frame; transforming a trajectory of the
weapon from said engagement coordinate to a target body coordinate
frame; and transforming said trajectory of the weapon from said
target body coordinate to said target zone coordinate frame for
each of said plurality of ellipsoids.
7. The weapon flyout simulation method of claim 1, further
comprising: computing impact coordinates on the target.
8. The weapon flyout simulation method of claim 7, wherein said
step of computing impact coordinates comprises: calculating impact
coordinates in a target zone coordinate system based on a point of
closest approach for at least one of said plurality of ellipsoidal
zones; and determining impact location in a target body coordinate
system by rotating said impact coordinates from said target zone
coordinate system.
9. The weapon flyout simulation method of claim 1, further
comprising: computing a miss distance of the target by the
weapon.
10. The weapon flyout simulation method of claim 9, wherein said
step of computing a miss distance of the target by the weapon
comprises: computing a first vector representing said trajectory of
the weapon; computing a second vector representing a distance a
first trajectory point of the weapon and a centroid of at least one
of said plurality of ellipsoidal zones; computing a third vector
indicating a direction of a line running from said centroid of said
at least one ellipsoidal zone perpendicular to said first vector
based on said first and second vectors; scaling a magnitude of said
third vector to unity to obtain a unit direction vector; and
computing a miss vector based on a dot product of said unit
direction vector and said second vector.
11. The weapon flyout simulation method of claim 1, further
comprising: assessing impact damage on said target.
12. The weapon flyout simulation method of claim 11, wherein said
step of assessing impact damage is based on at least one of a
weapon lethality, a target survivability, or a zone sensitivity of
at least one of said plurality of ellipsoidal zones.
13. The weapon flyout simulation method of claim 11, wherein said
step of assessing impact damage comprises: determining a weapon
lethality of the weapon; determining an effective lethality of the
weapon on the target based on said weapon lethality and a zone
sensitivity of at least one of said plurality of ellipsoidal zones;
and determining if said effective lethality exceeds a survivability
threshold of the target.
14. The weapon flyout simulation method of claim 1, further
comprising: assessing damage to the target based on proximate
detonation of the weapon.
15. The weapon flyout simulation method of claim 14, wherein said
step of assessing damage to the target comprises: computing a miss
distance to a centroid of at least one of said plurality of
ellipsoidal zones; computing a range loss for said miss distance;
determining weapon lethality of the weapon; determining effective
lethality of the weapon on the target based on said weapon
lethality, a zone sensitivity of at least one of said plurality of
ellipsoidal zones, and said range loss; and determining if said
effective lethality exceeds a survivability threshold of the
target.
16. The weapon flyout simulation method of claim 1, wherein said
target comprises an aircraft.
17. The weapon flyout simulation method of claim 16, wherein said
plurality of zones on the target comprise at least one of: a
circumscribing sphere; a forward fuselage; an aft fuselage; a left
sing; a right wing; a left rear stabilizer; a right rear
stabilizer; a vertical stabilizer; and an extra surface.
18. A weapon flyout simulation system comprising: a target modeling
unit adapted to model a target as a plurality of ellipsoidal zones
corresponding to a plurality of zones on the target; and a hit/miss
assessment unit adapted to determine if a trajectory of a weapon
interferes with at least one of said plurality of ellipsoids.
19. The weapon flyout simulation system of claim 18, further
comprising: a closest point of approach determination unit adapted
to determine if the weapon has reached a closest point of approach
of the target.
20. The weapon flyout simulation system of claim 19, wherein said
hit/miss assessment unit is adapted to compute an elliptical
magnitude at said point of closest approach based on parameters
relating to said at least one ellipsoidal zone, and determine
whether said trajectory of the weapon interferes with said at least
one ellipsoidal zone based on said elliptical magnitude.
21. The weapon flyout simulation system of claim 18, further
comprising: a coordinate transformation unit adapted to transform a
trajectory of the weapon to a target zone coordinate frame for each
of said plurality of ellipsoidal zones; wherein said hit/miss
assessment unit determines if a trajectory of the weapon in said
target zone coordinate frame interferes with at least one of said
plurality of ellipsoids.
22. The weapon flyout simulation system of claim 18, further
comprising: an impact coordinate computation unit adapted to
compute impact coordinates on the target based on a point of
closest approach for at least one of said plurality of ellipsoidal
zones.
23. The weapon flyout simulation system of claim 18, further
comprising: a miss distance computation unit adapted to compute a
distance by which the weapon has missed the target.
24. The weapon flyout simulation system of claim 18, further
comprising: an impact damage assessment unit adapted to assess
impact damage on said target based on at least one of weapon
lethality, target survivability, or zone sensitivity of at least
one of said plurality of ellipsoidal zones.
25. The weapon flyout simulation system of claim 18, further
comprising: a proximate damage assessment unit adapted to assess
damage to the target based on proximate detonation of the
weapon.
26. The weapon flyout simulation system of claim 18, wherein said
target comprises an aircraft and said plurality of zones on the
target comprise at least one of: a circumscribing sphere; a forward
fuselage; an aft fuselage; a left sing; a right wing; a left rear
stabilizer; a right rear stabilizer; a vertical stabilizer; and an
extra surface.
27. A computer readable medium embodying program logic, which, when
executed, performs a method comprising: modeling a target as a
plurality of ellipsoidal zones corresponding to a plurality of
zones on the target; and determining whether a trajectory of a
weapon interferes with at least one of said plurality of
ellipsoids.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is a non-provisional application and claims
the benefit under 35 U.S.C. .sctn. 119(e) of U.S. Provisional
Application No. 60/872,064, Atty. Docket No. 13346-239106, filed
Dec. 1, 2006, entitled "Weapon Flyout & Damage Assessment
Modeling" to Jaklitsch et al., of common assignee to the present
application, the contents of which are incorporated herein by
reference in their entirety.
BACKGROUND
[0002] 1. Field
[0003] The present invention relates generally to weapon simulators
and more particularly to modeling weapon flyout modeling and
assessment of target damage.
[0004] 2. Related Art
[0005] While modern simulation systems use extremely detailed
visual models, these graphics entities are not well suited for
mathematically determining whether a projectile of a weapon such as
a missile having been fired at a target aircraft has physically hit
the target aircraft. Most existing simulations model the simulated
aircraft as a point in space, with the visual graphics rendered
about the point, in an appropriate attitude. Impact is typically
estimated probabilistically, based on proximity to the point
target. Alternatively, any projectile that passes within a fixed
radius may be declared as a "Hit" (i.e., target geometry is
contained within a sphere).
[0006] One of the issues associated with performing an accurate
assessment of a Hit or Miss engagement on an airborne target, with
a missile or ballistic projectile, is the extremely high rate of
motion involved in the scenario. In the engagement of a super-sonic
aircraft with a hypersonic projectile or missile, the rate of
closure between the two objects could easily reach Mach 5 (5500
ft/sec). At such rates, the time increment used for digital
simulation is far too coarse to accurately assess if an impact has
occurred. For example, if the simulation is running at a 30 Hz
update rate (33.000 ms period), the objects may experience 183 ft
of relative motion between two adjacent updates. Thus, the missile
or the projectile of the missile could pass clear through the body
of the aircraft from one sample rate to the next, without the
interference test at each sample in time revealing that a collision
had actually occurred.
[0007] What is needed is a Hit/Miss assessment model that overcomes
the limitations of the conventional Hit or Miss engagement on an
airborne target.
SUMMARY OF THE INVENTION
[0008] An exemplary system, method and computer program product for
weapon flyout modeling, hit/miss assessment, and target damage
assessment is disclosed herein, according to an exemplary
embodiment.
[0009] In an exemplary embodiment of the invention, there may be
provided a weapon flyout simulation method, which may include:
modeling a target as a plurality of ellipsoidal zones corresponding
to a plurality of zones on the target; and determining whether a
trajectory of a weapon interferes with at least one of the
plurality of ellipsoids.
[0010] In an exemplary embodiment, the weapon flyout simulation
method may further include determining whether the weapon has
reached a closest point of approach of the target. In an exemplary
embodiment, the determining if a closest point of approach of the
target has been reached may include: determining a relative
position of the target with respect to the weapon; calculating an
engagement closure state for the weapon based on the relative
position; comparing the engagement closure state to a previous
engagement closure state; and denoting that the closest point of
approach has been reached based on a change in the engagement
closure state.
[0011] In an exemplary embodiment, the step of determining if the
trajectory of the weapon interferes with at least one of the
plurality of ellipsoidal zones, according to the weapon flyout
simulation method of the invention, may include: computing an
elliptical magnitude at the point of closest approach based on
parameters relating to the at least one ellipsoidal zone; and
determining whether the trajectory of the weapon interferes with
the at least one ellipsoidal zone based on the elliptical
magnitude.
[0012] In an exemplary embodiment, the weapon flyout simulation
method may further include transforming a trajectory of the weapon
to a target zone coordinate frame for each of the plurality of
ellipsoidal zones. In an exemplary embodiment, the step of
determining whether a trajectory of a weapon interferes with at
least one of the plurality of ellipsoids may be performed using the
trajectory of the weapon in the target zone coordinate frame.
[0013] In an exemplary embodiment, the step of transforming a
trajectory of the weapon to a target zone coordinate frame for each
of the plurality of ellipsoidal zones may include: determining
coordinates of the weapon and the target in an engagement
coordinate frame; transforming a trajectory of the weapon from the
engagement coordinate to a target body coordinate frame; and
transforming the trajectory of the weapon from the target body
coordinate to the target zone coordinate frame for each of the
plurality of ellipsoids.
[0014] In an exemplary embodiment, the weapon flyout simulation
method of the invention may further include computing impact
coordinates on the target. In an exemplary embodiment, the step of
computing impact coordinates on the target may include: calculating
impact coordinates in a target zone coordinate system based on a
point of closest approach for at least one of the plurality of
ellipsoidal zones; and determining impact location in a target body
coordinate system by rotating the impact coordinates from the
target zone coordinate system.
[0015] In an exemplary embodiment, the weapon flyout simulation
method of the invention may include computing a miss distance of
the target by the weapon. In an exemplary embodiment, the step of
computing a miss distance of the target by the weapon may include:
computing a first vector representing the trajectory of the weapon;
computing a second vector representing a distance a first
trajectory point of the weapon and a centroid of at least one of
the plurality of ellipsoidal zones; computing a third vector
indicating a direction of a line running from the centroid of the
at least one ellipsoidal zone perpendicular to the first vector
based on the first and second vectors; scaling a magnitude of the
third vector to unity to obtain a unit direction vector; and
computing a miss vector based on a dot product of the unit
direction vector and the second vector.
[0016] In an exemplary embodiment, the weapon flyout simulation
method of the invention may include assessing impact damage on the
target. In an exemplary embodiment, the assessing impact damage may
be based on at least one of weapon lethality, target survivability,
or zone sensitivity of at least one of the plurality of ellipsoidal
zones. In an exemplary embodiment, the step of assessing impact
damage may include: determining weapon lethality of the weapon;
determining effective lethality of the weapon on the target based
on the weapon lethality and a zone sensitivity of at least one of
the plurality of ellipsoidal zones; and determining if the
effective lethality exceeds a survivability threshold of the
target.
[0017] In an exemplary embodiment, the weapon flyout simulation
method of the invention may include assessing damage to the target
based on proximate detonation of the weapon. In an exemplary
embodiment, the step of assessing damage to the target based on
proximate detonation of the weapon may include: computing a miss
distance to a centroid of at least one of the plurality of
ellipsoidal zones; computing a range loss for the miss distance;
determining weapon lethality of the weapon; determining effective
lethality of the weapon on the target based on the weapon
lethality, a zone sensitivity of at least one of the plurality of
ellipsoidal zones, and the range loss; and determining if the
effective lethality exceeds a survivability threshold of the
target.
[0018] In an exemplary embodiment of the invention, there may be
provided a weapon flyout simulation system, including: a target
modeling unit adapted to model a target as a plurality of
ellipsoidal zones corresponding to a plurality of zones on the
target; and a hit/miss assessment unit adapted to determine if a
trajectory of a weapon interferes with at least one of the
plurality of ellipsoids.
[0019] In an exemplary embodiment, the weapon flyout simulation
system of the invention may include a closest point of approach
calculation unit adapted to determine if the weapon has reached a
closest point of approach of the target. In an exemplary
embodiment, the hit/miss assessment unit may be adapted to compute
an elliptical magnitude at the point of closest approach based on
parameters relating to the at least one ellipsoidal zone, and
determine whether the trajectory of the weapon interferes with the
at least one ellipsoidal zone based on the elliptical
magnitude.
