U.S. patent application number 13/326201 was filed with the patent office on 2012-04-12 for secure information transfer based on global position.
Invention is credited to David S. DeLorenzo, Per K. Enge, Sherman C. Lo.
Application Number | 20120087444 13/326201 |
Document ID | / |
Family ID | 46332627 |
Filed Date | 2012-04-12 |
United States Patent
Application |
20120087444 |
Kind Code |
A1 |
DeLorenzo; David S. ; et
al. |
April 12, 2012 |
Secure Information Transfer Based on Global Position
Abstract
Secure communication of information is effected from a first
party to a second party when the first party knows its own global
location and the global location of the second party, and employs
what essentially is an undiscoverable code signal that is broadcast
to, and received by, both the first and the second parties. The
first party securely communicates information to the second party
by modifying the code signal with the information that is to be
communicated and sends the modified code signal to the second
party. Illustratively, the code signal is related to the Y
component of a GPS signal.
Inventors: |
DeLorenzo; David S.; (Palo
Alto, CA) ; Enge; Per K.; (Mountian View, CA)
; Lo; Sherman C.; (San Mateo, CA) |
Family ID: |
46332627 |
Appl. No.: |
13/326201 |
Filed: |
December 14, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12231094 |
Aug 29, 2008 |
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13326201 |
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12012327 |
Feb 2, 2008 |
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12231094 |
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Current U.S.
Class: |
375/316 |
Current CPC
Class: |
G01S 19/21 20130101 |
Class at
Publication: |
375/316 |
International
Class: |
H04L 27/00 20060101
H04L027/00 |
Claims
1. A method executed by a first unit that is coupled to a first
antenna that is situated at a first location, which antenna is
constructed to receive a signal comprising a sum of constituent
signal, each from a different source of a plurality of sources, and
each of the constituent signals containing a component that is
modulated by a known code and a component that is modulated by a
code that is not publicly known and not available to said first
unit (secret code), for communicating a data signal from said first
unit to a second unit that is coupled to a second antenna that is
situated at a second location that is known to said firs unit,
comprising the steps of: processing said signal to remove a Doppler
frequency shift that said signal experiences in arriving at said
first antenna, thereby creating a signal A; creating a signal B
that corresponds to a signal that is expected to have been received
at said second antenna in response to a signal transmitted by a
particular one of said sources; combining signal A, signal B, and
said data signal to form a signal C, where said data signal is
expressed as time delay, frequency shift, or both; and sending
signal C to said second unit.
Description
RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 12/231,094, which was filed on Aug. 29, 2008
which is a continuation in part of U.S. patent application, Ser.
No. 12/012,327, which was filed on Feb. 2, 2008.
BACKGROUND OF THE INVENTION
[0002] When information needs to be communicated in a secure manner
one typically turns to cryptographic techniques. It is generally
recognized that with many cryptographic techniques the encrypted
data can be recovered by an adversary, but only if the adversary
has sufficient resources (e.g., computing power) and sufficient
time. Most users are satisfied when a method is secure "enough,"
meaning that the time, effort, or expense to recover the data
embedded in an encrypted message is too great to make the data
useful to an adversary.
[0003] With the above in mind, cryptographic techniques usually
depend on encryption and decryption keys being in possession of the
communicating parties. Aside from the concern about the inherent
security of message encrypted with a particular method, the biggest
concern is with the secure creation, distribution and maintenance
of the keys.
SUMMARY OF THE INVENTION
[0004] An advance in the art is achieved with a method that
implements secure transmission of information from one party to
another without the need for cryptographic keys but, rather, based
on unique geographic attributes such as position as well as time.
More specifically, secure communication of information is effected
from a first party to a second party when the first party knows its
own global location and the global location of the second party,
and employs a code signal that is broadcast to, and received by,
both the first and the second parties. The first party securely
communicates information to the second party by modifying the code
signal with the information that is to be communicated and sends
the modified code signal to the second party. The code signal that
is received by the first party and is used to convey information to
the second party need not to be actually known to either of the
parties, and from the standpoint of secure communication it is
advantageous for the broadcasted code signal (and the corresponding
related received signals) to not be known to either of the parties
and to be essentially impossible for the parties to discover. The
signal that is employed in the disclosed illustrative example is
related to the Y component of a GPS signal. Other wireless sources
that are modified to include a signal like the Y component of the
GPS signal can also be employed.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] FIG. 1 depicts a first unit that securely transmits
information without the use of cryptographic keys;
[0006] FIG. 2 shows some of the processing within processor 40 of
FIG. 1; and
[0007] FIG. 3 depicts some of the processing within a unit that
receives the signal transmitted by the FIG. 1 unit.
