U.S. patent application number 09/784405 was filed with the patent office on 2001-12-06 for system and method of locating lightning strikes.
Invention is credited to Medelius, Pedro J., Starr, Stanley O..
Application Number | 20010048297 09/784405 |
Document ID | / |
Family ID | 26878069 |
Filed Date | 2001-12-06 |
United States Patent
Application |
20010048297 |
Kind Code |
A1 |
Medelius, Pedro J. ; et
al. |
December 6, 2001 |
System and method of locating lightning strikes
Abstract
A system and method of determining locations of lightning
strikes has been described. The system includes multiple receivers
located around an area of interest, such as a space center or
airport. Each receiver monitors both sound and electric fields. The
detection of an electric field pulse and a sound wave are used to
calculate an area around each receiver in which the lighting is
detected. A processor is coupled to the receivers to accurately
determine the location of the lighting strike. The processor can
manipulate the receiver data to compensate for environmental
variables such as wind, temperature, and humidity. Further, each
receiver processor can discriminate between distant and local
lightning strikes.
Inventors: |
Medelius, Pedro J.; (Merritt
Island, FL) ; Starr, Stanley O.; (Indialantic,
FL) |
Correspondence
Address: |
National Aeronautics & Space Administration
Mail Code: CC-A/Diana M. Cox, Patent Counsel
John F. Kennedy Space Center
Kennedy Space Center
FL
32899
US
|
Family ID: |
26878069 |
Appl. No.: |
09/784405 |
Filed: |
February 13, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60182404 |
Feb 14, 2000 |
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Current U.S.
Class: |
324/72 |
Current CPC
Class: |
G01R 29/0842 20130101;
G01W 1/16 20130101 |
Class at
Publication: |
324/72 |
International
Class: |
G01R 031/02 |
Claims
What is claimed is:
1. A system to determine a location of lighting strikes comprising:
a processor; and a plurality of receivers coupled to the processor,
wherein each of the plurality of receivers comprises an electric
field sensor, an acoustic sensor, and a controller to provide a
receiver output indicating a calculated time differential between
an electric field pulse and a sound wave, the processor determines
the location of lighting strikes in response to the output from the
plurality of receivers.
2. The system of claim 1 wherein each of the plurality of receivers
are located up to at least one kilometer apart.
3. The system of claim 1 wherein the processor compensates for wind
speed and wind direction while determining the location of lighting
strikes.
4. The system of claim 3, wherein the processor compensates for
wind speed and wind direction in the absence of wind speed and wind
direction measurements.
5. The system of claim 1 wherein the processor compensates for
temperature while determining the location of lighting strikes.
6. The system of claim 1 wherein the processor compensates for
humidity while determining the location of lighting strikes.
7. The system of claim 1 wherein the plurality of receivers
comprise three receivers.
8. A system to determine a location of lighting strikes comprising:
at least three receivers wherein each receiver comprises an
electric field sensor, an acoustic sensor, and a controller to
provide a receiver output indicating a calculated time differential
between an electric field pulse and a sound wave; and a processor
coupled to the receivers to determine the location of lighting
strikes in response to the output from the receivers.
9. The system of claim 8 wherein the processor compensates for
environmental conditions including wind speed and wind direction,
temperature and humidity while determining the location of lighting
strikes.
10. The system of claim 9, wherein wind speed is corrected for by
using angles between the receivers and the lighting location to
compute estimated ranges R, using the following
formula:R=TOA*V=TOA*(c-V.sub.w cos (.theta.-.THETA.))where
TOA=measured time interval between the electromagnetic and sonic
signals V=effective sonic velocity c=actual sonic velocity based on
temperature V.sub.w=wind speed .theta.=azimuth direction measured
from receiver to source .THETA.=azimuth of wind vector.
11. The system of claim 8 wherein each of the receivers are located
up to one kilometer apart.