[0020] In an exemplary embodiment, the weapon flyout simulation
system of the invention may include a coordinate transformation
unit adapted to transform a trajectory of the weapon to a target
zone coordinate frame for each of the plurality of ellipsoidal
zones. In an exemplary embodiment, the hit/miss assessment unit may
determine whether a trajectory of the weapon in the target zone
coordinate frame interferes with at least one of the plurality of
ellipsoids.
[0021] In an exemplary embodiment, the weapon flyout simulation
system of the invention may include an impact coordinate
computation unit adapted to compute impact coordinates on the
target based on a point of closest approach for at least one of the
plurality of ellipsoidal zones. In an exemplary embodiment, the
weapon flyout simulation system of the invention may also include a
miss distance computation unit adapted to compute a distance by
which the weapon has missed the target.
[0022] In an exemplary embodiment, the weapon flyout simulation
system of the invention may include an impact damage assessment
unit adapted to assess impact damage on the target based on at
least one of weapon lethality, target survivability, or zone
sensitivity of at least one of the plurality of ellipsoidal zones.
In an exemplary embodiment, the weapon flyout simulation system of
the invention may include a proximate damage assessment unit
adapted to assess damage to the target based on proximate
detonation of the weapon.
[0023] In an exemplary embodiment, the target comprises an
aircraft. In an exemplary embodiment, the plurality of zones on the
target include at least one of: a circumscribing sphere; a forward
fuselage; an aft fuselage; a left sing; a right wing; a left rear
stabilizer; a right rear stabilizer; a vertical stabilizer; and an
extra surface.
[0024] According to an exemplary embodiment of the invention, there
may be provided a computer readable medium embodying program logic,
which, when executed, performs a method including: modeling a
target as a plurality of ellipsoidal zones corresponding to a
plurality of zones on the target; and determining whether a
trajectory of a weapon interferes with at least one of the
plurality of ellipsoids.
[0025] Further features and advantages of the invention, as well as
the structure and operation of various embodiments of the
invention, are described in detail below with reference to the
accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] The foregoing and other features and advantages of the
invention will be apparent from the following, more particular
description of a preferred embodiment of the invention, as
illustrated in the accompanying drawings wherein like reference
numbers generally indicate identical, functionally similar, and/or
structurally similar elements.
[0027] FIGS. 1A-1F illustrate an exemplary three-dimensional
ellipsoidal interference model of an exemplary target aircraft,
according to exemplary embodiment of the invention.
[0028] FIG. 2 depicts an exemplary block diagram of an exemplary
weapon flyout dynamics model, according to an exemplary embodiment
of the invention.
[0029] FIGS. 3A-3C illustrate an exemplary process flow diagram for
weapon kinematics flyout simulation, according to an exemplary
embodiment of the invention.
[0030] FIG. 4 illustrates an exemplary process flow diagram for
weapon guidance processing for an IR Seeker missile, according to
an exemplary embodiment of the invention.
[0031] FIG. 5 illustrates an exemplary Generalized Guidance Filter
500 implementing the Difference Equation, according to an exemplary
embodiment of the invention.
[0032] FIG. 6 illustrates an exemplary process flow diagram for
weapon guidance processing of a Laser Beam-Riding Seeker (RBS-70),
according to an exemplary embodiment of the invention.
[0033] FIG. 7 illustrates an exemplary Hit/Miss Assessment process
flow diagram for a target aircraft, according to an exemplary
embodiment of the invention.
[0034] FIG. 8 illustrates an exemplary process flow diagram for
determining whether a zone of the aircraft intercepts the weapon
trajectory, according to an exemplary embodiment of the
invention.
[0035] FIG. 9 illustrates an exemplary process flow diagram for
calculating the aircraft damage assessment, according to an
exemplary embodiment of the invention.
[0036] FIG. 10 depicts an exemplary computer system that may be
used in implementing an exemplary embodiment of the present
invention.
DETAILED DESCRIPTION OF AN EXEMPLARY EMBODIMENT OF THE PRESENT
INVENTION
[0037] An exemplary embodiment of the invention is discussed in
detail below. While specific exemplary embodiments are discussed,
it should be understood that this is done for illustration purposes
only. A person skilled in the relevant art will recognize that
other components and configurations can be used without parting
from the spirit and scope of the invention.
[0038] The exemplary embodiments of the invention are described
using a missile as an exemplary weapon. It should be understood,
however, that the present invention is not limited to one type of
weapon and may be used for any types of weapons, including, e.g.,
but not limited to, cruise missiles, anti-aircraft weapons,
anti-ship weapons, anti-tank weapons, anti-submarine weapons,
anti-personnel weapons, guided missiles, remote-control guided
missiles, homing-guided missiles, and/or unguided ballistic
munitions, etc. Any reference made herein to a missile should be
construed to include any type of weapon. Further, the exemplary
embodiments of the invention may be described with reference to an
aircraft as exemplary targets. It should also be understood that a
present invention may be used for hit/miss and damage assessment on
any type of target including, e.g., but not limited to, aircrafts,
aircraft carriers, ships, tanks, and/or any other type of mobile
and/or stationary targets. Accordingly, exemplary references made
in the FIGs. and the corresponding description should not be seen
as limiting the present invention to a certain type of weapon or a
certain type of target.
[0039] Exemplary embodiments of the present invention provide a
system, method, and/or computer program product that provide
modeling of a target aircraft interference geometry using
open-source performance data, simulation of weapon fly-out
dynamics, assessment of miss/hit of the target aircraft, assessment
of impact damage of the target aircraft, and/or assessment of
proximity detonation damage on the target aircraft.
[0040] According to an exemplary embodiment of the invention, in
order to maximize fidelity and provide user flexibility, the weapon
and/or the target may be modeled at a high level of parametric
abstraction to cover a wide range of weapons such as, for example,
but not limited to, missiles, unguided ballistic missiles,
remote-control guided missiles, etc., as well as a wide range of
targets such as, e.g., but not limited to, helicopters, bombers,
tankers, transport aircrafts, and/or cargo aircrafts, etc. In an
exemplary embodiment, the model having a high level of parametric
abstraction may be adapted to each specific case of a weapon and
target. In an exemplary embodiment, user-accessible model data
tables may be adapted to define the parameters for various weapons
and targets.
Exemplary Target Interference Geometry Modeling
[0041] The modeling approach according to embodiments of the
present invention may enable a high fidelity simulation of the
engagement dynamics, using a physics-based implementation. For
example, it may be possible to determine the part of a target
aircraft has been hit, and provide impact coordinates for the part
that has been hit. Further, the modeling approach according to
exemplary embodiments of the invention may significantly reduce
risk of not detecting a true "Hit" by de-coupling the model
development from the parametric data. Thus, development of a
software application embodying various aspects of the present
invention may proceed independently of specific data pertaining to
the weapons and/or targets.
[0042] Further, according to an exemplary embodiment of the
invention, modeling data to be populated at iterative levels of
detail. Thus, in cases where obtaining very detailed parametric
data may be difficult or impractical, less specific data estimates
may be allowed for modeling the weapon and/or the target. For
example, in some instances the exact parameters of the weapon or
target may be unavailable due to classification, or may not even be
included in the manufacturer's specifications. Also, there may be
US export issues with specific weapons data. In such cases, the
models may be populated with generic data, where such data is
available, or estimated, where such data is not available, and
later revised with additional levels of specific detail. In
addition, the parametric approach according to exemplary
embodiments of the present invention may provide more flexibility
by allowing a user to easily tune the performance parameters or
even define new models.
[0043] In an exemplary embodiment, it may be assumed that the
weapon as well as the target aircraft are in a normal, fixed
coordinate frame (X North, Y East, Z Down), hereinafter referred to
as the Engagement Coordinate Frame (ECF). In an exemplary
embodiment, any coordinates in the ECF may be expressed in the
Gunner Centric Coordinate System (GCCS) (X East, Y North, Z up) by
applying a simple transform:
XForm.sub.ECF.sub.--.sub.to.sub.--.sub.GCCS=DCM[Yaw=90.degree.,Pitch=0,R-
oll=180.degree.] (Eq. 1)
[0044] In an exemplary embodiment, in order to create a high
fidelity physical simulation and hit/miss assessment of the weapon
to the target aircraft, a physical geometry of aircraft entities
may be modeled such that it may be possible to accurately determine
if a projectile of the weapon has hit the aircraft. As previously
discussed, most convent ional simulation systems use extremely
detailed graphics models that may not be suited for mathematically
determining whether a projectile has physically hit a target
aircraft. Thus, many existing simulations may fly the simulated
aircraft as, for example, a point in space, with the visual
graphics rendered about the point, in an appropriate attitude. In
such conventional systems, impact may be estimated
probabilistically based on proximity to the point target or may be
estimated deterministically based on passes of a projectile of the
weapon within a fixed radius of the point.
[0045] Accordingly, in an exemplary embodiment of the invention, in
order to provide a higher fidelity approximation of target physical
geometry, the target aircraft may be modeled using a series of
three-dimensional ellipsoidal zones corresponding to approximate
key features of the target aircraft. For example, the target
aircraft may be divided into ten different zones, such as, but not
limited to, the circumscribing sphere, the forward fuselage, the
aft fuselage, the left wing, the right wing, the left rear
stabilizer, the right rear stabilizer, the vertical stabilizer, and
two extra surfaces. Thereafter, each zone may be modeled as an
ellipsoid. In an exemplary embodiment, these ellipsoidal zones may
be used to determine if a trajectory of the weapon has passed
through the target aircraft.
[0046] Referring now to FIGS. 1A-1F, there is illustrated an
exemplary three-dimensional ellipsoidal interference model of an
exemplary target aircraft, according to an exemplary embodiment of
the invention. In FIGS. 1A-1F, the exemplary aircraft is an F-16
jet and the exemplary interference model may include a series of 7
ellipsoidal structures. FIG. 1A-1F illustrate the left-rear
elevated view 102, left-front elevated view 104, front view, rear
view 108, right view 110, and left view 112, respectively. In an
exemplary embodiment, the ellipsoids may have different stretching,
lateral offset, and angular rotation, so as to closely approximate
various parts of the aircraft geometry. In an exemplary embodiment,
each ellipsoid may model a specific zone on the aircraft and may be
used to assess impact damage to the specific zone which it models.
This basic technique may be easily adapted to model a wide range of
targets, such as, e.g., but not limited to, various aircraft
types.
[0047] The use of ellipsoids may provide a very easy and convenient
technique for building reasonably accurate physical interference
models, with a minimum of effort, as well as evaluating the model
for physical interference (e.g., ballistic impact) with minimal
computational load. In an exemplary embodiment, where the target is
embodied as an aircraft, a standard model structure for the target
aircraft may include, e.g., but not limited to, 10 zones, which may
be arranged, in an exemplary embodiment, as shown in Table 1
below.
TABLE-US-00001 TABLE 1 Target Aircraft ellipsoidal Zones Zone 0
Circumscribing Sphere Zone 1 Forward Fuselage Zone 2 Aft Fuselage
Zone 3 Left Wing Zone 4 Right Wing Zone 5 Left Rear Stabilizer Zone
6 Right Rear Stabilizer Zone 7 Vertical Stabilizer Zone 8 First
Extra Surface Zone 9 Second Extra Surface
[0048] In an exemplary embodiment, each zone (ellipsoid) may be
defined by a set of parameters, such as, e.g., but not limited to,
nice (9) parameters. In an exemplary embodiment, the nine
parameters defining a zone may include: [0049] {a, b, c, x0, y0,
z0, zone_yaw, zone_pitch, zone_roll}
[0050] In an exemplary embodiment, these parameters may define the
ellipsoidal surface of each zone in accordance to the following
equation:
( x - x 0 ) 2 a 2 + ( y - y 0 ) 2 b 2 + ( z - z 0 ) 2 c 2 = 1 ( Eq
. 2 ) ##EQU00001##
[0051] In this equation, the offset parameters (x.sub.0, y.sub.0,
z.sub.0) denote the center of the ellipsoid in {x, y, z} vector
space. The dimensions of the resulting surface in {x, y, z} vector
space are directly related to the gain parameters (a, b, c). Thus,
by changing the coefficient (a, b, c), the surface may be made
spherical (i.e., where a=b=c), the surface may be stretched to
approximate the cylindrical shape of a fuselage (e.g., where
b=c<a), or flattened to approximate the surface of a wing or
stabilizer (e.g., where a is very small compared to b and c). The
location of the shaped surface in vector space may be controlled by
the offset parameters (x0, y0, z0). By changing the offset
parameters, a modeled surface may be moved forward/backward,
left/right, or up/down within the aircraft body coordinate system.
Further, in an exemplary embodiment, a rotational transformation
(yaw, pitch, roll) may be used to rotate the surface to an angle
necessary to approximate a specific aircraft feature or region. In
an exemplary embodiment, the rotational transform may define a
local coordinate frame for the ellipsoid with respect to aircraft
body coordinates.