DETAILED DESCRIPTION
[0008] U.S. patent application Ser. No. 12/012,327 discloses an
approach whereby a first device, at location x, can verify an
assertion by a second device, at location y, as to the global
position of the second device. The disclosure presented an
illustrative embodiment that is based on the Global Positioning
System (GPS) but the principles disclosed therein are broader and
are not limited to the GPS. For examples, they can be readily
applied to the other global navigation satellite systems being
developed and deployed worldwide.
[0009] To assist the reader in understanding the instant invention
without having to read the aforementioned application, the
following repeats a significant portion of the mathematical
underpinnings presented in the 12/012,327 application. It should be
kept in mind that here, as well, the principles of the disclosed
invention are broader than the illustrative example that uses the
GPS.
[0010] FIG. 1 shows unit 100 that belongs to Remote Device B, which
simultaneously receives a number of GPS satellite signals on
frequency L1, where the signal transmitted by satellite n can be
expressed as
S.sub.transmitted.sup.n=A.sup.nD.sup.n(t)x.sub.C.sup.n(t)cos(2.pi.(f.sub-
.L1)t+.phi..sub.1)+B.sup.nD.sup.n(t)x.sub.Y.sup.n(t)sin(2.pi.(f.sub.L1)t+.-
phi..sub.1) (1)
where D.sup.n(t) is the data signal of satellite n,
x.sub.C.sup.n(t) is a code signal assigned to satellite n that is
publicly known, x.sub.Y.sup.n(t) is a code signal assigned to
satellite n that is not publicly known, f.sub.L1 is the frequency
of the carrier, and .phi..sub.1 is the phase of the carrier
relative to the beginning of the data and code signals. Unit 100 is
the party that wishes to send information to a remote unit 200
without the use of cryptographic keys.
[0011] A GPS receiver receives a signal corresponding to the sum of
the signals of the individual satellites. The receiver can engage
in the processing of signals as if all of the possible satellites
are present but, of course, some of the satellites are not within
range of the GPS receiver's antenna (i.e., not detectible) so the
processing results for those satellites are not viable. In other
words, the signal arriving at the FIG. 1 antenna corresponds to
n = 1 K [ A n D n ( t ) x C n ( t ) cos ( 2 .pi. ( f L 1 ) t +
.PHI. 1 ) + B n D n ( t ) x Y n ( t ) sin ( 2 .pi. ( f L 1 ) t +
.PHI. 1 ) ] + Noise ( 1 a ) ##EQU00001##
where K is the number of satellites that are within view of the
antenna.
[0012] The following analysis follows the signal of only one
satellite and, for sake of simplicity superscript n is omitted from
the equations. The fact that other satellite signals exist is
addressed later.
[0013] The transmitted signal is subjected to transit time delay
before reaching the receiver, and the signal that is received by a
first receiver's antenna experiences a Doppler frequency shift,
f.sub.D, due to the satellite's movement in its orbit and possible
receiver motion. Also, the transmitter and the receiver do not have
a common clock, which means that even when the transmitter and the
receiver clocks are at identical frequency, there is a phase
difference between them. To make the equations more general, one
might assume that there is a time shift (the transitions are not
fully aligned) between the AD(t)x.sub.C(t) and the BD(t)x.sub.Y(t)
, so the signal received at the first receiver can be expressed
as
S.sub.received,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1)cos(2.-
pi.(f.sub.L1+f.sub.D,1)(t-.tau..sub.1)+.phi..sub.1,1)+B.sub.1D(t-.tau..sub-
.Y,1)x.sub.Y(t-.tau..sub.Y,1)sin(2.pi.(f.sub.L1+f.sub.D,1)(t-.tau..sub.1)+-
.phi..sub.1,1) (2)
or simplified to
S.sub.received,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1)cos(2.-
pi.(f.sub.L1+f.sub.D,1)t+.phi..sub.1,1-.phi..sub.2,1)+B.sub.1D(t-.tau..sub-
.Y,1)x.sub.Y(t-.tau..sub.Y,1)sin(2.pi.(f.sub.L1+f.sub.D,1)t)+.phi..sub.1,1-
-.phi..sub.2,1) (3)
It may be noted that for GPS, the C/A code and Y code are aligned,
so this generalization is not needed for a GPS-based
embodiment.