12. A method for determining a location of lightning strikes
comprising: locating a network of at least three electric field
sensors and at least three sonic sensors in an area of interest;
collecting lightning strike information, including a time of
arrival of an electric field pulse and an associated sound wave
from a lightning strike; processing the lightning strike
information recorded by the at least three electric field sensors
and the at least three sonic sensors, including measuring a time
difference between the arrival of the electric field pulse and the
sound wave at each electric field and sonic sensor; and determining
the location of the lightning strike.
13. The method of claim 12 wherein determining the location of the
lightning strike comprises compensating for environmental
conditions including wind speed and wind direction, temperature and
humidity.
14. The method of claim 12 wherein the at least three electric
field sensors are located up to one kilometer apart, and the least
three sonic sensors are located up to one kilometer apart.
15. The method of claim 12 wherein determining the location of the
lightning strike comprises comparing the arrival of the electric
field pulse and the sound wave for each pair of receivers.
16. The method of claim 12 wherein the network comprises at least
four electric field sensors and at least four associated sonic
sensors.
17. The method of claim 16, wherein wind speed is corrected for by
using angles between the receivers and the lighting location to
compute estimated ranges R, using the following
formula:R=TOA*V=TOA*(c-V.sub.w cos (.theta.-.THETA.))where
TOA=measured time interval between the electromagnetic and sonic
signals V=effective sonic velocity c=actual sonic velocity based on
temperature V.sub.w=wind speed .theta.=azimuth direction measured
from receiver to source .THETA.=azimuth of wind vector.
18. The method of claim 12 wherein the processor compensates for
wind speed and wind direction while determining the location of
lighting strikes.
19. The method of claim 12, wherein the processor compensates for
wind speed and wind direction in the absence of wind speed and wind
direction measurements.
20. The method of claim 12 wherein processing the lightning strike
information comprises discriminating between lightning strikes
based upon distance to filter out lightning strikes outside the
area of interest.
Description
ORIGIN OF THE INVENTION
[0001] The invention described herein was made in the performance
of work under a NASA contract and is subject to the provisions of
Section 305 of the National Aeronautics and Space Act of 1958, as
amended, Public Law 85-568 (72 Stat. 435; 42 U.S.C. .sctn.2457).
This patent application is related to U.S. Provisional Patent
Application Ser. No. 60/182,404, entitled "Method and Apparatus for
Accurate Location of Lightning Strikes", filed on Feb. 14,
2000.
[0002] The present invention relates generally to identifying
locations of lightning strikes.
BACKGROUND OF THE INVENTION
[0003] Electronic equipment is susceptible to damage caused by
nearby lightning strikes. The accurate knowledge of a lightning
striking point is important to determine which equipment or system
needs to be tested following a lightning strike. Existing lightning
location systems can provide coverage of a wide area. For example,
a lightning location system can provide coverage of an area having
a 30 km radius. This system, however, has a 50% confidence region
of about 500 meters. That is, the system has a 50% confidence that
a lighting strike is within 500 meters of an identified location.
As such, present lightning location systems cannot be used to
determine whether a lightning strike occurred inside or outside of
a parameter of an area of concern. One such application of a
lightning location system is a space shuttle launch pad for the
National Aeronautics and Space Administration (NASA). By accurately
determining lightning strike locations, electronic equipment
located within the launch pad area can be tested and/or reset to
avoid erroneous operation.
[0004] One method of determining the location of lightning strikes
uses a set of video cameras that are pointed in different
directions within the area of concern. If a lightning strike occurs
within the field of view of three or more cameras, the location of
the strike can be determined. However, if the cameras are not
pointed in the correct direction, or either an object or a heavy
rain downpour obscures their field of view, it is difficult or
impossible to accurately determine a striking point of the
lightning. Further, this method has a relatively large uncertainty
and does not facilitate an accurate location of the exact point of
contact to the ground.
[0005] For the reasons stated above, and for other reasons stated
below which will become apparent to those skilled in the art upon
reading and understanding the present specification, there is a
need in the art for the system and method to accurately locate
locations of lightning strikes.
SUMMARY OF THE INVENTION
[0006] The above-mentioned problems with lightning strike location
and other problems are addressed by the present invention and will
be understood by reading and studying the following
specification.