[0052] In an exemplary embodiment of the invention, as depicted in
FIGS. 1A-1F, seven (7) different ellipsoids are combined, each
ellipsoid appropriately scaled, offset, and rotated, to model an
F-16 aircraft. In other types of aircraft, a greater or lesser
number of ellipsoids may be adapted to represent the various parts
of the aircraft. For example, a generic fighter aircraft with a jet
engine may be modeled using six (6) ellipsoids (e.g., two wings,
two rear stabilizers, vertical stabilizer, and the main
fuselage).
[0053] In an exemplary embodiment, various types of aircrafts may
be grouped into eight (8) broad categories, each category having a
specific number of ellipsoids to model the aircraft. In an
exemplary embodiment, the aircrafts may be categorized as, e.g.,
but not limited to, fast jets, tankers, commercial airliners, large
propeller jet, small propeller jet, helicopters, and Unmanned
Aerial Vehicles (UAV). In an exemplary embodiment, a generic
aircraft model may be designed for each aircraft category and may
later be parameterized for the specific aircraft being simulated.
Accordingly, it is possible to model a wide variety of aircrafts
with a reasonable fidelity coverage.
Exemplary Weapon Flyout Dynamics Modeling
[0054] According to an exemplary embodiment of the invention, the
weapon flyout dynamics model may replicate the physics associated
with flying a weapon through space. The model may be defined at a
level of abstraction that enables it to represent a wide range of
various weapons, yet faithfully replicate the physics involved with
the weapon projectile flyout. In an exemplary embodiment, the same
weapon flyout model may be used for both guided and un-guided
weapons. In an exemplary embodiment, a general model may be
constructed for the guided weapons and the un-guided weapons may
use the same model wherein the guidance parameters are
inapplicable.
[0055] FIG. 2 depicts an exemplary block diagram of an exemplary
weapon flyout dynamics model 200, according to an exemplary
embodiment of the invention. As illustrated, the model 200 may
include subsystems including a Weapon Kinematics Processing 202,
Guidance Processing 204, and a Weapon Properties Data File 206. In
an exemplary embodiment, the Weapon Kinematics Processing 202 may
execute generalized kinematics equations common applicable to all
weapons and projectiles. The Guidance Processing 204 may include an
executable module generating real-time steering vector commands to
the Weapon Kinematics Processing 202. In an exemplary embodiment,
the Guidance Processing 204 may be type-specific, including type
definitions for specific weapons such as, e.g., but not limited to,
IR Homing, Laser Beam Rider, Un-guided, etc.
[0056] The Weapon Properties Data File 206 may include a data file,
which may be a text file, providing the parametric input to
configure the generalized kinematics equations to reflect the
performance parameters of a specific weapon. The Weapon Properties
Data File 206 may also provide parametric input to configure the
guidance processing algorithms of the Guidance Processing 204. In
an exemplary embodiment, such parametric input may include, e.g.,
but not limited to, type definitions for specific weapons as well
as data pertaining to properties of specific weapons, which may
needed for modeling the guidance performance of the specific
weapons.
[0057] According to an exemplary embodiment of the invention, the
Weapon Kinematics Processing 202 may include a target modeling unit
210, a coordinate transformation unit 212, a hit/miss assessment
unit 214, a point of closest approach (PCA) determination unit 216,
an impact coordinate computation unit 218, a miss distance
computation unit 220, an impact damage assessment unit 222, and a
proximate damage assessment unit 224.
[0058] In an exemplary embodiment, the target modeling unit 210 may
model the target in ellipsoidal zones, as previously described. For
example, the target modeling unit 210 may receive parametric data
regarding the target aircraft and model the aircraft into
exemplary, but non-limiting, 10 ellipsoidal zones, each zone
corresponding to a section of the aircraft.
[0059] In an exemplary embodiment, the coordinate transformation
unit 212 may perform zone transformations from one coordinate
system to another. For example, the coordinate transformation unit
212 may transform coordinates of a point in a three-dimensional
space from any of the Engagement Coordinate Frame (ECF), Aircraft
Body Coordinate Frame, and Aircraft Zone Coordinate Frame, to one
another. The coordinate transformation unit 212 may also perform
transformation from any of these coordinate frames to weapon's
Attitude Eulerian angles. These transformations will be described
in more detail later.
[0060] In an exemplary embodiment, the hit/miss assessment unit 214
may perform assessment on whether a trajectory of the weapon passes
through at least one zone of the target aircraft. If so, the
hit/miss assessment unit 214 may declare the weapon as a "Hit".
[0061] In an exemplary embodiment, the hit/miss assessment unit 214
may make this determination by utilizing a point of closest
approach of the weapon. The point of closest approach may denote
the point detected by the simulation at which the weapon was
closest to the target aircraft. In an exemplary embodiment, the PCA
determination unit 216 may be responsible for calculating the point
of closest approach. Calculation of the point of closest approach
will be discussed in detail later.
[0062] In an exemplary embodiment, the impact coordinate
computation unit 218 may compute the coordinates at which the
weapon may hit the target. Alternatively, if it is determined that
the weapon has missed the target, the miss distance computation
unit 220 may calculate the distance by which the weapon missed the
target. Computation of the impact coordinates and miss distance are
discussed later in detail.
[0063] In an exemplary embodiment, the impact damage assessment
unit 222 may measure the damage on the target aircraft by the
weapon impact. If the weapon does not hit the aircraft directly,
but detonates near the aircraft, the aircraft may be damaged by the
proximate detonation of the weapon. In an exemplary embodiment, the
proximate damage assessment unit 224 may measure such proximate
damage on the target aircraft. Computation of impact damage and
proximate damage are discussed later in detail.
[0064] According to various exemplary embodiments of the weapon
flyout dynamics modeling approach, the user may be allowed to tune
the parametric performance of simulated weapons and define new
models for emerging weapons with a minimum of effort. For example,
if the guidance functions of a new missile are more esoteric than
the algorithms contained in existing type definitions, the user may
create a new type guidance model for the missile. However, most
existing air-defense missiles can be classified as one of infrared
(IR) Guided missiles, Laser Beam Rider missiles, and Un-guided
missiles. Thus, for most existing air-defense missiles, the user
may use one of the guidance data of one of these weapon types.
[0065] According to an exemplary embodiment of the invention, the
parametric inputs to the weapon flyout dynamics model may include,
e.g., but not limited to, weapon properties, initial conditions,
and perturbations. Weapon properties are related to the properties
of the weapon such as, e.g., but not limited to, the missile, which
do not change from one simulation scenario to the next. In an
exemplary embodiment, the weapon properties may be stored a Weapon
Properties Data File 206 as, e.g., but not limited to, text files
including such data. In an exemplary embodiment, the initial
conditions may include scenario-dependent conditions that are set
at the moment the weapon is launched. In an exemplary embodiment,
perturbations may include parameters that are real-time inputs to
the simulation, including, e.g., but not limited to, wind, steering
commands, etc.
Exemplary Weapon Kinematics Processing Inputs
[0066] In an exemplary embodiment, weapon properties parametric
input to the Weapon Kinematics Processing 202 may include, e.g.,
but not limited to, "acceleration vs. time characteristic",
weapon's "projected area vector", "wind sensitivity coefficient",
"missile maneuverability limit", "maximum range of interest", and
data relating to warhead lethality and propagation. Table 2 below
depicts exemplary weapon properties for Weapon Kinematics
Processing 202, according to an exemplary embodiment of the
invention.
TABLE-US-00002 TABLE 2 Weapon Properties for Kinematics Processing
PARAMETER DESCRIPTION UNITS Acceleration vs. Data table of
acceleration vs. time, in Meters/ Time increments of .tau., where
.tau. denotes the Sec.sup.2 update interval Area_Vec {Area.sub.x,
Area.sub.y, Area.sub.z} vector giving Meters.sup.2 the weapon's
projected area onto each of the three axes in the weapon body
coordinate system. K.sub.w Wind sensitivity coefficient,
1/Meter.sup.3 describing the acceleration resulting from wind.
G_limit Missile maneuverability limit (i.e., G max turning
acceleration) Maximum Range Flight range beyond which the Meters of
Interest simulated flyout may be stopped for non-detonated missiles
Warhead_.mu. Mean value of warhead lethality Damage Units
Warhead_.sigma. Standard Deviation of warhead Damage lethality
Units Warhead_n Warhead propagation exponent (1/ Dimension-
R.sup.n) less
[0067] In an exemplary embodiment, the "acceleration v. time
characteristic" may include a data table of acceleration vs. time,
in increments of .tau., where .tau. denotes the update interval. In
an exemplary embodiment, the time interval may be, e.g., but not
limited to, 30 ms. The "acceleration v. time characteristic" may be
a scalar quantity and may include both thrust & drag effects
along the weapon x-axis (i.e., the longitudinal body axis). The
"acceleration v. time characteristic" may not include other
environmental accelerations (e.g., but not limited to, G, G rate of
Turn, Windage, etc.), which may be computed in the Earth-fixed
Engagement Coordinate Frame.
[0068] In an exemplary embodiment, the "acceleration v. time
characteristic" may include a level of parametric abstraction
designed to increase simulation fidelity without compromising the
ability to closely replicate device physics. This characteristic
may include the acceleration along the weapon (e.g., the missile)
axis or the projectile longitudinal axis, including, e.g., but not
limited to, thrust, drag, and variable-mass effects. In an
exemplary embodiment, to the extent that detailed information is
available for thrust, drag, and mass, the acceleration may be
accurately pre-calculated from the known data. Alternately, if
detailed open-source data is not available, the acceleration
characteristic mat be computed based on the approximate flight time
vs. range. In either case, the basic model may remain unaffected
while the parametric data is modified.
[0069] In a further exemplary embodiment of the invention, the
level of abstraction used for "acceleration v. time characteristic"
may also enable differences in booster design to be captured
without changing the basic model. For example, a two stage booster
may include two independent periods of acceleration, each followed
by drag-induced deceleration, and finally a second stage burn-out.
A single stage boost, however, may only include one period of
acceleration followed by drag-induced deceleration, and a ballistic
shot may only include drag-induced deceleration. The acceleration
v. time characteristic may define the various booster stages.
[0070] In an exemplary embodiment, the weapon's "projected area
vector" may included a three dimensional vector {Area.sub.x,
Area.sub.y, Area.sub.z} providing the weapon's projected area onto
each of the three axes in the weapon body coordinate system. The
projected area vector may be used along with the wind sensitivity
coefficient to compute the acceleration induced by wind-load on the
missile or projectile. In an exemplary embodiment, the wind
sensitivity coefficient (K.sub.w) may describe the acceleration
result from the wind such that a=K.sub.wV.sub.w.sup.2A, where a is
the acceleration, A is area, and V.sub.w is the wind velocity
(equivalent to the combination of aero terms 0.5.rho.Cd/m). In an
exemplary embodiment, the wind acts on the projected area, A, and
produces an acceleration of K.sub.wV.sub.w.sup.2A.
[0071] In an exemplary embodiment, the "missile maneuverability
limit" (G) may specify the maximum turning acceleration for the
weapon. In an exemplary embodiment, the missile maneuverability
limit may be a result of aerodynamic limitations, but can be
expressed parametrically. In an exemplary embodiment, the maximum
range of interest may specify a max range, beyond which the weapon
flyout is discontinued for non-detonated weapons.
[0072] In an exemplary embodiment, the "warhead lethality" may
include, e.g., but not limited to, the mean value of warhead
lethality (Warhead_.mu.), the standard deviation of warhead
lethality (Warhead_.sigma.), and warhead propagation exponent
(Warhead_n).
[0073] In an exemplary embodiment of the invention, initial
conditions parametric inputs for the Weapon Kinematics Processing
202 may include, e.g., but not limited to, "initial weapon
position", "initial weapon attitude", and "launch/missile speed".
In an exemplary embodiment, the "initial weapon position" may
include an {x, y, z} initial position vector in the Engagement
Coordinate Frame (ECF), measures in, e.g., but not limited to,
Meters. The "initial weapon attitude" may include a {yaw, pitch,
roll} initial attitude measured in, e.g., but not limited to,
Radians. The "launch/missile speed" may indicate the initial weapon
scalar speed in, e.g., but not limited to, Meters/Sec. Table 3
below shows exemplary initial conditions parametric inputs for the
Weapon Kinematics Processing 202, according to an exemplary
embodiment of the invention.