[0014] As shown in FIG. 1, the received signal is detected and
amplified in element 10, conventionally downshifted in element 12
to a preselected intermediate frequency (IF) by multiplying the
received signal by signal
sin(2.pi.(f.sub.L1-f.sub.IF)t+.phi..sub.3,1) (4)
and low pass filtered by element 15. The signal of equation (4) is
generated from reference oscillator 20 by frequency synthesizer 22,
where .phi..sub.3 is the phase of the locally generated signal
(relative to the beginning of the data and code signals at the
transmitting satellite which, of course, is unknown). The result at
the output of the low pass filter is
S.sub.downshifted,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1)cos-
(2.pi.(f.sub.IF+f.sub.D,1)t+.phi..sub.1,1-.phi..sub.2,1-.phi..sub.3,1)+B.s-
ub.1D(t-.tau..sub.Y,1)x.sub.Y(t-.tau..sub.Y,1)sin(2.pi.(f.sub.IF+f.sub.D,1-
)t+.phi..sub.1,1-.phi..sub.2,1-.phi..sub.3,1) (5)
or simplified to
S.sub.downshifted,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1)cos-
(2.pi.(f.sub.IF+f.sub.D,1)t+.theta..sub.1)+B.sub.1D(t-.tau..sub.Y,1)x.sub.-
Y(t-.tau..sub.Y,1)sin(2.pi.(f.sub.IF+f.sub.D,1)t+.theta..sub.1).
(6)
[0015] It may be noted that the above-described use of downshifting
by use of an IF modulator and low pass filter is illustrative, and
that the A/D can be connected directly to the amplifier, and
controlled to generate a digital signal as if it were downshifted
as shown in FIG. 1.
[0016] As depicted, the output signal of the low pass filter is
digitized in A/D converter 18 and applied to a combination of
processor 40 and associated memory 41, where the remainder of the
processing takes place.
[0017] The processing in accord with the instant disclosure, shown
in FIG. 2, begins with a carrier generator module 31 creating the
signal
cos(2.pi.(f.sub.IF+{circumflex over (f)}.sub.D)t+{circumflex over
(.theta.)}.sub.1)-isin(2.pi.(f.sub.IF+{circumflex over
(f)}.sub.D)t+{circumflex over (.theta.)}.sub.1), (7)
where {circumflex over (f)}.sub.D is an estimate of the Doppler
frequency shift f.sub.D, and {circumflex over (.theta.)}.sub.1 is
an estimate of the phase .theta..sub.1. To be clear, the Doppler
frequency shift and the phase estimates are estimates for a
particular satellite. Multiplying the received (and downshifted)
signal of equation (6) by the phasor of equation (7) in element 32
yields
A 1 D ( t - .tau. C , 1 ) x C ( t - .tau. C , 1 ) { + cos ( 2 .pi.
( f D , 1 - f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1 ) + i sin ( 2
.pi. ( f D , 1 - f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1 ) } + B 1
D ( t - .tau. Y , 1 ) x Y ( t - .tau. Y , 1 ) { + sin ( 2 .pi. ( f
D , 1 - f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1 ) - i cos ( 2 .pi.
( f D , 1 - f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1 ) } ( 8 )
##EQU00002##
which can be viewed as a real or inphase component (which is not
shown in FIG. 2)
S.sub.I,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1){+cos(2.pi.(f-
.sub.D,1-{circumflex over (f)}.sub.D,1)t+.theta..sub.1-{circumflex
over
(.theta.)}.sub.1)}+B.sub.1D(t-.tau..sub.Y,1)x.sub.Y(t-.tau..sub.Y,1){+sin-
(2.pi.(f.sub.D,1-{circumflex over
(f)}.sub.D,1)t+.theta..sub.1-{circumflex over (.theta.)}.sub.1)}
(9)
and a quadrature component (which is shown in FIG. 2)
S.sub.Q,1=A.sub.1D(t-.tau..sub.C,1)x.sub.C(t-.tau..sub.C,1){sin(2.pi.(f.-
sub.D,1-{circumflex over (f)}.sub.D,1)t+.theta..sub.1-{circumflex
over
(.theta.)}.sub.1)}-B.sub.1D(t-.tau..sub.Y,1)x.sub.Y(t-.tau..sub.Y,1){cos(-
2.pi.(f.sub.D,1-{circumflex over
(f)}.sub.D,1)t+.theta..sub.1-{circumflex over (.theta.)}.sub.1)}
(10)
Integrating this signal in element 33 over a preselected interval
that is long enough to filter out the 2f.sub.IF signal component
yields
.intg. A 1 D ( t - .tau. C , 1 ) x C ( t - .tau. C , 1 ) { cos ( 2
.pi. ( f IF + f ^ D , 1 ) t + .theta. ^ 1 ) cos ( 2 .pi. ( f IF + f
D , 1 ) t + .theta. 1 ) - i sin ( 2 .pi. ( f IF + f ^ D , 1 ) t +
.theta. ^ 1 ) cos ( 2 .pi. ( f IF + f D , 1 ) t + .theta. 1 ) } +
.intg. B 1 D ( t - .tau. Y , 1 ) x Y ( t - .tau. Y , 1 ) { cos ( 2
.pi. ( f IF + f ^ D , 1 ) t + .theta. ^ 1 ) sin ( 2 .pi. ( f IF + f
D , 1 ) t + .theta. 1 ) - i sin ( 2 .pi. ( f IF + f ^ D , 1 ) t +
.theta. ^ 1 ) sin ( 2 .pi. ( f IF + f D , 1 ) t + .theta. 1 ) } (
11 ) ##EQU00003##
which can be written as
.intg. A 1 D ( t - .tau. C , 1 ) x C ( t - .tau. C , 1 ) { cos ( 2
.pi. ( 2 f IF + f D , 1 + f ^ D , 1 ) t + .theta. 1 + .theta. ^ 1 )
+ cos ( 2 .pi. ( f D , 1 - f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1
) - i sin ( 2 .pi. ( 2 f IF + f D , 1 + f ^ D , 1 ) t + .theta. 1 +
.theta. ^ 1 ) + i sin ( 2 .pi. ( f D , 1 - f ^ D , 1 ) t + .theta.