[0007] In one embodiment, a system to determine a location of
lighting strikes comprises a processor, and a plurality of
receivers coupled to the processor. Each of the receivers comprises
an electric field sensor, an acoustic sensor, and a processor to
provide a receiver output indicating a calculated time differential
between an electric field pulse and a sound wave (thunder). The
processor determines the location of lighting strikes in response
to the output from the plurality of receivers.
[0008] A method is provided for determining a location of lightning
strikes. The method comprises locating a network of at least three
electric field sensors and at least three sonic sensors in an area
of interest, and collecting lightning strike information, including
a difference of the time of arrival of an electric field pulse and
an associated sound wave from a lightning strike. The method
processes lightning strike information recorded by the at least
three electric field sensors and at least three sonic sensors,
including measuring a time difference between the arrival of the
electric field pulse and the sound wave at each electric field and
sonic sensor. The processor uses the time differentials to produce
estimates of the range between the receiver and the lightning
strike. The processed information is used to determine the location
of the lightning strike.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a block diagram of one embodiment of a receiver of
the present invention;
[0010] FIG. 2 illustrates circles defined by a time difference
between the arrival of an electric field signal and a sonic signal;
and
[0011] FIG. 3 is a block diagram of a system of the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0012] In the following detailed description of the preferred
embodiments, reference is made to the accompanying drawings that
form a part hereof, and in which is shown by way of illustration
specific preferred embodiments in which the inventions may be
practiced. These embodiments are described in sufficient detail to
enable those skilled in the art to practice the invention, and it
is to be understood that other embodiments may be utilized and that
logical, mechanical and electrical changes may be made without
departing from the spirit and scope of the present invention. The
following detailed description is, therefore, not to be taken in a
limiting sense, and the scope of the present invention is defined
only by the claims.
[0013] The present invention provides a system and method that can
accurately locate a lightning strike within an area of interest. In
one embodiment, the present invention can accurately locate a
lightning strike within a few meters. Further, receivers used to
detect lightning strikes can be located at distances of
approximately one kilometer and greater apart. As explained below,
the present invention uses a combination of electric field and
sonic sensors.
[0014] The fast varying electric current associated with lightning
discharges generates large electric field variations. The electric
field waveform propagates at the speed of light in a radial
direction from the striking point of lightning. The sudden heating
of the air caused by the large currents associated with the
lightning discharge produces a sudden expansion of the air near the
lightning channel. This results in a sound wave (thunder) that
initially, for the first few meters, propagates at a supersonic
speed and later propagates at a sonic speed.
[0015] For an observer located remotely from a lightning strike
location, the electric field waveform arrives earlier than the
sonic sounds. This is because the electric field waveform travels
and a speed of approximately 300,000,000 m/s, while the sound wave
travels and approximately 350 m/s. The observer can estimate the
distance to striking point by measuring the time difference between
the arrival of the electric field waveform and the arrival of the
sound wave. This measurement defines a circle, with the observer at
the center, on which the lightning strike might have occurred. The
second observer and a different location using the same type of
measurement also has a circle defined around them in which the
lightning might have occurred. These two circles intersect at two
points. With the addition of a third observer, a single striking
point can be determined. The present invention provides receivers
that can be located remotely from each other to accurately
determine lightning strike locations.
[0016] Referring to FIG. 1, a block diagram of one embodiment of a
receiver 100 of the present invention is illustrated. The receiver
includes an electric field antenna 110, a microphone 120 and a
microcontroller 130 coupled to receive amplified signals from the
antenna and microphone. In operation, multiple receivers are
located around an area of interest. Each receiver is used to detect
changes in an electric field and detection of sonic sounds. The
combination of the electric field and sonic level are used to
determine a location of the lightning strike. In operation, the
electric field antenna 110 detects changes in the electric field
surrounding the antenna. The microphone 120 is used to detect sonic
sounds surrounding the antenna. The output of each of these
components can be amplified by amplifiers 140 and 150, if
necessary, and the microcontroller 130 performs an analysis of the
outputs to determine a radius around the receiver in which a
lightning strike may have occurred. An example of this analysis is
described in more detail below. By using three remotely located
receivers, an accurate location of lightning strikes can be
determined.