TABLE-US-00003 TABLE 3 Initial Conditions for Kinematics Processing
PARAMETER DESCRIPTION UNITS Initial Missile Position {x, y, z}
Initial Position Vector Meters (Missile_Pos_ECF.sub.0) in the ECF
Initial Missile Attitude {Yaw, Pitch, Roll} Initial attitude
Radians Launch/Missile Speed Missile Initial Speed Meters/Sec
[0074] In an exemplary embodiment of the invention, the real-time
perturbations parametric inputs for the Weapon Kinematics
Processing 202 may include, e.g., but not limited to, "wind
velocity" and "steering vector". The "wind velocity" may include an
{x, y, z} wind velocity vector in the Engagement Coordinate Frame
(ECF). The "steering vector" may include a {Az, El} attitude
correction vector in the weapon body coordinates. Table 4 below
shows exemplary real-time perturbations parametric inputs for the
Weapon Kinematics Processing 202, according to an exemplary
embodiment of the invention.
TABLE-US-00004 TABLE 4 Real-Time Perturbations for Kinematics
Processing PARAMETER DESCRIPTION UNITS Wind Velocity {x, y, z} Wind
Velocity Vector Meters/Sec (Wind_Vel_ECF) in the ECF Steering
Vector Required {Az, El} Attitude Correction Radians Vector in
missile body coordinates (Req_Steer_BC)
Exemplary Guidance Processing Inputs
[0075] In an exemplary embodiment, the parametric input, e.g.,
weapon properties, initial conditions, and real-time perturbations,
for the Guidance Processing 204 may vary depending on the type of
weapon being simulated. For example, the parametric inputs to a
Guidance Processing 204 of a Infrared (IR) seeker may be different
from the parameter used for a laser beam-rider missile or an
unguided missile. For purposes of illustration, the exemplary
Guidance Processing 204 parametric inputs for an IR Seeker are
herein described.
[0076] In an exemplary embodiment, the weapon properties parametric
inputs for Guidance Processing 204 of an IR Seeker may include,
e.g., but not limited to, a guidance filter proportional gain
(K.sub.P), a guidance filter integral gain (K.sub.i), a guidance
filter differential gain (K.sub.d), a gimbal limit, and an
aim-point dynamics bias.
[0077] In an exemplary embodiment, the K.sub.P, K.sub.i, and
K.sub.d parameters may specify the proportional, integral and
differential gains of a guidance filter, respectively, if this
level of detail is known. In an exemplary embodiment, these
parameters may be measured using transfer functions from measured
error to steering vector. If all that is known is max rate of
turning acceleration for the missile, Kp, Ki, and Kd may be set to
1, 0, 0, respectively, and the maximum rate of turn may be
specified through the gimbal limit parameter in the Weapon
Kinematics Processing 202.
[0078] In an exemplary embodiment, the gimbal limit may specify the
maximum rate and/or the free range of the seeker gimbal. In an
exemplary embodiment, an angular error beyond this range may cause
the weapon to move beyond the range of detection and the target
track to be lost.
[0079] In an exemplary embodiment, the aim-point dynamics bias may
be a mechanism for programming profile effects such as, e.g., but
not limited to, pop-up or corkscrew flyout. In an exemplary
embodiment, the dynamic aim-point bias may be used to cause the
missile to lead the target, or otherwise bias the aim-point away
from the target centroid. Table 5 below shows exemplary weapon
properties parametric inputs for the Guidance Kinematics Processing
204 of an IR Seeker missile, according to an exemplary embodiment
of the invention.
TABLE-US-00005 TABLE 5 Weapon Properties for Guidance Processing of
an IR Seeker PARAMETER DESCRIPTION UNITS KP Guidance Filter
Proportional Gain Dimensionless Ki Guidance Filter Integral Gain
Sec Kd Guidance Filter Differential Gain 1/Sec Gimbal_limit {Az,
El} ordered pair, denoting the Radians max .+-. free range of the
seeker. Aim-point Data table of {Az, El} ordered pairs vs. Radians
Dynamic Bias time, in increments of .tau., where .tau. denotes the
update interval (30 ms)
[0080] In an exemplary embodiment, initial conditions parametric
inputs for the Guidance Processing 204 of an IR Seeker may include,
e.g., but not limited to, target lock/unlock, warhead enable,
target position state, target altitude state, and warhead detonate
command. In an exemplary embodiment, the aim-point static bias may
denote the aim-point bias to be added as an offset to the aim-point
error and may be specified by the weapon operator immediately prior
to launch. The aim-point static bias may be specified as a signed
{Az, El} angular bias having an aim-point with respect to the
target and may be added to the steering vector. Table 6 below shows
exemplary initial conditions parametric inputs for the Guidance
Kinematics Processing 204 of an IR Seeker missile, according to an
exemplary embodiment of the invention.
TABLE-US-00006 TABLE 6 Initial Conditions for Guidance Processing
of an IR Seeker PARAMETER DESCRIPTION UNITS Aim-point {Az, El}
ordered pair, denoting aim-point bias Radians Static Bias to be
applied as an offset to the aim error
[0081] In an exemplary embodiment, the real-time perturbations
parametric inputs for the Guidance Processing 204 may include,
e.g., but not limited to, aim-point static bias. In an exemplary
embodiment, the "target lock/unlock" parameter may denote
successful target lock. The target may be unlocked during flyout to
simulate a loss of track event or seek seeker malfunction. In an
exemplary embodiment, the "warhead enable" parameter may denote
proper functioning of the warhead fusing. The "target position
state" and "target attitude state" may respectively denote the
target position vector and the target Eulerian angles. The "warhead
detonate command" may denote the command used to detonate the
warhead at times other than normal fused detonation on the impact
of the point of closest approach of the weapon. Table 7 below shows
exemplary real-time perturbations parametric inputs for the
Guidance Kinematics Processing 204 of an IR Seeker missile,
according to an exemplary embodiment of the invention.
TABLE-US-00007 TABLE 7 Real-Time Perturbations for Guidance
Processing of an IR Seeker PARAMETER DESCRIPTION UNITS Target Lock/
Boolean State Input denoting successful Boolean Un-Lock target lock
if True. T/F Warhead Boolean State Input denoting proper Boolean
Enable functioning of the warhead fusing. False T/F denotes
detonate malfunction Target Position {x, y, z} Target Position
Vector Meters State Target Attitude {Yaw, Pitch, Roll} Target
Eulerian Angles Radians State Warhead Boolean Command to detonate
warhead at Boolean Detonate Cmd times other than normal fused
detonation T/F
[0082] In an exemplary embodiment of the invention, the seeker
failures may be simulated by setting the "target lock/unlock" to
"False", causing the seeker to stop tracking and instead output a
static steering vector {0,0} to the Kinematics Processing 202.
Also, successful ECM events, such as, e.g., but not limited to,
acquisition of a flare by an IR Seeker, can be simulated by
transferring the missile aim-point off the target and onto a bogus
object, such as, e.g., but not limited to, a flare, and then
continuing to run the simulation with the missile seeking the bogus
object.
[0083] The Guidance Processing 204 of other types of weapons such
as, e.g., but not limited to, may be simulated with parameters that
are similar to the parameters for an IR Seeker discussed above. For
example, for a laser beam rider missile, all the Guidance
Processing parameters, including the missile properties, initial
conditions, and real-time perturbations, are similar to the
parameters used for the Guidance Processing 204 of an IR Seeker,
except that a laser aiming state in the form of {Yaw, Pitch} Laser
Eulerian angle is used instead of the "target position state" and
"target attitude state" parameters.
[0084] In an exemplary embodiment, un-guided missiles may be
treated as a subset of the guided missile case. However, because
there is no seeker, the "steering vector" input to the Weapon
Kinematics Processing 202 may be held statically at {0,0}.
Accordingly, a model similar to the one discussed for an IR Seeker
may be used. In an alternative exemplary embodiment, however,
computational efficiency may be increased by using a sub-set of the
more general case for the Weapon Kinematics Processing 202, so that
time is not wasted computing parameters that are known to be not
applicable.
Exemplary Missile Kinematics Processing
[0085] FIGS. 3A-3C collectively illustrate an exemplary process
flow diagram for weapon (e.g., missile) kinematics flyout
simulation, according to an exemplary embodiment of the
invention.
[0086] The exemplary physical constants for this process 300 may be
as follows:
TABLE-US-00008 Gravity: G_Acc_Scalar = 9.80665 (m/sec.sup.2) Update
Period: T = .033000 (sec)
[0087] Beginning with FIG. 3A, process 300 for initializing weapon
settings may start at 302 and may continue to initialize Missile
Position, block 304:
Mis_Pos_ECF0={X,Y,Z} (Eq. 3)
[0088] According to an exemplary embodiment, Missile Attitude
(i.e., aim orientation) may then be initialized with respect to the
ECF, block 306:
Mis_Att_ECF0={Yaw,Pitch,Roll} (Eq. 4)
[0089] Initial Missile Velocity in an exemplary embodiment, may
then, in an exemplary embodiment, be initialized in Body Centered
Coordinates, block 308:
Mis_Vel_BC0={Initial speed,0,0} (Eq. 5)
[0090] In an exemplary embodiment, Missile Attitude Direction
Cosine Matrix (DCM) may then be computed from Missile Attitude
Eulerian angles (Mis_Att_ECF), block 310. Computation of DCM from
Eulerian angles are discussed later in detail.
EECF_to_Missile,0=DCM_XForm[{Yaw,Pitch,Roll] (Eq. 6)
[0091] Missile Velocity may then be transformed to Missile Velocity
Vector in ECF, block 312:
Mis_Vel_ECF0=Transpose[EECF_to_Missile,0]Mis_Vel_BC0 (Eq. 7)
[0092] Gravity Acceleration Vector may then be formed in the ECF,
block 314, according to any exemplary embodiment. In an exemplary
embodiment, the acceleration of gravity may be aligned with the
positive z axis in the ECF:
Gravity_Acc_ECF={0,0,G_Acc_Scalar} (Eq. 8)
[0093] Thereafter, process 300 may continue to A, where the missile
may be launched and the flyout loop may begin, block 316.
[0094] FIG. 3B illustrates an exemplary process 320 of weapon
flyout loop, according to an exemplary embodiment of the invention.
Starting at block 316, corresponding to A in process 300, the
process 320 may continue to compute current missile acceleration,
in block 322. In an exemplary embodiment, Accel.sub.n=Scalar from
Acceleration vs. time table.
[0095] In an exemplary embodiment, a Missile Linear Acceleration
Vector may be formed in the missile body coordinates, in block
324:
Mis_Lin_Acc_BCn={Acceln,0,0} (Eq. 9)
[0096] Thereafter, in an exemplary embodiment, a wind-induced
acceleration may be computed in ECF (Wind_Acc_ECF). Computation of
wind-included acceleration is discussed later in detail.
[0097] In an exemplary embodiment, an applicable Guidance Function
relating to the missile may be executed, in block 328. The Guidance
Function may return the Required Steering Vector (Req_Steer_BC) of
the missile. The Required Steering Vector may not have the effects
of acceleration limiting. In an exemplary embodiment, the Required
Steering Vector may be a {Yaw, Pitch} Eulerian.
[0098] In an exemplary embodiment, the Actual Steering Vector
(Act_Steer_BC) may be computed by applying acceleration limiting to
the Required Steering Vector, in block 330. Application of
acceleration limits to missile steering are discussed later in
detail.
[0099] In an exemplary embodiment, the Missile Steering
Accelerations may be computed Missile Body Coordinates
(Mis_Steer_Acc_BC) based on the Actual Steering Vector, in block
332. Computation of missile body accelerations due to steering is
discussed later in detail.
[0100] In an exemplary embodiment, the Missile Body Acceleration
may be computed by summing the Linear Body Acceleration and the
Steering Accelerations, in block 334:
Mis_Body_Acc_BCn=Mis_Lin_Acc_BCn+Mis_Steer_Acc_BCn (Eq. 10)
[0101] The Missile Body Acceleration, in an exemplary embodiment,
may then be transformed to ECF as (Mis_Acc_ECF), in block 336:
Mis_Acc_ECF.sub.n=Transpose[E.sub.ECF.sub.--.sub.to.sub.--.sub.Missile,n-
]Mis_Body_Acc_BC.sub.n (Eq. 11)
[0102] In an exemplary embodiment, all the acceleration vectors
(e.g., but not limited to, Wind-Induced Acceleration,
Gravity-Acceleration, and/or Missile Body Acceleration), may then
be added in ECF to compute the Total Acceleration Vector in ECF, in
block 338:
TAV_ECF.sub.n=Mis_Acc_ECF.sub.n+Wind_Acc_ECF.sub.n+Gravity_Acc_ECF
(Eq. 12)
[0103] Once the Total Acceleration is calculated, it may be
integrated into Velocity in ECF, in block 340, according to an
exemplary embodiment:
Mis_Vel_ECF.sub.n+1=Mis_Vel_ECF.sub.n+TAV_ECF.sub.nT (Eq. 13)
[0104] Similarly, according to an exemplary embodiment, the
integrate Velocity may be further integrated into Position in ECF,
in block 342:
Mis_Pos_ECF.sub.n+1=Mis_Pos_ECF.sub.n+Mis_Vel_ECF.sub.nT (Eq.