1 - .theta. ^ 1 ) } + .intg. B 1 D ( t - .tau. Y , 1 ) x Y ( t -
.tau. Y , 1 ) { sin ( 2 .pi. ( 2 f IF + f D , 1 + f ^ D , 1 ) t +
.theta. 1 + .theta. ^ 1 ) + sin ( 2 .pi. ( f D , 1 - f ^ D , 1 ) t
+ .theta. 1 - .theta. ^ 1 ) + i cos ( 2 .pi. ( 2 f IF + f D , 1 + f
^ D , 1 ) t + .theta. 1 + .theta. ^ 1 ) - i cos ( 2 .pi. ( f D , 1
- f ^ D , 1 ) t + .theta. 1 - .theta. ^ 1 ) } . ( 12 )
##EQU00004##
[0018] In accord with one implementation of the principles
disclosed herein, unit 100 knows its own global position and it
also knows the global position of a particular remote unit 200.
[0019] Illustratively, unit 100 is situated on the roof of a
corporate headquarters building in one city, and unit 200 is
situated on the roof of a corporate building in another city. If
unit 100 does not know the location of unit 200, it may obtain it
from unit 200 and verify that the location is bona fide in the
manner disclosed in the parent application identified above. Armed
with this knowledge, unit 100 is able to send information to unit
200 by generating and processing a signal that is a close facsimile
of the signal that unit 100 knows is received by unit 200.
Specifically, unit 100 may modulate its signal with a time delay
(delay-based encoding), a frequency shift (frequency-based
encoding), or both, in order to effect secure information
transmittal to unit 200. To realize frequency-based encoding, unit
100 may proceed as follows: from readily available information,
unit 100 obtains a fairly good estimate of the Doppler frequency
shift, {circumflex over (f)}.sub.D,2, of the signal arriving at the
unit 200 location from a particular satellite (which is a fairly
good estimate), generates a reference signal with this frequency in
element 35, frequency shifts that signal by a chosen frequency
value, f.sub.datum in element 36, to obtain a frequency {tilde over
(f)}.sub.D,2 (i.e., {tilde over (f)}.sub.D,2={circumflex over
(f)}.sub.D,2+f.sub.datum), and thus creates the signal
cos[2.pi.(f.sub.IF+{tilde over (f)}.sub.D,2)(t)+{circumflex over
(.theta.)}.sub.2]-isin[2.pi.(f.sub.IF+{tilde over
(f)}.sub.D,2)(t)+{circumflex over (.theta.)}.sub.2] (13)
that is applied to element 37. To realize delay-based encoding,
unit 100 may proceed as follows: element 37 multiplies the signal
of equation (13) by the quadrature signal of equation (12), delays
it by .delta..sub.datum in element 38, and outputs the signal
s Q , 1 , 2 , .delta. = { A 1 D ( t - .tau. C , 1 - .delta. datum )
x C ( t - .tau. C , 1 - .delta. datum ) sin [ 2 .pi. ( f D , 1 - f
^ D , 1 ) ( t - .delta. datum ) + .theta. 1 - .theta. ^ 1 ] - B 1 D
( t - .tau. Y , 1 - .delta. datum ) x Y ( t - .tau. Y , 1 - .delta.