[0017] Referring to FIG. 2, the location of a lightning strike can
be determined by the intersection of three circles 180, 190 and 200
defined by the time difference between the arrival of an electric
field signal and a sonic signal. Each of the three circles are
located around three remotely spaced receivers, 210, 220 and 230,
respectively. As explained above, each of the receivers determines
a radius within which the lightning strike may have occurred. This
radius, or distance d.sub.n, can be defined as the speed of sound
(c) times the time difference (t.sub.n) between electric field
signal in the sonic signal (d.sub.n=c*t.sub.n).
[0018] The present system relies on the accurate determination of
the time elapsed between the reception of the electric field
waveform and the reception of the sound waveform. The electric
field waveform has a rise time in the order of a few microseconds,
and its start can be determined with an accuracy of a fraction of a
microsecond. At close distances, the sound waveform has a sharp
wavefront. That is, its high frequency content (frequency>10
kHz) is a large. The sound waves propagating through air suffer
large attenuation at high frequencies as compared to the
attenuation of the low frequencies. The attenuation of the high
frequencies is further enhanced by heavy rain. Thus, at close
distances, the start of the sound wavefront can be easily measured
since it has a fast rise time. At distances of greater than one or
two kilometers, the wavefront rises slower, making it difficult to
detect the exact time of the sound wave.
[0019] In one embodiment of the present invention, the system
includes a network of at least three receivers at different
locations within a perimeter of interest to be monitored for
lightning strikes. The microcontroller of each receiving station is
used to measure the time difference between the arrival of the
electric field pulse and the arrival of the sound wave. The timing
information from each receiver 210, 220 and 230 is transmitted back
to a central processing location 250, where the timing information
is processed to obtain the location of the lightning strike, see
FIG. 3. The accuracy of the system can be enhanced in one
embodiment by using more than three receivers, such as receiver
240. A network of four or more receivers, for example, can be used
to resolve uncertainties introduced by wind speed. Echoes and
reflections from objects within the monitored area can be removed
using common digital signal processing techniques.
[0020] The present invention allows for the accurate location of a
lightning strike within a few meters using a combination of
electric field and sonic sensors. One advantage of the present
system includes the fact that high-speed digitizers are not
required. The electric field pulse is used to start a time counter,
and the sound wave is used to stop the time counter. A
one-millisecond error in determination of the timing can result in
an error of about 30 cm. Existing wideband, large baseline
lightning location systems require timing accuracies better than a
fraction of a nanosecond to achieve this kind of accuracy. The
present invention provides an inexpensive and easy to install
system, with minimal maintenance and calibration requirements.
[0021] The present invention allows for the determination of the
distance to a lightning strike without requiring fast recording or
digitizing equipment. Further, an algorithm to combine the
information from a network of receivers allows for fine-tuning the
system. Also, for example, an algorithm can be implemented to
determine the location of a lightning strike when the wind is
nonzero. This is important since nonzero wind will result in
noncircular distance patterns around each receiver.
[0022] In another embodiment, the present system discriminates
between nearby and distant thunder. Because sound waves are
attenuated as they propagate through air, with high frequencies
decaying faster than low frequencies, the frequency spectrum of
nearby thunder contains higher frequency components than thunder
from a distant lightning strike. The characteristic "rumble" from
thunder consists mainly of frequencies below 100 Hz, while the
"clap" occurred following a close lightning strike contains
components above several kHz.