14)
[0105] According to an exemplary embodiment, a new Missile Attitude
may also be determined, in block 344:
E.sub.ECF.sub.--.sub.to.sub.--.sub.Missile,n+1=DCM_XForm[{Act_Yaw.sub.n,-
Act_Pitch.sub.n,0]E.sub.ECF.sub.--.sub.to.sub.--.sub.Missile,n
(Eqs. 15)
Where Act_Yaw & Act_Pitch are as previously defined :
##EQU00002## Act_Yaw n = Act_Steer _BC n [ [ 1 ] ] ##EQU00002.2##
Act_Pitch n = Act_Steer _BC n [ [ 2 ] ] ##EQU00002.3##
[0106] Using the new Missile Attitude, in an exemplary embodiment,
a new Missile Velocity Vector may be transformed from ECF to
Missile Body Coordinates, in block 346:
Mis_Vel_BC.sub.n+1=E.sub.ECF.sub.--.sub.to.sub.--.sub.Missile,n+1Mis_Vel-
_ECF.sub.n+1 (Eq. 16)
[0107] In an exemplary embodiment, Range-To-Impact (RTI)
calculation may be performed to determine the relative position of
target with respect to the missile, in block 348:
Tx=Tgt_Pos_ECFn[[1]]
Ty=Tgt_Pos_ECFn[[2]]
Tz=Tgt_Pos_ECFn[[3]]
Mx=Mis_Pos_ECFn[[1]]
My=Mis_Pos_ECFn[[2]]
Mz=Mis_Pos_ECFn[[3]]
RTIn=Sqrt[(Tx-Mx)2+(Ty-My)2+(Tz-Mz)2] (Eqs. 17)
[0108] Thereafter, in an exemplary embodiment, the Range-To-Impact
Derivative (RTID.sub.n=RTI.sub.n-RTI.sub.n-1) may be computed based
on the RTI, in block 350. The RTID may be the indicator for the
engagement closure state, with a negative RTID indicating "Closing"
and a positive RTID indicating "Opening". In an exemplary
embodiment, for tail-aspect engagements, the closure state may
initially be "Opening" as the missile accelerates off the launch
rail, but may transition to "Closing" and remain there until the
point of closest approach is reached. The process may end at B, in
block 354, which is described with reference to FIG. 3C.
[0109] In FIG. 3C, starting with block 354, which corresponds to B
in process 320, an exemplary embodiment may continue to compare the
calculated RTID its previous value (RTID.sub.n to RTID.sub.n-1),
block 362. In an exemplary embodiment, if a negative to positive
transition has occurred, indicating a change in engagement closure
state from "Closing" to "Opening", it may be indicative that the
missile has reached its closest point of approach sometime between
time.sub.n and time.sub.n-2. Thus, a determination may be made as
to whether the missile has reached the point of closest approach
based on a change in the engagement closure state, in block 364. If
so, flow diagram 360 may continue with 366. In an exemplary
embodiment, the aircraft state (x, y, z position and Yaw, Pitch,
Roll attitude) and missile position (x, y, z) at time.sub.n and
time.sub.n-2 may be logged. Further, the process may continue with
hit/miss assessment and/or damage assessment algorithm, which may
determine where the missile has impacted the aircraft, and if so,
where such impact has occurred, in block 366. The damage assessment
algorithm may also determine if the missile has missed, but
detonated the warhead within sufficient proximity to damage the
aircraft.
[0110] In an exemplary embodiment, if no hit has occurred with the
aircraft, a Terrain Hit/Miss assessment in block 366 and/or Terrain
Impact computation may be performed, in block 368.
[0111] From 368, in an exemplary embodiment, a determination may be
made as to whether the a terrain or the aircraft has been impacted,
in block 370. If so, the flyout loop may be terminated and the
impact event may be reported, in block 372.
[0112] If it is determined at block 364 that the missile has not
reached the closest point of approach, or if it is determined at
block 370 that the missile has not impacted a terrain or the target
aircraft, a second determination may be made as to whether the
maximum range of interest has been reached, in block 374. If so,
the flyout loop may be terminated and the impact event may be
reported, in block 372. Otherwise, the missile fly-out may continue
with 322 until either the maximum range of interest is reached, or
the missile impacts the target or the terrain, in block 374.
Exemplary Missile Guidance Processing
[0113] Exemplary Weapon (e.g., missile) Guidance Processing 204 is
described herein for two exemplary missiles--the IR Seeker and the
Laser Beam-Rider Guidance. It should be noted, however, that the
Guidance Processing 204 is weapon specific. Thus, the two
embodiments described herein are exemplary and should not be
interpreted as limiting the present invention.
[0114] In an exemplary embodiment of the invention, for a missile
with an IR seeker, the target position may be denoted as Aim-Point
Error {Az,El} missile body coordinates. It may be assumed that
variables and quantities computed as part of the Missile Kinematics
Processing 202 are available to the seeker.
[0115] FIG. 4 illustrates an exemplary process 400 for a Weapon
Guidance Processing 204 for an IR Seeker missile, according to an
exemplary embodiment of the invention. In an exemplary embodiment,
beginning with 402, the process 400 may obtain Target Position
Vector and Missile Position Vector in ECF coordinates (Tgt_Pos_ECF
and Mis_Pos_ECF, respectively), in block 404. The Relative Target
Position may then be calculated relative to missile position in ECF
by subtracting the two vector, in block 406, according to an
exemplary embodiment:
Tgt_Rel_Pos_ECFn=Tgt_Pos_ECF-Mis_Pos_ECF (Eq. 18)
[0116] The Relative Target Position, in an exemplary embodiment,
may then be transformed into Missile Body Coordinates, in block
408:
Tgt_Rel_Pos_BCn=EECF_to_Missile,nTgt_Rel_Pos_ECF (Eq. 19)
[0117] The {Az,El} vector to target (i.e., Aim-Point Error) may
then be calculated, in block 410 according to an exemplary
embodiment. The {x, y, z} below may be components of the
Tgt_Rel_Pos_BC position vector.
El=ArcSin[-z]
Az=If[x>0,ArcSin[y/Cos [El]],If[y>0,Pi-ArcSin[y/Cos
[El]],-Pi-ArcSin[y/Cos [El]]]] (Eqs. 20)
[0118] From 410, in an exemplary embodiment, a determination may
then be performed as to whether the gimbal limits has been
exceeded, i.e., the Aim-point Error is greater than Gimbal_limit in
either Az or El, in block 412. If so, in an exemplary embodiment, a
Loss of Track event may be declared, the Aim-Point Error and
Aim-Point Bias may be set to a static {0,0}, and the process may be
held for the remainder of the missile flyout, in block 414. From
414, the process may then end, in block 420. If the gimbal limits
are not exceeded, Aim-Point Bias (Static and Dynamic) may be added
to the Aim-Point Error to compute Target Error, in block 416. In an
exemplary embodiment, .+-.{Az, El} bias may be applied to account
for missile aim-point lead or lag, or aim-point super-elevation or
sub-elevation.
[0119] From 416, in an exemplary embodiment, the Required Steering
Correction (Req_Steer_BC) may be computed using a Guidance Filter
Difference Equation, in block 418. In an exemplary embodiment, the
Difference Equation may be run on a per axis basis. From 418, the
process may then end at 420.
[0120] FIG. 5 illustrates an exemplary Generalized Guidance Filter
500 implementing the Difference Equation. The exemplary Difference
Equation of the Generalized Guidance Filter 500 may be as
follows:
In=Target_Errorn
In-1=Target_Errorn-1
On-1=Req_Steer_BCn-1
.alpha.=(Kp+(Kd/T)+KiT)
.beta.=(Kd/T)
On=.alpha.In-.beta.In-1+On-1
Req_Steer_BCn=On (Eqs. 21)
[0121] FIG. 6 illustrates an exemplary process 600 for a Weapon
Guidance Processing 204 for a Laser Beam-Riding Seeker (RBS-70),
according to an exemplary embodiment of the invention. For the
RBS-70, the Aim-Point Error may be the {Az,El} laser orientation in
missile body coordinates. In an exemplary embodiment, beginning
with 602, the process 600 may get Laser Beam Unit Direction Vector
in ECF coordinates (Laser_UDV_ECF), in block 604. The Laser Beam
Unit Direction Vector may then be transformed to Laser Beam Vector
in Missile Body Coordinates, in block 606:
Laser_UDV_BCn=EECF_to_Missile,nLaser_UDV_ECF (Eq. 22)
[0122] The {Az,El} Eulerians to Laser UDV (i.e., Aim-Point Error)
may then be computed, in block 608. The {x, y, z} below may be
components of the Laser_UDV_BC vector.
El=ArcSin[-z]
Az=If[x>0,ArcSin[y/Cos [El]],If[y>0,Pi-ArcSin[y/Cos
[El]],-Pi-ArcSin[y/Cos [El]]]] (Eqs. 23)
[0123] In an exemplary embodiment, a determination may then be
performed as to whether the gimbal limits has been exceeded, i.e.,
the Aim-point Error is greater than Gimbal_limit in either Az or
El, in block 610. If so, in an exemplary embodiment, a Loss of
Track event may be declared, the Aim-Point Error and Aim-Point Bias
may be set to a static {0,0}, and the process may be held for the
remainder of the missile flyout, in block 612. From 612 the process
may then end, in block 618.
[0124] Otherwise, Aim-Point Bias (Static and Dynamic) may be added
to the Aim-Point Error to compute Target Error, in block 614. In an
exemplary embodiment, .+-.{Az, El} bias may be applied to account
for missile aim-point lead or lag, or aim-point super-elevation or
sub-elevation. In an exemplary embodiment, the Required Steering
Correction (Req_Steer_BC) may then be computed, as detailed above
for the IR Seeker, in block 616. From 616, the process 600 may then
end at 618.
Exemplary Computational Details for DCM from {Yaw, Pitch, Roll}
Eulerian
[0125] In an exemplary embodiment, Direction Cosine Matrix may be a
3.times.3 Matrix used to transform coordinates (vectors) between
reference frames. The exemplary DCM transform may be computed as
follows:
DCM_XForm [ { yaw_ , pitch_ , roll_ } ] := { { Cos [ yaw ] Cos [
pitch ] , Sin [ yaw ] Cos [ pitch ] , - Sin [ pitch ] } , { - Sin [
yaw ] Cos [ roll ] + Cos [ yaw ] Sin [ pitch ] Sin [ roll ] , Cos [
yaw ] Cos [ roll ] + Sin [ yaw ] Sin [ pitch ] Sin [ roll ] , Cos [
pitch ] Sin [ roll ] } , { Sin [ yaw ] Sin [ roll ] + Cos [ yaw ]
Sin [ pitch ] Cos [ roll ] , - Cos [ yaw ] Sin [ roll ] + Sin [ yaw
] Sin [ pitch ] Cos [ roll ] , Cos [ pitch ] Cos [ roll ] } } ( Eq
. 24 ) ##EQU00003##
[0126] A DCM may have an intrinsic directionality. For example, if
the DCM is defined to describe missile orientation with respect to
the ECF, its sense of direction may be from the ECF to the Missile
Body Coordinate Frame. A Vector may be transformed from the ECF to
missile body coordinates by pre-multiplying by the DCM:
Vector_BC=DCMVector_ECF (Eq. 25)
[0127] To go the other direction, a vector in missile body
coordinates can be pre-multiplied by the "Transpose" of the
DCM:
Vector_ECF=Transpose[DCM]Vector_BC (Eq. 26)
Exemplary Computational Details for Wind-Induced Acceleration in
ECF
[0128] In an exemplary embodiment, acceleration due to wind may be
taken as a magnitude of K.sub.wV.sub.w.sup.2A, in the direction of
the wind, where A is the projected area in the direction of the
wind, found by taking the vector dot product of the missile Area
Vector onto a Unit Direction Vector indicating wind direction:
Wind_Mag_Sq=Wind_Vel_ECFWind_Vel_ECF (Vector Dot Product)
Wind_Mag=Sqrt[Wind_Mag_Sq]
Wind_Dir_ECF=Wind_Vel_ECF/Wind_Mag (Unit Dir. Vector)
Area_Proj=Area_VecWind_Dir_ECF (Vector Dot Product)
Wind_Acc_Mag=KwWind_Mag_Sq Area_Proj (Scalar Multiply)
Wind_Acc_ECF=Wind_Acc_Mag Wind_Dir_ECF (Scalar.times.Unit Vector)
(Eqs. 27)
Exemplary Computational Details for Application of Acceleration
Limits to Missile Steering
[0129] In an exemplary embodiment, the Required Steering Vector may
exceed the maneuverability limits of the missile, as specified by
the G_limit parameter. The Actual Steering Vector may therefore be
an acceleration-restricted version of the Required Steering
Vector.