datum ) cos [ 2 .pi. ( f D , 1 - f ^ D , 1 ) ( t - .delta. datum )
+ .theta. 1 - .theta. ^ 1 ] } .times. 2 { cos [ 2 .pi. ( f IF + f ^
D , 2 ) ( t - .delta. datum ) + .theta. ^ 2 ] - i sin [ 2 .pi. ( f
IF + f ^ D , 2 ) ( t - .delta. datum ) + .theta. ^ 2 ] } ( 14 )
##EQU00005##
which can be expressed more compactly as
s Q , 1 , 2 , .delta. = { A 1 D ( t - .tau. C , 1 - .delta. datum )
x C ( t - .tau. C , 1 - .delta. datum ) sin ( .alpha. ) - B 1 D ( t
- .tau. Y , 1 - .delta. datum ) x Y ( t - .tau. Y , 1 - .delta.
datum ) cos ( .alpha. ) } .times. 2 { cos ( .beta. ) - i sin (
.beta. ) } where .alpha. = 2 .pi. ( f D , 1 - f ^ D , 1 ) ( t -
.delta. datum ) + .theta. 1 - .theta. ^ 1 and .beta. = 2 .pi. ( f
IF + f ~ D , 2 ) ( t - .delta. datum ) + .theta. ^ 2 . ( 15 )
##EQU00006##
[0020] It might be remembered that the analysis above focuses on
the signal of one satellite while recognizing that signals from a
number of satellites are concurrently processed, and it also should
be remembered that the signal of equation (13) that is created
within unit 100 pertains, relative to the Doppler shift and delay,
to a single satellite that is chosen by unit 100. Thus, it should
be realized that the equation (15) signal is really a sum of
signals of the form found within the brackets { } that are all
multiplied by the 2{cos(.beta.)-isin(.beta.)} term that is adjusted
to parameters for the one chosen satellite; to wit, the output
signal of unit 100, S.sub.100, is
s 100 = 2 { cos ( .beta. ) - i sin ( .beta. ) } n = 1 K { A 1 n D n
( t - .tau. C , 1 - .delta. datum ) x C n ( t - .tau. C , 1 -
.delta. datum ) sin ( .alpha. i ) - B 1 n D n ( t - .tau. Y , 1 -
.delta. datum ) x Y n ( t - .tau. Y , 1 - .delta. datum ) cos (
.alpha. i ) } where .alpha. i = 2 .pi. ( f D , 1 ( i ) - f ^ D , 1
) ( t - .delta. datum ) + .theta. 1 ( i ) - .theta. ^ 1 ( 15 a )
##EQU00007##
f.sub.D,1.sup.(i) is the Doppler of satellite i as measured at unit
100 .theta..sub.1.sup.(i) is the phase shift of the signal from
satellite i as measured at unit 100.
[0021] Unit 100 sends the signal of equation (15a) to unit 200,
which also receives its own GPS signal, s.sub.2. Within unit 200
signal s.sub.2 is downshifted to develop the signal
s.sub.2s.sub.mix,2=A.sub.2D(t-.tau..sub.C,2)x.sub.C(t-.tau..sub.C,2)cos[-
2.pi.(f.sub.IF+f.sub.D,2)t+.theta.'.sub.2]+B.sub.2D(t-.tau..sub.Y,2(x.sub.-
P(t-.tau..sub.Y,2)sin[2.pi.(f.sub.IF+f.sub.D,2)t+.theta.'.sub.2],
(16)
where .tau..sub.c,2, .tau..sub.c,2 and f.sub.D,2 are the delays and
Doppler frequency shift experienced by the signal that reaches unit
200. It is noted that in a conventional manner the Doppler
frequency f.sub.D,2 may be determined, for example by tracking in a
frequency-lock or phase-lock loop.
[0022] In accord with one embodiment of the principles disclosed
herein and depicted in FIG. 3, unit 200 receives a signal by means
of elements that correspond to elements 10, 12, 15, 18, 20 and 22
of FIG. 1, but which are not shown in FIG. 2 for sake of clarity,
and within the processor of unit 200 (which corresponds to
processor 40 of FIG. 1) performs what effectively is a
two-dimensional correlation between the signal received from the
satellites and the signal received from unit 100, by shifting the
signal received from the satellites (i.e., the signal of equation
(16)) by f.sup.* in element 53, delaying the shifted signal by
.delta..sup.* in element 54, multiplying the output of element 54
by the signal received from unit 100 (i.e., the signal of equation
(15) in element 55), integrating in element 56, and repeating the
process with different values of f.sup.* and .delta..sup.* to find
a peak, all under management of controller 57.