[0023] The following receiver algorithm illustrates discrimination
between local and distant lightning strikes to avoid erroneous
detection outside an area of interest:
1 x =rf("data) Read data file. h =rf("hpf") Read highpass filter,
cutoff of 200 Hz, finite impulse response (FIR), 31st order. y =x$h
Perform time-domain convolution between data file and filter
impulse response. This is equivalent to multiplying the spectrum of
the thunder data by the frequency response of the filter. The
result of the convolution is stored in variable y. y =y-avg(y)
Center variable y around zero (remove DC component). z =abs(y) Get
the absolute value of y and storage in variable z. This is
equivalent to performing a rectification of the filtered thunder
signal. I =rf("Ipf") Read low pass filter, cut off of 10 Hz, finite
impulse response (FIR), 31st order. z =z$l Perform a time-domain
convolution between the rectified thunder signal and the low pass
filter impulse response. This results in the envelope of the
thunder signal. pop =FALSE Determine the start of the thunder
waveform by eliminating the for(i=0:len:1) "pop" sound caused by
nearby lightning. This is done by for(j:=0:500) eliminating pulses
with a duration shorter than 50 ms. if(z[i+j]<thr) then pop=TRUE
end end if(pop=FALSE) thunderstart=i The start of the thunder
waveform is the amplitude "i" of the end data set. This is the
value that is used to determine the end spatial location of the
lightning strike.
[0024] The primary sources of location error in the described
invention are due to variations in the speed of sound and due to
the effect of wind. The sound speed in air is a function of the
temperature (changing as the square root of the absolute
temperature) and the molecular weight. The latter changes are due
to variations in humidity, which can typically be ignored. By
augmenting the present invention with externally measured
temperature, wind direction and wind speed, the accuracy of the
system can be preserved. An environmental factors component 252 can
be included with the present invention to input environmental data
such as temperature, wind direction and wind speed. One embodiment
of the described invention includes a temperature measurement at
the central processor, which allows for the calculation of acoustic
speed. In another embodiment, data is acquired from another source,
such as a local meteorological station to provide the input to
compute sound speed. This computation is performed using widely
known and accepted equations.
[0025] To correct for wind speed, note that sound will travel with
respect to the terrain as a sum of the wind speed and direction
vector and the sound speed. Therefore the component of wind along
the direction between the receiver and the lightning source can
either retard or advance the effective velocity of the thunder. In
one embodiment of the invention, three remote receivers are used
and the central processor acquires external information on the wind
speed and direction from a local measuring station. The three
receivers are used to compute a preliminary source location. The
angles between the receivers and the estimated source location are
used to recompute the estimated ranges, R, using the following
formula:
R=TOA*V=TOA*(c-V.sub.w cos (.theta.-.THETA.))
[0026] where TOA=measured time interval between the electromagnetic
and sonic signals
[0027] V=effective sonic velocity
[0028] c=actual sonic velocity based on temperature
[0029] V.sub.w=wind speed
[0030] .theta.=azimuth direction measured from receiver to
source
[0031] .THETA.=azimuth of wind vector as measure from North
[0032] These new range estimates are used to determine a new
location as previously described. This process can be iterated
until the estimated position of the source does not vary more than
the expected variance based on the GDOP.
[0033] Alternatively, if wind speed and direction information are
not available externally, the wind speed and direction can be
estimated if a fourth (or more) receiver 240 is included. Again,
the measured ranges are used to compute a source location using
iterative least squares procedure (i.e. guess a location, then use
linearized range equations to derive a correction vector, etc.).
Once this procedure has resulted in an estimate, a second,
nonlinear programming technique operating on the range equation
given above is used to estimate the location (x, y) of the source
along with the wind velocity and direction. This procedure
minimizes the variance of all four variables jointly. This accuracy
of this process improves as the number of receivers is increased.
The efficacy of this nonlinear process is also improved by using
the residuals (the differences between the range to the estimated
point and the measured ranges) to estimate the wind speed and
direction.