[0130] In an exemplary embodiment, at time t.sub.n, the missile has
a velocity, in body coordinates, of Mis_Vel_BC.sub.n. This velocity
may be aligned with the missile x-axis, though it may not to be
aligned exactly on it. Thus, it may be needed to compute the
velocity magnitude:
Mis_Vel_MagSqn=Mis_Vel_BCnMis_Vel_BCn (Vector Dot Product)
Mis_Vel_Magn=Sqrt[Mis_Vel_MagSqn] (Eqs. 28)
[0131] The Required Steering Vector (Req_Steer_BC) may be a {Yaw,
Pitch} Eulerian:
Req_Yawn=Req_Steer_BCn[[1]]
Req_Pitchn=Req_Steer_BCn[[2]] (Eqs. 29)
[0132] The rate of turn (Angular limit per update) may be inversely
proportional to the magnitude of velocity, and computed as
follows:
Angle_Limitn=ArcSin[(TG_Acc_Scalar G_limit)/Mis_Vel_Magn] (Eq.
30)
[0133] The Actual Steering Vector may be limited to have both Yaw
and Pitch with the .+-.Angle Limit:
Act_Yawn=If[Req_Yawn>Angle_Limitn,Angle_Limitn,If[Req_Yawn<=Angle_-
Limitn,-Angle_Limitn,Req_Yawn]]
Act_Pitchn=If[Req_Pitchn>Angle_Limitn,Angle_Limitn,If[Req_Pitchn<--
Angle_Limitn,-Angle_Limitn,Req_Pitchn]]
Act_Steer_BCn={Act_Yawn,Act_Pitchn} (Eqs. 31)
Exemplary Computational Details for Missile Body Accelerations Due
to Steering
[0134] When the missile is steered, accelerations result due to
changes in velocity. Since the steering occurs in body coordinates,
these accelerations may be computed in body coordinates, then
transformed into the ECF for integration into velocity and
position.
Rotated_Mis_Vel_BCn=DCM_XForm[{Act_Yawn,Act_Pitchn,0}]Mis_Vel_BCn
Mis_Steer_Acc_BCn=(Rotated_Mis_Vel_BCn-Mis_Vel_BCn)/T (Eqs. 32)
Exemplary Hit/Miss Assessment
[0135] According to an exemplary embodiment of the invention, in
order to resolve the issues pointed out with the conventional
simulation models caused by high rates of weapon and target speed,
the Hit/Miss assessment may be performed on the Aircraft Body
Coordinate Frame.
[0136] In conventional assessment modeling, at some time (t.sub.0),
both the aircraft and weapon would have an instantaneous position
in a common frame of reference, e.g., but not limited to, the
Engagement Coordinate Frame (ECF), which is an earth-fixed
coordinate frame. At the time increment following the point of
closest approach (t.sub.2), both aircraft and weapon would have a
new position. However, due to the rate of speed of both the weapon
and the target aircraft, the two could have easily flown through
one other, leaving the instant of collision undetected.
[0137] Accordingly, in an exemplary embodiment of the invention, in
order to ensure that a miss is not undetected, the weapon position
may be mathematically transformed from the fixed Engagement
Coordinate Frame (ECF) to the Aircraft Body Coordinate Frame. In an
exemplary embodiment, performing this transformation may express
the weapon position with respect to a set of coordinates that are
fixed to the aircraft. When both the weapon position at time
t.sub.0 (time.sub.n-2) and time t.sub.2 (time.sub.n) are
transformed into aircraft coordinates, we are left with two points
in aircraft coordinate space. In an exemplary embodiment, these two
points may be separated in time by, e.g., but not limited to,
66.000 ms, where the weapon is known to have been located with
respect to the target aircraft.
[0138] According to an exemplary embodiment of the invention, if a
straight line between these two locations passes through one of the
ellipsoid surfaces that comprise the aircraft interference model,
as described above, it may be determined that a trajectory of the
weapon has made impact with the aircraft. In an exemplary
embodiment, the ellipsoid that has been intersected may represent
the section of the aircraft that has been damaged, and the
coordinates of the intersection may represent the coordinates at
which a hit has occurred.
[0139] FIG. 7 demonstrates an exemplary Hit/Miss Assessment process
700 for a target aircraft, according to an exemplary embodiment of
the invention. The process 700 may begin at 702 and may continue
with modeling the target aircraft interference geometry, in block
704. In an exemplary embodiment, the aircraft may be modeled as,
e.g., but not limited to, 10 zones. In an exemplary embodiment,
each zone (ellipsoid) may be defined by the following set of 9
parameters: [0140] {a, b, c, x.sub.0, y.sub.0, z.sub.0, zone_yaw,
zone_pitch, zone_roll} where the "zone_" prefix denotes the yaw,
pitch, or roll of the specific ellipsoidal zone.
[0141] In an exemplary embodiment, the determination of Hit/Miss
Assessment on the target plane may be defined by two samples in
time, in which both the aircraft and the weapon are in motion with
respect to the Engagement Coordinate Frame (ECF). Thus, from 704,
the process 700 may continue with determining the aircraft and
weapon coordinates in the ECF, in block 706. In an exemplary
embodiment, the two time samples, t.sub.n and t.sub.n-2 may bracket
the point of closest approach. Exemplary parameters to determine
the aircraft and weapon (e.g., missile) coordinates are as
follows:
AC_Pos_ECF.sub.0={x,y,z} aircraft position vector in ECF at time
t.sub.n-2
AC_Pos_ECF.sub.2={x,y,z} aircraft position vector in ECF at time
t.sub.n
AC_Att_ECF.sub.0={Yaw,Pitch,Roll} aircraft attitude vector in ECF
at time t.sub.n-2
AC_Att_ECF.sub.2={Yaw,Pitch,Roll} aircraft attitude vector in ECF
at time t.sub.n
Mis_Pos_ECF.sub.0={x,y,z} missile position vector in ECF at time
t.sub.n-2
Mis_Pos_ECF.sub.2={x,y,z} missile position vector in ECF at time
t.sub.n
[0142] In an exemplary embodiment, after determining weapon and
aircraft coordinates in the ECF, the weapon coordinates may be
transformed to Aircraft Body Coordinate Frame, in block 708. The
weapon position relative to the aircraft in the ECF, at both points
in time, t.sub.n and t.sub.n-2, may be calculated by subtracting
the Aircraft position vectors from the Weapon Position vectors in
the ECF. Weapon position in Aircraft Body Coordinates (ACBC) may
then be found by transforming the relative weapon coordinates from
the ECF to the ACBC. Exemplary formulas for performing this
transformation are as follows:
Mis_Rel_Pos_ECF0=Mis_Pos_ECF0-AC_Pos_ECF0
Mis_Rel_Pos_ECF2=Mis_Pos_ECF2-AC_Pos_ECF2 (Eq. 33)
E.sub.ECF.sub.--.sub.to.sub.--.sub.AC,0=DCM_XForm[AC_Att_ECF.sub.0]
E.sub.ECF.sub.--.sub.to.sub.--.sub.AC,2=DCM_XForm[AC_Att_ECF.sub.2]
(Eq. 34)
Mis_Rel_Pos_ACBC.sub.0=E.sub.ECF.sub.--.sub.to.sub.--.sub.AC,0Mis_Rel_Po-
s_ECF.sub.0
Mis_Rel_Pos_ACBC.sub.2=E.sub.ECF.sub.--.sub.to.sub.--.sub.AC,2Mis_Rel_Po-
s_ECF.sub.2 (Eq. 35)
[0143] In an exemplary embodiment, as described above, each
aircraft zone may include its own attitude defined by zone_yaw,
zone_pitch, and zone_roll parameters. The ellipsoid al zone may be
rotated from aircraft coordinates by the zone_yaw, zone_Pitch, and
zone_roll parameters. Thus, in an exemplary embodiment, the
relative weapon coordinates in ACBC may be transformed to get the
trajectory points of the weapon with relative to the aircraft zones
in the Aircraft Zone Coordinates, in block 710. Exemplary formulas
for performing this transformation are as follows:
E.sub.AC.sub.--.sub.to.sub.--.sub.zone=DCM_XForm[{zone_yaw,zone_pitch,zo-
ne_roll}] (Eq. 36)
Mis_Rel_Pos_ACZC.sub.0=E.sub.AC.sub.--.sub.to.sub.--.sub.zoneMis_Rel_Pos-
_ACBC.sub.0
Mis_Rel_Pos_ACZC.sub.2=E.sub.AC.sub.--.sub.to.sub.--.sub.zoneMis_Rel_Pos-
_ACBC.sub.2 (Eq. 37)
[0144] Once the weapon coordinates have been determined with
respect to the ellipsoidal zones, a determination may be made as to
whether a zone of the aircraft intercepts the weapon trajectory, in
block 712. If an intercept occurs, it may be determined that the
aircraft has been hit, in block 714. Otherwise, it may be
determined that the weapon ha missed the aircraft, in block
716.
[0145] In a further exemplary embodiment, if it is determined that
a hit has occurred (i.e., Hit=True), from 714 the impact
coordinates may then be computed, in block 718. Further, from 718
the damage caused by the weapon on the aircraft may also be
assessed, in block 720 before ending with 726.
[0146] Similarly, if it is determined that the elliptical zone was
not impacted (i.e., Hit=False), from 716 the distance by which the
weapon missed the aircraft may be calculated, in block 722.
Further, while the weapon does not actually impact the aircraft, if
the aircraft is within a blast range of the weapon warhead, the
aircraft may still be damaged. Thus, the proximity damage of the
aircraft may be assessed, in block 724. These steps will be
discussed later in great detail. From 724, process 700 may end at
726.
[0147] Referring now to FIG. 8, an exemplary process 800 for
determining whether a zone of the aircraft intercepts the weapon
trajectory (block 712 of FIG. 7) is illustrated according to an
exemplary embodiment of the invention. Process 800 may start at 802
and may continue with determining a parametric expression for a
line-segment through the two trajectory points in zone coordinates,
in block 804. This parametric expression may be needed to determine
whether an intercept occurs. Exemplary parametric expressions are
as follows:
S=Mis_Rel_Pos_ACZC.sub.2-Mis_Rel_Pos_ACZC.sub.0
x=S[[1]]; Sy=S[[2]]; Sz=S[[3]]
0x=Mis_Rel_Pos_ACZC.sub.0[[1]]
P0y=Mis_Rel_Pos_ACZC.sub.0[[2]]
P0z=Mis_Rel_Pos_ACZC.sub.0[[3]]
x=P0x+iSx
y=P0y+iSy
z=P0z+iSz (Eqs. 38)
[0148] The x, y, and z parameters listed above may form a
parametric vector trajectory connecting the two weapon relative
position points. In the exemplary embodiment shown, when i=0, the
position is Mis_Rel_Pos_ACZC.sub.0, and when i=1, the position is
Mis_Rel_Pos_ACZC.sub.2. At some point between i=0 and i=1, the
trajectory may pass through the ellipsoid or reach a point of
closest approach.
[0149] From 804, in an exemplary embodiment, the point of closest
approach may be calculated, in block 806. The exemplary closed-form
solution to the value of i that represents the point of closest
approach is as follows:
iSolution = - ( b 2 c 2 P 0 xSx + a 2 c 2 P 0 ySy + a 2 b 2 P 0 zSz
- b 2 c 2 Sx x 0 - a 2 c 2 Sy y 0 - a 2 b 2 Sz z 0 ) b 2 c 2 Sx 2 +
a 2 c 2 Sy 2 + a 2 b 2 Sz 2 ( Eq . 39 ) ##EQU00004##
[0150] From 806, after calculating the point of closest approach,
according to an exemplary embodiment, an Elliptical Magnitude may
be computed at the point of closest approach, in block 808. In an
exemplary embodiment, the Elliptical Magnitude (EMag) for the zone
may be defined as follows:
EMag = ( x - x 0 ) 2 a 2 + ( y - y 0 ) 2 b 2 + ( z - z 0 ) 2 c 2 =
1 ( Eq . 40 ) ##EQU00005##
[0151] By definition, the surface of the ellipsoid is the locus of
points for which the EMag function is equal to 1. Therefore, in an
exemplary embodiment, in 810 if the EMag function at the point of
closest approach is less than 1, it may be determined that the
surface has been struck, in block 812. Otherwise, if PCA is not
less than 1 in 810, then it may be determined that the projectile
has missed, in block 814. From 812 and 814, process 800 may then
end at block 816.