[0023] The frequency shifting and the time delaying of the equation
(16) signal yields
s.sub.2,.delta.=A.sub.2D(t-.tau..sub.C,2-.delta..sup.*)x.sub.C(t-.tau..s-
ub.C,2-.delta..sup.*)cos[2.pi.(f.sub.IF+{hacek over
(f)}.sub.D,2)(t-.delta..sup.*)+.theta..sub.2']+B.sub.2D(t-.tau..sub.Y,2-.-
delta..sup.*)x.sub.P(t-.tau..sub.Y,2-.delta..sup.*)sin[2.pi.(f.sub.IF+{hac-
ek over (f)}.sub.D,2)(t-.delta..sup.*)+.theta..sub.2'] (17)
where {hacek over (f)}.sub.D,2=f.sub.D,2+f.sup.*. Labeling
2.pi.(f.sub.IF+{hacek over
(f)}.sub.D,2)(t-.delta..sup.*)+.theta..sub.2' as .gamma. yields
s.sub.2,.delta.=A.sub.2D(t-.tau..sub.C,2-.delta..sup.*)x.sub.C(t-.tau..s-
ub.C,2-.delta..sup.*)cos(.gamma.)
+B.sub.2D(t-.tau..sub.Y,2-.delta..sup.*)x.sub.P(t-.tau..sub.Y,2-.delta..s-
up.*)sin(.gamma.) (18)
The multiplication of the equation (18) signal by the signal of
equation (15) yields
s Q , 1 , 2 , .delta. s 2 , .delta. * = { A 1 D ( t - .tau. C , 1 -
.delta. ) x C ( t - .tau. C , 1 - .delta. ) sin ( .alpha. ) - B 1 D
( t - .tau. Y , 1 - .delta. ) x P ( t - .tau. Y , 1 - .delta. ) cos
( .alpha. ) } .times. 2 { cos ( .beta. ) - i sin ( .beta. ) }
.times. { A 2 D ( t - .tau. C , 2 - .delta. * ) x C ( t - .tau. C ,
2 - .delta. * ) cos ( .gamma. ) + B 2 D ( t - .tau. Y , 2 - .delta.
* ) x P ( t - .tau. Y , 2 - .delta. * ) sin ( .gamma. ) } . ( 19 )
##EQU00008##
Carrying out the multiplication, grouping terms, and dropping the
terms involving cos(.gamma.+.beta.) and sin(.gamma.+.beta.) because
subsequent integration acts as low pass filtering, yields
s Q , 1 , 2 , .delta. s 2 , .delta. * = ( U - V ) .times. ( W + iX
+ Y - iZ ) = { UW + iUX + UY - iUZ - VW - iVX - VY + iVZ } where (
20 ) U = A 1 D ( t - .tau. C , 1 - .delta. ) x C ( t - .tau. C , 1
- .delta. ) sin ( .alpha. ) ( 21 ) V = B 1 D ( t - .tau. Y , 1 -
.delta. ) x Y ( t - .tau. Y , 1 - .delta. ) cos ( .alpha. ) ( 22 )
W = A 2 D ( t - .tau. C , 2 - .delta. * ) x C ( t - .tau. C , 2 -
.delta. * ) cos ( .gamma. - .beta. ) ( 23 ) X = A 2 D ( t - .tau. C
, 2 - .delta. * ) x C ( t - .tau. C , 2 - .delta. * ) sin ( .gamma.
- .beta. ) ( 24 ) Y = B 2 D ( t - .tau. Y , 2 - .delta. * ) x Y ( t
- .tau. Y , 2 - .delta. * ) sin ( .gamma. - .beta. ) ( 25 ) Z = B 2
D ( t - .tau. Y , 2 - .delta. * ) x Y ( t - .tau. Y , 2 - .delta. *
) cos ( .gamma. - .beta. ) ( 26 ) ##EQU00009##
[0024] The signal of equation (19) is integrated for various values
of the delay .delta..sup.* and frequency offset f.sup.* to
develop
S .delta. , .delta. * = .intg. s Q , 1 , 2 , .delta. s 2 , .delta.
* = .intg. { UW + iUX + UY - iUZ - VW - iVX - VY + iVZ } . ( 27 )
##EQU00010##
[0025] At this point it may be noted that although the signal of
equation (18) shows the signal of one satellite, unit 200 actually
develops a signal that includes a contribution from all visible
satellites. It can be shown that each of the integration results
therefore may result in a plurality of peaks, but the one that
pertains to the chosen satellite is the peak with highest energy.
The energy of this peak, relative to the peaks for the other
satellites commonly visible to units 100 and 200, may be further
enhanced through signal processing; for example, with a directional
antenna or a beamsteering antenna array focused to enhance the
signal of the satellite of interest.