[0034] The process is now described in detail. The equation for the
range in terms of Xp and Yp the coordinates of the source point and
Xi and Yi the coordinates of receiver "i" is given by (ignoring for
the moment the wind): 1 T i = R i c = 1 c ( ( X P - X i ) 2 + ( Y P
- Y i ) 2 ) 1 / 2
[0035] where there is one such equation for each detector. If this
equation is expanded in terms of the coordinates of the event the
following is obtained: 2 T m = T P + ( R X P ) X P + ( R Y P ) Y
P
[0036] Take .DELTA.Tm to be the measured time difference while
.DELTA.Tp is the time difference that would be measured from an
assumed position p and evaluate the derivatives at the assumed
position p, and interpret that the .DELTA.X.sub.P and
.DELTA.Y.sub.P are components of a first order correction to the
assumed position in a direction to reduce the difference between
the measured .DELTA.Tm and the computed .DELTA.Tp. By listing these
linear equations in rows a matrix equation can be constructed and
solve for the .DELTA.X.sub.P and .DELTA.Y.sub.P values. The
derivative terms are: 3 ( R X P ) = X P R ( R Y P ) = Y P R
[0037] which are easily calculated using the value for an assumed
point Xp and Yp. Our total equation in matrix form looks like: 4 (
T m1 - T P T m2 - T P T m3 - T P ) = ( X p R 1 Y P R 1 X P R 2 X P
R 2 X p R 3 Y p R 3 ) ( X P Y P )
[0038] In matrix notation this same equations reads:
.delta..DELTA.T=H.multidot..DELTA.X
[0039] To solve for the .DELTA.X matrix the generalized inverse of
the matrix H is taken. The solution is given by:
.DELTA.X=(H.sup.TH).sup.-1H.sup.T.delta..DELTA.T
[0040] Once the correction vector .DELTA.X is solved, it can be
added to the presumed values of Xp and Yp to create a new estimate.
Thus the estimate at time step n is transformed into a new estimate
a step n+1. After each step, the size of the residuals, the
elements of the .delta..DELTA.T vector, are evaluated. When they
become sufficiently small the process can be considered complete.
The final values of the Xp and Yp coordinates are used as the
initial values of the next step which will estimate the event
position jointly with wind speed and direction.
[0041] Since each measurement of .DELTA.T contains errors due to
the wind speed, direction, and other errors (refraction, timing
errors, errors in estimating the peak of the sound waveform, and so
on) it is desirable to develop a figure of merit for the resulting
solution. Specifically relating the errors in the .DELTA.T's to the
errors in X.sub.P and Y.sub.P that represent our final and best
estimates is desirable. The covariance matrix of the errors in the
four .DELTA.T measurements given as follows: 5 COV ( T i ) = E { T
i T i T } = t = ( 1 2 12 13 14 12 2 2 23 24 31 32 3 2 34 41 42 43 4
2 )
[0042] where the diagonal terms represent the variances of each
measurement and the off-diagonal terms represent the covariances
between measurements. The off diagonal terms represent the degree
of correlation between the measurements. In the case of random
errors only (such a digitizing timing jitter and random variations
in the sound waveform) these terms are zero. In the case of
systematic errors including the effects of wind, they will not be
zero. If the error sources are unknown, such as the wind speed and
direction, it can be assumed that the covariances are zero. The
matrix can be constructed by inserting identical values for the
diagonal elements representing .DELTA.T measurement errors derived
from field tests or other considerations. The covariance matrix
becomes the unit matrix multiplied by a scalar quantity
.sigma..DELTA.T which represents the level of confidence chosen.
Typically the sigma value is selected to represent a level of
confidence such that the probability of a randomly chosen value of
delta T falling within that distance of the mean is 68.3%. The
following steps will result in error figures for the coordinates
that will be based on the same confidence limit. The covariance
matrix then is a unit matrix of rank four multiplied by a scalar
value of error in units of time.
[0043] Likewise, there is a covariance matrix of the estimated
position values X.sub.P and Y.sub.P given as follows: 6 COV ( X ) =
E { X X T } = X = ( x 2 xy yx y 2 )
[0044] where again, the diagonal terms are the variances of each
coordinate and the off diagonal terms are their covariants already
derived transformation from the delta T equation to the delta X's
can be used to find the covariance matrix in X as follows:
.SIGMA..sub.X=(H.sup.TH).sup.-1H.sup.T.SIGMA..sub..DELTA.T
[0045] Since the covariance matrix is symmetrical and positive
definite it represents a quadratic form. If expressed in the
following form it gives rise to an ellipse centered on the final
estimates of X.sub.P and Y.sub.P:
.function.(x)=x.sup.T.SIGMA..sub.xx
[0046] This ellipse has semimajor and semiminor axes given by: 7 a
2 = 1 2 ( x 2 + y 2 ) + 1 4 ( x 2 - y 2 ) 2 + xy 2 b 2 = 1 2 ( x 2
+ y 2 ) - 1 4 ( x 2 - y 2 ) 2 + xy 2
[0047] So unless the covariances are zero, the ellipse is inclined
with respect to the x axis so that the angle between the semimajor
axis and the x axis is given by: 8 tan 2 = 2 xy x 2 - y 2
[0048] Note that the value of confidence applied was 68.3%, the
probability that the actual value falls within the ellipse is
significantly reduced to only 39.4%. Thus many practitioners derive
an ellipse based on 2.447 times the one sigma values to get an
ellipse encircling a 95% confidence level.