[0152] In an exemplary embodiment, the determination may be made by
evaluating EMag at the {x,y,z} values produced by setting i equal
to iSolution, as follows:
Hit=If[(EMag/i->iSolution)<1,True,False] (Eq. 41)
Exemplary Computation of Impact Coordinates
[0153] According to an exemplary embodiment of the invention, if
the impact has occurred (i.e., Hit=True), the impact coordinates of
the weapon may be computed, as previously discussed briefly. In an
exemplary embodiment, the impact coordinates may be computed in the
Aircraft Zone Coordinate System by evaluating the parametric
trajectory at i=iSolution, as follows:
Hit_Loc_ACZC={x,y,z}/i->iSolution (Eq. 42)
[0154] In a further exemplary embodiment, the impact location in
Aircraft Body Coordinates may be found by rotating the Hit Location
coordinates from the Aircraft Zone Coordinates (ACZC) to the
aircraft body coordinates (ACBC), as follows:
Hit_Loc_ACBC=Transpose[E.sub.AC.sub.--.sub.to.sub.--.sub.zone]Hit_Loc_AC-
ZC (Eq. 43)
Exemplary Miss Distance Computation
[0155] In an exemplary embodiment, if the ellipsoidal zone was not
impacted (Hit=False), the distance by which the weapon missed the
aircraft may be computed, as previously discussed briefly. In
Aircraft Zone Coordinates, as described with reference to block 804
of FIG. 8 and Eqs. 38, the following may represent the relation for
the trajectory segment:
S1=S=Mis_Rel_Pos_ACZC.sub.2-Mis_Rel_Pos_ACZC.sub.0 (Eq. 44)
[0156] Also, in Aircraft Zone Coordinates, the centroid of the
ellipsoid resides at C={x.sub.0, y.sub.0, z.sub.0}. Thus, the
distance of the first trajectory point with respect to the centroid
may be computed as:
S2=Mis_Rel_Pos_ACZC.sub.0-C (Eq. 45)
[0157] In an exemplary embodiment, the miss-distance may be
computed using vector mathematics and the distances S1, S2. To do
so, in an exemplary embodiment, two orthogonal vectors may be
defined. The first orthogonal vector (Ortho1) may be found by
taking the vector cross product of S2 into S1. This creates a
vector that is perpendicular to the plane that contains both the
trajectory and Point C. The second orthogonal vector (Ortho2) may
be found by taking the vector cross product of S1 into Ortho1. This
creates a vector that is perpendicular to both the trajectory and
Ortho1, which means that it is both perpendicular to the trajectory
and it lies in the plane that contains both the trajectory and
Point C. Thus, Ortho 2 indicates the direction of line running from
the centroid of the ellipsoidal zone (Point C) that will intersect
the trajectory at right angles.
Ortho1=(S2.times.S1)
Ortho2=(S1.times.Ortho1) (Eqs. 46)
[0158] In an exemplary embodiment, to determine the miss distance,
the magnitude of Ortho 2 may be scaled to unity to obtain a Unit
Direction Vector (UDV). Then, to compute a vector from Point C to
the trajectory of closest point of approach (i.e., Miss Vector) by
computing the vector projection (i.e., dot product) of vector S2
onto the UDV. The magnitude of the Miss Vector is the miss
distance. Exemplary equations for performing this computation is as
follows:
Ortho2Mag=Sqrt[Ortho2Ortho2] (Magnitude of Ortho 2)
Ortho2UDV=Ortho2/Ortho2Mag (Unit Direction Vector)
Miss_Vec=S2Ortho2UDV
Miss_Dist=Sqrt[Miss_VecMiss_Vec] (Eqs. 47)
[0159] In an exemplary embodiment, the coordinates of the point of
closest approach (e.g., Miss Coordinates) may be computed in
Aircraft Zone Coordinates as follows:
Miss_Loc_ACZC=Miss_Vec+C (Eq. 48)
[0160] Further, in an exemplary embodiment, the miss location in
Aircraft Body Coordinates may be computed by rotating the Miss
Coordinates from the Aircraft Zone Coordinates (ACZC) to the
Aircraft Body Coordinates (ACBC), as follows:
Miss_Loc_ACBC=Transpose[E.sub.AC.sub.--.sub.to.sub.--.sub.Zone]Miss_Loc_-
ACZC (Eq. 49)
Exemplary Impact Damage Assessment
[0161] In an exemplary embodiment, if an impact occurs, the damage
on the aircraft may be computed from a statistical model that
considers factors such as, e.g., but not limited to, weapon
lethality, the survivability of the target aircraft, and the
location of impact on the aircraft. In an exemplary embodiment,
where there are multiple hits on the aircraft, damage may be
integrated from each hit until a survivability threshold is
reached, at which time the target is considered "Killed".
[0162] In an exemplary embodiment, the overall damage model has the
following components:
TABLE-US-00009 Weapon Lethality (Property of Weapon) Target
Survivability (Property of Aircraft) Zone Sensitivity (Property of
Aircraft Zones)
[0163] In an exemplary embodiment, Weapon Lethality may specify the
single-shot, direct impact, potency of the weapon. Weapon Lethality
may be measured in Damage Units. In an exemplary embodiment, the
assumed reference for Damage Units may be, for example, that 100
Damage Units are required to Kill a Fast Jet. Weapon Lethality may
be modeled as Log-Normal probability distribution, in which the
Mean (.mu.) and Standard Deviation (.sigma.) may be
user-configurable model parameters.
[0164] In an exemplary embodiment, for each hit, a random draw may
be taken from a probability distribution function to determine the
number of Damage Units resulting from that hit. Damage Units may be
integrated from multiple hits, across all zones, to assess the
overall damage state of the aircraft.
[0165] In an exemplary embodiment, the lethality of different
weapons may be modeled by assigning appropriate Mean and Standard
Deviation parameters for each weapon. For example, a single 35 mm
shell may have a Mean of 20 Damage Units, with a Standard Deviation
of 10. Thus, on average, 5 hits of a 35 mm shells would be needed
to take down a Fast Jet, though more or fewer number of shots may
be needed. For example, 3 "lucky shots" may be able to kill a Fast
Jet.
[0166] Alternatively, the RBS-70 Warhead is so potent that it might
be modeled with a Mean of 1000 Damage Units, and Standard Deviation
of 70, if the warhead detonates. With such a model there is unity
probability that a hit with a RBS-70 warhead would bring down a
Fast Jet on impact, and a significant probability of kill at a 10
meter miss distance (as discussed below). However, if the RBS-70
warhead fails to detonate, e.g., due to warhead malfunction, the
impact damage might be modeled as a Mean of 100 Damage Units, with
a Standard Deviation of 50. Thus, if the exemplary RBS-70 fails to
detonate, it might or might not take down the aircraft, due to the
force of collision alone.
[0167] In an exemplary embodiment, the Target Survivability
component is the number of Damage Units that a target can sustain
before it is killed. In an exemplary embodiment, each type of
aircraft may be modeled with a representative Survivability
Threshold, and when the integrated damage exceeds this threshold,
the target may be considered to be "killed". In an exemplary
embodiment, the defined reference benchmark for Survivability
Threshold may be 100 Damage Units to kill a Fast Jet. Sturdier
targets (e.g., Large Propeller Aircraft) may be modeled with a
higher threshold, while more vulnerable targets (e.g., helicopter)
may be modeled with a lower threshold. In an exemplary embodiment,
survivability threshold, in Damage Units, is a user-configurable
model parameter.
[0168] In an exemplary embodiment, Zone Sensitivity may include a
set of user-configurable model parameters. Each of the ellipsoidal
zones used to form the Target Interference Geometry, as previously
discussed, may have a Sensitivity Coefficient, an exemplary
embodiment of which is illustrated in Table 8 below:
TABLE-US-00010 TABLE 8 Example Proximity Zone Sensitivity Model
(Fast Jet Aircraft) SENSITIVITY ZONE DESCRIPTION COEFFICIENT 1
Forward Fuselage 1.5 2 Aft Fuselage 2 3 Left Wing 0.7 4 Right Wing
0.7 5 Left Rear Stabilizer 0.7 6 Right Rear Stabilizer 0.7 7
Vertical Stabilizer 0.7
[0169] In an exemplary embodiment, the sensitivity coefficients may
provide a mechanism to account for the fact that all areas of the
aircraft are not equally sensitive to damage. For example, a
non-explosive bullet may cause relatively little damage if it
impacts a wing, but a great deal of damage if it impacts the center
fuselage, where the jet turbines reside. In an exemplary
embodiment, the sensitivity coefficients may be used as "weighting
factors" that adjust the damage levels resulting from different
regions of impact.
[0170] Referring now to FIG. 9, an exemplary process 900 for
calculating the aircraft damage assessment is described, according
to an exemplary embodiment of the invention. In an exemplary
embodiment, the process 900 may start at 902, in which the aircraft
has zero initial damage (AC_Damage.sub.0=0). When a weapon has been
determined to have passed the point of closest approach, the
process 900 may follow to determine if zone has been hit (as
discussed with reference to FIG. 4), in block 904. If so, the
process 900 may follow to 906 to continue to make a random draw
from the probability distribution function of the appropriate
Weapon Lethality model, in block 906. The exemplary equation for
making a random draw for Weapon Lethality may be as follows:
Weap_Lethality=LogNormalRandom[.mu.,.sigma.] (Eq. 50)
[0171] Thereafter, from 906, in an exemplary embodiment, Weapon
Lethality may be multiplied by Zone Sensitivity to determine
effective lethality of the weapon on the target aircraft, in block
908, as follows:
Effective_Lethality=Weap_Lethality.times.Sensitivity_Coeff (Eq.
51)
[0172] The Effective Lethality of the weapon on the aircraft may
then be integrated into the existing damage on the aircraft, in
block 910, as follows:
AC_Damage.sub.n+1=AC_Damage.sub.n+Effective_Lethality (Eq. 52)
[0173] Thereafter, in 912 a determination may be made as to whether
the total damage on the aircraft exceeds its Survivability
Threshold, which may indicate that the Aircraft has been killed, in
block 912. This "Test for Kill" may be determined as follows:
Kill=If[AC_Damage>Survivability_Threshold,True,False] (Eq.
53)
[0174] From 912 flow diagram 900 may end with 914.
Exemplary Proximity Damage Assessment
[0175] According to an exemplary embodiment of the invention, if
the missile does not actually impact the aircraft, but the closest
point of approach is within the blast range of a missile warhead,
the aircraft may still be damaged. For proximity damage, in an
exemplary embodiment, the warhead lethality model described above
may be weighted with a range term, to account for energy loss as a
function of miss distance.
[0176] The energy from weapon explosion may be modeled as a sphere.
Energy from an expanding sphere dissipates according to 1/R.sup.2.
If the warhead uses a shaped charge different from a spear, e.g.,
but not limited to, to form an annular ring, the dissipation
function may be closer to, e.g., but not limited to, 1/R or
1/R.sup.1.2. To account for these possibilities, the exemplary
parametric model for the warhead may include a user definable
coefficient (e.g., Warhead_n), that represents the exponent in the
proximity propagation function.
[0177] In an exemplary embodiment, proximity damage may be modeled
similarly to the impact damage model, with the addition of a factor
for Range Loss. Referring back to FIG. 9, when a weapon has been
determined to have passed the point of closest approach, but the
determination in 904 indicates that the zone has not been hit, then
flow diagram 900 may continue with 914, each zone of the aircraft
may be assessed for damage from a proximity detonation, unless the
weapon malfunctions or fails to detonate.
[0178] In an exemplary embodiment, the process 900 in such scenario
may continue to compute the miss distance to zone centroid, as was
discussed previously, in block 914. From 914, the Range Loss may
then be computed at the computed miss distance, in block 916, as
follows:
Range_Loss=(Miss_Dist+1).sup.-Warhead.sup.--.sup.n (Eq. 54)
[0179] Thereafter, from 916, a random draw may be made from the
probability distribution function of the appropriate Weapon
Lethality model, as shown in Eq. 27, in block 918. From 918, the
Weapon's Effective Lethality may then be calculated by multiplying
the Weapon Lethality by Zone Sensitivity and Range Loss, in block
920, as follows:
Effective_Lethality=Weap_Lethality.times.Sensitivity_Coeff.times.Range_L-
oss (Eq. 55)
[0180] The process 900 from 920 may then follow to blocks 910, and
912, where aircraft damage may be integrated and the test for kill
may be performed and may complete with 914.
[0181] In an exemplary embodiment, proximity damage may only apply
to weapons with explosive warheads. In an exemplary embodiment, the
same model may be used for non-explosive weapons, e.g., but not
limited to, bullet, but the "Warhead_n" parameter may be set to a
large value (e.g., but not limited to, 1000) to effectively disable
any proximity damage effect.