[0026] The Doppler frequency estimate {circumflex over (f)}.sub.D,1
is very close to f.sub.D,1, and the expression .theta..sub.1 is
very close to {circumflex over (.theta.)}.sub.1 (as a result of the
capture and tracking operations). Consequently, all terms
containing the factor "U" (which includes
sin(.alpha.).apprxeq..alpha..apprxeq.0) drop out. Also, the
cos(.alpha.) can be replaced by 1. Likewise, it is noted that the
code sequence x.sub.C is orthogonal to the code sequence x.sub.Y
(meaning that following integration the sum of their product is
zero). Consequently, the "VW" and "VX" terms drop out.
Additionally, the "V" term, which contains the cos(.alpha.) reduces
to V=B.sub.1 D(t-.tau..sub.Y,1-.delta.) x.sub.Y
(t-.tau..sub.Y,1-.delta.), leaving
S.sub..delta.,.delta..sub.*=.intg.{-VY+iVZ}=-.intg.VY+i.intg.VZ.
(28)
[0027] As indicated above, the expression of equation (27) is
evaluated for different values of .delta..sup.* and f.sup.*
(effectively a two-dimensional correlation), and values
.delta..sub.best.sup.* and f.sub.best.sup.* are found that yield
the maximum magnitude; i.e.,
S .delta. , .delta. * | max 2 = max ( ( .intg. .PSI. ( t , .delta.
* ) cos ( .alpha. ) sin ( .gamma. - .beta. ) ) 2 + ( .intg. .PSI. (
t , .delta. * ) cos ( .alpha. ) cos ( .gamma. - .beta. ) ) 2 )
where .PSI. ( t , .delta. * ) = ( B 1 D ( t - .tau. Y , 1 - .delta.
) ) ( B 2 D ( t - .tau. Y , 2 - .delta. * ) ) x Y ( t - .tau. Y , 1
- .delta. ) x Y ( t - .tau. Y , 2 - .delta. * ) . ( 29 )
##EQU00011##
[0028] When the approximations are good; that is,
f.sub.D,1.apprxeq.{circumflex over (f)}.sub.D,1 and
.theta..sub.1.apprxeq.{circumflex over (.theta.)}.sub.1 then
cos(.alpha.).apprxeq.1, and reinstating what .gamma. and .beta.
stand for, and looking only within the brackets, we have
( ( .intg. .PSI. ( t , .delta. * ) x Y ( t - .tau. Y , 1 - .delta.
) x Y ( t - .tau. Y , 2 - .delta. * ) sin ( 2 .pi. ( f D , 2 - f D
, 2 ) t + .GAMMA. ) ) 2 + ( .intg. .PSI. ( t , .delta. * ) x Y ( t
- .tau. Y , 1 - .delta. ) x Y ( t - .tau. Y , 2 - .delta. * ) cos (
2 .pi. ( f D , 2 - f D , 2 ) t + .GAMMA. ) ) 2 ) where ( 30 )
.GAMMA. = 2 .pi. [ ( f IF + f ~ D , 2 ) .delta. - ( f IF + f D , 2
) .delta. * ] + .theta. 2 ' - .theta. ^ 2 . ( 31 ) ##EQU00012##
[0029] Under the assumption that the code and the data take on
value of only +1 or -1, and because the autocorrelation of
x.sub.Y(t) is close to zero at all but t=0, it follows that
equation (29) is essentially 0 except when
(-.tau..sub.Y,1-.delta.)=(-.tau..sub.Y,2-.delta..sup.*), or
.delta.=.delta..sub.best.sup.*-.tau..sub.Y,1+.tau..sub.Y,2.
(32)
at which point it degenerates to
S .delta. , .delta. * | max = ( B 1 B 2 ) 2 [ ( .intg. sin ( 2 .pi.
( f D , 2 - f ~ D , 2 ) t + .GAMMA. ) ) 2 + ( .intg. cos ( 2 .pi. (
f D , 2 - f ~ D , 2 ) t + .GAMMA. ) ) 2 ] = ( B 1 B 2 ) 2 [ (
.intg. sin ( 2 .pi. ( .DELTA. f ) t + .GAMMA. ) ) 2 + ( .intg. cos
( 2 .pi. ( .DELTA. f ) t + .GAMMA. ) ) 2 ] ( 33 ) ##EQU00013##
where .DELTA.f={hacek over (f)}.sub.D,2-{tilde over (f)}.sub.D,2
which leads to
.DELTA.f=(f.sub.D,2-{circumflex over
(f)}.sub.D,2)+(f.sub.best.sup.*-f.sub.secret) (34)
[0030] The peak in the value of
S.sub..delta.,.delta..sub.*|.sub.max occurs when .DELTA.f is very
small. Since the estimate {circumflex over (f)}.sub.D,2 is very
close to f.sub.D,2, equation (34) degenerates to
f.sub.secret=f.sup.*, and that equation (33) reduces to:
S.sub..delta.,.delta..sub.*|.sub.max=(B.sub.1B.sub.2).sup.2.