[0049] The GDOP is given by: 9 GDOP = TRACE ( ( H T H ) - 1 H T
)
[0050] This represents the magnification factor of the error based
on the geometry of the lightning detectors and the computed
lightning location. The GDOP is relevant to the present invention
only in that should it be possible to select the best subset of
available measurements (more than 4 receivers) the processor will
select those that gave the best GDOP.
[0051] A preliminary solution has been provided without modeling
any wind effects. Next, estimates of the wind speed and direction
from at least four lightning delta T measurements can be derived.
By returning to the basic equation of delta T as a function of wind
speed and direction: 10 T = R ( c - V W cos ( - ) )
[0052] Again, if a lightning location is assumed and a set of
values for the wind speed and direction, this function can be
expanded in a first order Taylor series as follows: 11 T M = T P +
( F X P ) X + ( F Y P ) Y P + ( F V W ) V W + ( F )
[0053] where each derivative is evaluated at the assumed values of
position and wind characteristics. If four such measurement
equations are written in matrix form the following results: 12 ( T
1 T 2 T 3 T 4 ) = ( 1 1 1 1 2 2 2 2 3 3 3 3 4 4 3 4 ) ( X P Y P V W
) or T = A X
[0054] where the A matrix elements are the values of the
derivatives evaluated at the assumed values of the position, wind
speed and direction. The equations for the derivatives are: 13 i =
X P { R c ( 1 - V W c cos ( - ) } = ( X i - X P ) cR ( 1 - V W c
cos ( - ) ) i = ( Y i - Y P ) cR ( 1 - V W c cos ( - ) ) i = R cos
( - ) c 2 ( 1 - V W c cos ( - ) ) 2 i = R sin ( - ) c 2 ( 1 - V W c
cos ( - ) ) 2
[0055] When the values of the coefficients are evaluated, a simple
matrix inversion is computed to find the values of the elements of
the .DELTA.X vector. These four values are then added to the
original set of assumed values for the four sought parameters to
derive a new set. The residuals (elements of .delta.T matrix) are
evaluated between each iteration. When the residuals become
sufficiently small, the process is complete. To compute the
variances proceed as before with:
.SIGMA..sub.x=A.sup.-1.SIGMA..sub..delta.T
[0056] and the error ellipse and GDOP are computed as before with
the exception of only using the upper left block of four elements
of the sigma x matrix.
[0057] This process results in optimal least square estimates of
the position of the lightning strike and the errors in those
estimates.
Conclusion
[0058] A system and method of determining locations of lightning
strikes has been described. The system includes multiple receivers
located around an area of interest, such as a space center or
airport. Each receiver monitors both sound and electric fields. The
detection of an electric field pulse and a sound wave are used to
calculate a range circle around each receiver in which the lighting
is detected. A processor is coupled to the receivers to accurately
determine the location of the lighting strike. The processor can
manipulate the receiver data to compensate for environmental
variables such as wind, temperature, and humidity. Further, the
system can discriminate between distant and local lightning
strikes.
[0059] Although specific embodiments have been illustrated and
described herein, it will be appreciated by those of ordinary skill
in the art that any arrangement, which is calculated to achieve the
same purpose, may be substituted for the specific embodiment shown.
This application is intended to cover any adaptations or variations
of the present invention. Therefore, it is manifestly intended that
this invention be limited only by the claims and the equivalents
thereof.
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