Exemplary Weapon Data
[0182] The listings below summarize exemplary parameters of the
weapon systems. It should be noted that these parameters are for
illustration purposes only and may not accurately represent the
actual weapon parameters. Also, it should be understood that the
present invention is by no means limited to the weapons listed
herein.
TABLE-US-00011 BOFORS RBS-70 Basic Laser-Guided SAM, reportedly
virtually smokeless. Can Description: be in either of 2
configurations: Mounted on V200 AFV, or dismounted on Tripod.
Manufacturer claims "unique unjammable laser beam riding guidance"
provides high capability against small targets such cruise missiles
& UAVs Weight: 87 Kg Missile 1.735 m Length: Missile 152 mm
Diameter: Dia with 320 mm wings open: Warhead: 1.8 Kg shaped charge
& fragmentation Fusing: Adaptive Proximity Fuse or impact
Speed: Mach 2 (660 m/s) Flight time 8.5 sec to 3 Km: Effective Up
to 3 Km Altitude: Effective 0.3 to 5 Km Range: Guidance: Laser
beam-rider Normal Monocular telescope, 7.times. magnification,
9.degree. FOV Sight: Thermal IR Image, 1.times. mag, 9.15.degree. H
.times. 6.86.degree. V FOV (.+-.2%) Sight:
TABLE-US-00012 MATRA Mistral Basic Description: IR-Homing MANPADS,
manufactured by MBDA (French) Launch Mass: 18.7 Kg Power Plant:
two-stage solid rocket Length: 1.86 m Missile Caliber: 90 mm Dia
with wings open: 180 mm Warhead: 3 Kg HE Fusing: Laser Proximity or
impact Speed: Mach 2.5 (830 m/s) Flight time to 3 Km: 5.2 sec Max
Flight Time: 14 sec Effective Altitude: up to 3 Km Effective Range:
0.5-5.5 Km (4 Km against helicopters) Max Range: 6.5 km Acquisition
Sight: Clear Collimator, .+-.25.degree. H .times. ~15.degree. V FOV
Magnifying Sight: 3.times. magnification, 14.degree. FOV Guidance:
All-aspect IR, fire and forget
TABLE-US-00013 KBM SA-18 IGLA (Grouse) Basic Russian IR-Homing
MANPADS, similar to Description: Stinger, manufactured by KBM. Can
be used in either of two configurations (MANPADS Shoulder Launch,
or M113-mounted) Launch 10.6 Kg Mass: Length: 1.7 m Missile 72 mm
Caliber: Dia with 180 mm wings open: Warhead: 1.27 Kg HE Fusing:
Laser Proximity or impact Speed: Mach 1.7 (570 m/s) Effective 10 m
to 2 Km (FWA) or 3 KM (RWA) Altitude: Effective 0.5-2 Km (FWA) or
5.2 Km (RWA) Range: Manpads STIS Staring IR Image, 9.degree.
.times. 9.degree. FOV Accessory Sight: M113 DNSS Wide FOV:
9.degree., 3.times. Mag Day Channel: Narrow FOV: 2.degree.,
15.times. Mag M113 DNSS 2.degree., 1.times. Mag2.degree., 15.times.
Mag Night Channel: Guidance: All-aspect IR with proportional
convergence, fire and forget
TABLE-US-00014 OERLIKON-CONTRAVES Twin 35 mm AA Guns Basic
Description: Swiss AAA twin barrel gun for rapid fire of unguided
projectiles. Projectile Mass: 550 g Rate of Fire: 1100 rounds/min
(550 from each of 2 barrels) Muzzle Velocity: 1175 m/s Flight Time:
1000 m: 0.96 Sec 2000 m: 2.18 Sec 3000 m: 3.80 Sec 4000 m: 6.06 Sec
(up to 111 rounds in air) Magazine: 112 Ready; 126 Reserve; 238
total Effective Altitude: 3 Km Max Effective Range: 4 Km Manual
Fire Control: I ron Sight Radar Fire Control: Closed-Loop automated
fire control solution from Super Fledermaus Pulse Doppler radar
Exemplary Embodiment of Computer Environment
[0183] FIG. 10 depicts an exemplary computer system that may be
used in implementing an exemplary embodiment of the present
invention. Specifically, FIG. 10 depicts an exemplary embodiment of
a computer system 1000 that may be used in computing devices such
as, e.g., but not limited to, a client and/or a server, etc.,
according to an exemplary embodiment of the present invention. FIG.
10 depicts an exemplary embodiment of a computer system that may be
used as client device 1000, or a server device 1000, etc. The
present invention (or any part(s) or function(s) thereof) may be
implemented using hardware, software, firmware, or a combination
thereof and may be implemented in one or more computer systems or
other processing systems. In fact, in one exemplary embodiment, the
invention may be directed toward one or more computer systems
capable of carrying out the functionality described herein. An
example of a computer system 1000 may be shown in FIG. 10,
depicting an exemplary embodiment of a block diagram of an
exemplary computer system useful for implementing the present
invention. Specifically, FIG. 10 illustrates an example computer
1000, which in an exemplary embodiment may be, e.g., (but not
limited to) a personal computer (PC) system running an operating
system such as, e.g., (but not limited to) MICROSOFT.RTM.
WINDOWS.RTM. NT/98/2000/XP/CE/ME/VISTA/etc. available from
MICROSOFT.RTM. Corporation of Redmond, Wash., U.S.A. However, the
invention may not be limited to these platforms. Instead, the
invention may be implemented on any appropriate computer system
running any appropriate operating system. In one exemplary
embodiment, the present invention may be implemented on a computer
system operating as discussed herein. An exemplary computer system,
computer 1000 may be shown in FIG. 10. Other components of the
invention, such as, e.g., (but not limited to) a computing device,
a communications device, mobile phone, a telephony device, a
telephone, a personal digital assistant (PDA), a personal computer
(PC), a handheld PC, an interactive television (iTV), a digital
video recorder (DVD), client workstations, thin clients, thick
clients, proxy servers, network communication servers, remote
access devices, client computers, server computers, routers, web
servers, data, media, audio, video, telephony or streaming
technology servers, etc., may also be implemented using a computer
such as that shown in FIG. 10. Services may be provided on demand
using, e.g., but not limited to, an interactive television (iTV), a
video on demand system (VOD), and via a digital video recorder
(DVR), or other on demand viewing system.
[0184] The computer system 1000 may include one or more processors,
such as, e.g., but not limited to, processor(s) 1004. The
processor(s) 1004 may be connected to a communication
infrastructure 1006 (e.g., but not limited to, a communications
bus, cross-over bar, or network, etc.). Various exemplary software
embodiments may be described in terms of this exemplary computer
system. After reading this description, it may become apparent to a
person skilled in the relevant art(s) how to implement the
invention using other computer systems and/or architectures.
[0185] Computer system 1000 may include a display interface 1002
that may forward, e.g., but not limited to, graphics, text, and
other data, etc., from the communication infrastructure 1006 (or
from a frame buffer, etc., not shown) for display on the display
unit 1030.
[0186] The computer system 1000 may also include, e.g., but may not
be limited to, a main memory 1008, such as, e.g., but not limited
to, a random access memory (RAM), and a secondary memory 1010, etc.
The secondary memory 1010 may include, for example, (but not
limited to) a hard disk drive 1012 and/or a removable storage drive
1014, representing a floppy diskette drive, a magnetic tape drive,
an optical disk drive, a compact disk drive CD-ROM, etc. The
removable storage drive 1014 may, e.g., but not limited to, read
from and/or write to a removable storage unit 1018 in a well known
manner. Removable storage unit 1018, also called a program storage
device or a computer program product, may represent, e.g., but not
limited to, a floppy disk, magnetic tape, optical disk, compact
disk, etc. which may be read from and written to by removable
storage drive 1014. As may be appreciated, the removable storage
unit 1018 may include a computer usable storage medium having
stored therein computer software and/or data. In some embodiments,
a "machine-accessible medium" may refer to any storage device used
for storing data accessible by a computer. Examples of a
machine-accessible medium may include, e.g., but not limited to: a
magnetic hard disk; a floppy disk; an optical disk, like a compact
disk read-only memory (CD-ROM) or a digital versatile disk (DVD); a
magnetic tape; and a memory chip, etc.
[0187] In alternative exemplary embodiments, secondary memory 1010
may include other similar devices for allowing computer programs or
other instructions to be loaded into computer system 1000. Such
devices may include, for example, a removable storage unit 1022 and
an interface 1020. Examples of such may include a program cartridge
and cartridge interface (such as, e.g., but not limited to, those
found in video game devices), a removable memory chip (such as,
e.g., but not limited to, an erasable programmable read only memory
(EPROM), or programmable read only memory (PROM) and associated
socket, and other removable storage units 1022 and interfaces 1020,
which may allow software and data to be transferred from the
removable storage unit 1022 to computer system 1000.
[0188] Computer 1000 may also include an input device 1016 such as,
e.g., (but not limited to) a mouse or other pointing device such as
a digitizer, and a keyboard or other data entry device.
[0189] Computer 1000 may also include an output device such as,
e.g., (but not limited to) display 1030, and display interface
1002. The computer 1000 may also include other output devices 1030
such as, e.g., but not limited to, a printer.
[0190] Computer 1000 may include other input/output (I/O) devices
such as, e.g., (but not limited to) communications interface 1024,
cable 1028 and communications path 1026, etc. These devices may
include, e.g., but not limited to, a network interface card, and
modems (neither are labeled). Communications interface 1024 may
allow software and data to be transferred between computer system
1000 and external devices.
[0191] In this document, the terms "computer program medium" and
"computer readable medium" may be used to generally refer to media
such as, e.g., but not limited to removable storage drive 1014, a
hard disk installed in hard disk drive 1012, and signals 1028, etc.
These computer program products may provide software to computer
system 1000. The invention may be directed to such computer program
products.
[0192] References to "one embodiment," "an embodiment," "example
embodiment," "various embodiments," etc., may indicate that the
embodiment(s) of the invention so described may include a
particular feature, structure, or characteristic, but not every
embodiment necessarily includes the particular feature, structure,
or characteristic. Further, repeated use of the phrase "in one
embodiment," or "in an exemplary embodiment," do not necessarily
refer to the same embodiment, although they may.
[0193] In the following description and claims, the terms "coupled"
and "connected," along with their derivatives, may be used. It
should be understood that these terms may be not intended as
synonyms for each other. Rather, in particular embodiments,
"connected" may be used to indicate that two or more elements are
in direct physical or electrical contact with each other. "Coupled"
may mean that two or more elements are in direct physical or
electrical contact. However, "coupled" may also mean that two or
more elements are not in direct contact with each other, but yet
still co-operate or interact with each other.
[0194] An algorithm may be here, and generally, considered to be a
self-consistent sequence of acts or operations leading to a desired
result. These include physical manipulations of physical
quantities. Usually, though not necessarily, these quantities take
the form of electrical or magnetic signals capable of being stored,
transferred, combined, compared, and otherwise manipulated. It has
proven convenient at times, principally for reasons of common
usage, to refer to these signals as bits, values, elements,
symbols, characters, terms, numbers or the like. It should be
understood, however, that all of these and similar terms are to be
associated with the appropriate physical quantities and are merely
convenient labels applied to these quantities.
[0195] Unless specifically stated otherwise, as apparent from the
following discussions, it may be appreciated that throughout the
specification discussions utilizing terms such as "processing,"
"computing," "calculating," "determining," or the like, refer to
the action and/or processes of a computer or computing system, or
similar electronic computing device, that manipulate and/or
transform data represented as physical, such as electronic,
quantities within the computing system's registers and/or memories
into other data similarly represented as physical quantities within
the computing system's memories, registers or other such
information storage, transmission or display devices.
[0196] In a similar manner, the term "processor" may refer to any
device or portion of a device that processes electronic data from
registers and/or memory to transform that electronic data into
other electronic data that may be stored in registers and/or
memory. A "computing platform" may comprise one or more
processors.
[0197] Embodiments of the present invention may include apparatuses
for performing the operations herein. An apparatus may be specially
constructed for the desired purposes, or it may comprise a general
purpose device selectively activated or reconfigured by a program
stored in the device.
[0198] In yet another exemplary embodiment, the invention may be
implemented using a combination of any of, e.g., but not limited
to, hardware, firmware and software, etc.
[0199] While various embodiments of the present invention have been
described above, it should be understood that they have been
presented by way of example only, and not limitation. Thus, the
breadth and scope of the present invention should not be limited by
any of the above-described exemplary embodiments, but should
instead be defined only in accordance with the following claims and
their equivalents.
* * * * *