(35)
[0031] What we have, then, is that when the transit delay and
Doppler frequency shift information derived from published tables,
geometric considerations, etc. are accurate, the autocorrelation
has a peak only when
[0032] (a) equation (32) condition holds; i.e.,
.delta..sub.datum=.delta..sup.*-.tau..sub.Y,1+.tau..sub.Y,2,
and
[0033] (b) equation (34) condition holds; i.e.,
f.sub.datum=f.sup.*.
[0034] Since unit 200 can compute the transit delay difference
(.tau..sub.Y,2-.tau..sub.Y,1) using, for example, published tables
describing the satellite orbits, the .delta..sub.datum information
injected into the signal by unit 100 is easily recovered at unit
200 (equation 32). Conversely, when unit 100 wishes unit 200 to
recover a particular value .delta..sup.*, unit 100 accounts for the
transit delay difference and computes the .delta..sub.datum that it
needs to send. Also, when .delta..sub.datum=0, equation (32) yields
a value that corresponds to (.tau..sub.Y,1-.tau..sub.Y,2), and from
the above-mentioned tables, unit 200 can determine the location of
unit 100.
[0035] The same capability exists in connection with the
frequencies, in that information can be communicated from unit 100
to unit 200 via the f.sub.datum value.
[0036] Going back to equation (12), it is noted that it includes a
signal component that is modulated by the x.sub.C code, which is
publicly known. The chip rate of the x.sub.C code has a bandwidth
of about 2 MHz. (2 MHz main lobe).
[0037] Based on this observation, an alternative embodiment in
accord with the principles disclosed herein passes the signal of
equation (12) through a bandstop filter that is adjusted to remove
the publicly known x.sub.C code-modulated component (alternatively
one can pass the signal of equations (13) or (14) through the
bandstop filter). Passing the signal though the such a filter
alters the equation (15) signal to
s.sub.Q,1,2,.delta.=-2[B.sub.1D(t-.tau..sub.Y,1-.delta.)x.sub.Y(t-.tau..-
sub.Y,1-.delta.)cos(.alpha.)][cos(.beta.)-isin(.beta.)] (36)
but that does NOT change equation (28). The difference, of course,
is that the embodiment that includes the bandstop filter does not
send a signal that includes a knowable signal component that
perhaps might be used by an adversary, and yet accomplishes the
same result as an embodiment that does not use the bandstop
filter.
[0038] In yet another embodiment in accord with the principles
disclosed herein, the signal that is processed by unit 100 and sent
to unit 200 can be the signal of just a selected subset of the
visible satellites; perhaps just one of the satellites.
Illustratively, this is accomplished by having the input antenna of
unit 100 be steerable, though other more complicated techniques
that would work as well. Any of the known designs or techniques for
creating a steerable antenna is acceptable. There are also other
techniques that may be used which work as well. This method reduces
the number of peaks that are achievable at an adversary unit, as
well as at unit 200, and further it obscures the satellite signal
which was used for the delay-based and/or frequency-based encoding,
making reverse-engineering of the values of .delta..sub.datum
and/or f.sub.datum substantially harder (or impracticable) for an
adversary.
[0039] The above embodiments do not specify the duration of the
signal that unit 100 sends to unit 200. A short duration results in
a smaller correlation peak. A smaller peak is more difficult to
detect in the presence of peaks that result from spurious signals
(noise). It is, therefore, useful to limit the duration of the
signal that unit 100 sends.
[0040] The above discloses the notion that two pieces of
information can be send by unit 100 to unit 200, in a secure
manner, with each transmission of a signal segment: one embedded in
.delta..sub.datum and the other embedded in f.sub.datum. Data can
be communicated continuously, of course, by sending
{.delta..sub.datum, f.sub.datum}-tuples in successive frames.
[0041] It may be noted that although the above discloses the
principles of this invention in connection with GPS signals, that
is not a limitation of this invention. Alternate sources that can
create signal like the Y code include device that operate in a WiFi
protocol, Blue tooth protocol, cellular telephony protocols,
etc.
[0042] It may be further noted that the illustrative embodiment
disclosed above is adapted to a situation where the location of
unit 100 is known to unit 200.
* * * * *