CN107064903B - GLRT-based target detection method under multiple heterogeneous satellites - Google Patents

GLRT-based target detection method under multiple heterogeneous satellites Download PDF

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CN107064903B
CN107064903B CN201710354363.9A CN201710354363A CN107064903B CN 107064903 B CN107064903 B CN 107064903B CN 201710354363 A CN201710354363 A CN 201710354363A CN 107064903 B CN107064903 B CN 107064903B
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刘明骞
李兵兵
高修会
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Guilin Changhai Development Co ltd
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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Abstract

The invention belongs to the technical field of target detection and signal processing, and discloses a target detection method based on GLRT (global likelihood ratio real-time tracking) under a plurality of heterogeneous satellites, which comprises the following steps: modeling the received signals of the reference channel and the monitoring channel, separating the reference channel signals, and substituting the reference channel signals into the monitoring channel signals; establishing a binary hypothesis according to the received signals of the monitoring channel, and giving probability density functions of the signals under the two hypotheses; estimating the maximum likelihood estimation of the unknown parameters under two assumptions by using a maximum likelihood estimation method according to the two probability density functions; obtaining detection statistics based on the generalized likelihood ratio according to the maximum likelihood estimation of the unknown parameters to obtain a detector; and obtaining the optimal detection threshold of the detector according to the probability distribution of the detection statistics, and judging to detect the target. The invention can effectively realize the detection of the moving target under a plurality of heterogeneous satellite radiation sources.

Description

GLRT-based target detection method under multiple heterogeneous satellites
Technical Field
The invention belongs to the technical field of target detection and signal processing, and particularly relates to a target detection method based on GLRT (global likelihood ratio real-time tracking) under a plurality of heterogeneous satellites.
Background
Aiming at the problem that a traditional time-frequency two-dimensional coherent detection method is sensitive to reference channel noise, the existing method achieves the purpose of weak echo detection through a detection method based on a generalized likelihood ratio, however, the detection method is subjected to modeling analysis in a single radiation source scene and is not suitable for target detection in a plurality of satellite radiation source scenes in an actual environment. D.e. hack, l.k.pattern, b.himed et al have derived a generalized likelihood ratio detector for passive multi-base sounding with known noise variance by modeling the received signal as a deterministic signal but with unknown signal parameters, but the noise variance in the actual scene is generally unknown and does not match the actual scene. (D.E.Hack, L.K.Patton, B.Himed, and M.A.Saville, "On the application availability of source localization techniques to passive multistandard," in Proceedings of46 analytical Conference On Signals, Systems and units, Pacific Grove, CA, USA, November2012, pp.848-852). The general likelihood ratio detector of the reference signal of the reference channel polluted by noise is deduced by Cui G, Liu J, Li H and the like, but the applicable scene is a single radiation source, and the detection reliability is low. (Cui G, Liu J, Li H, et al. target detection for passive radiation with noise reference channel [ C ]. IEEE Radar reference. IEEE,2014: 0144-0148). A.zaimbashi, m.derakhian et al derived the expression of the detection statistics based on the generalized likelihood ratio, and also derived the false alarm probability and the detection probability, but the applicable scene is a single external radiation source, and is not applicable to target detection under multiple radiation sources. (A.Zaimmbashi, M.Derakhtian, and A.Sheikhi, "GLRT-based CFAR detection in passive biostatic radar," IEEE trans.Aerosp.Electron.Syst., vol.49, No.1, pp.134-159, Jan.2013). Liu J, Li H, Himed B et al derive expressions for generalized likelihood ratio detection when the monitoring channel has multiple receivers, and give expressions for detection probability and false alarm probability, but do not take into account the effect of the interfering target on the true target. (Liu J, Li H, high B.two Target Detection Algorithms for Passionmulti static Radar [ J ]. IEEE Transactions on Signal Processing,2014,62(22): 5930-.
In summary, the problems of the prior art are as follows: the traditional time-frequency two-dimensional coherent detection method is different from the actual scene, has low detection reliability and is not suitable for target detection under a plurality of radiation sources.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a target detection method based on GLRT under a plurality of heterogeneous satellites.
The invention is realized in such a way that a target detection method based on GLRT under a plurality of heterogeneous satellites comprises the following steps: modeling the received signals of the reference channel and the monitoring channel, separating the reference channel signals, and substituting the reference channel signals into the monitoring channel signals; establishing a binary hypothesis according to the received signals of the monitoring channel, and giving probability density functions of the signals under the two hypotheses; estimating the maximum likelihood estimation of the unknown parameters under two assumptions by using a maximum likelihood estimation method according to the two probability density functions; obtaining detection statistics based on the generalized likelihood ratio according to the maximum likelihood estimation of the unknown parameters to obtain a detector; and obtaining the optimal detection threshold of the detector according to the probability distribution of the detection statistics, and judging to detect the target.
Further, the method for detecting the target based on the GLRT under the plurality of heterogeneous satellites comprises the following steps:
separating a plurality of direct wave signals of a reference channel and using the signals as local reference signals;
secondly, establishing a binary hypothesis model and probability density functions of the signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
step three, estimating the unknown parameters α when the noise variance is known under two assumptions by using a maximum likelihood estimation methodη，cη,kUnknown parameters α when the noise variance is unknownη，cη,k，σ2And unknown parameters α when the noise variance is unknown and an interfering target is presentη，
Figure GDA0002442694730000021
cη,k，σ2；
Step four, constructing detection statistics based on the generalized likelihood ratio under three conditions;
and step five, setting detection thresholds under three conditions, and comparing and judging with the detection statistics under the three conditions to detect the target.
Further, the signal of the step one channel is expressed as:
Figure GDA0002442694730000031
where N is 0,1, … N-1, M represents the number of satellites, P is the number of multipath paths under a single satellite signal, Nη,Ωη,αηTime delay, doppler shift, and amplitude of the echo signal, respectively, and when k is 1, c isη,kIs the amplitude of the direct wave signal, and when k is 2,3, …, P,
Figure GDA0002442694730000032
cη,kis the Doppler shift, time delay, amplitude of the multipath signal, K represents the number of the interference targets,
Figure GDA0002442694730000033
respectively representing the Doppler shift, delay, amplitude, n of the interfering echo signals(t) is white Gaussian noise.
Further, in the second step:
the binary hypothesis model is represented as:
Figure GDA0002442694730000034
Figure GDA0002442694730000035
H0x [ n ] of]The probability density function of (a) is:
Figure GDA0002442694730000036
H1x [ n ] of]The probability density function of (a) is:
Figure GDA0002442694730000037
further, the unknown parameter α when the noise variance is known in the third stepη，cη,kThe maximum likelihood estimate of (c) is as follows:
H0the maximum likelihood estimate of the unknown parameters of:
Figure GDA0002442694730000041
wherein
Figure GDA0002442694730000042
Figure GDA0002442694730000043
It shows the assumption H0Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimated value of the amplitude of the direct wave signal corresponding to the satellite;
Rcrepresenting the correlation of multipath signals, RcIs a matrix of P, [ Rc]skIs RcIs represented as:
Figure GDA0002442694730000044
rxcrepresenting received signals and direct waves in the monitoring channel and multipath signals in
Figure GDA0002442694730000045
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure GDA0002442694730000046
H1the maximum likelihood estimate of the unknown parameters of:
Figure GDA0002442694730000047
wherein
Figure GDA0002442694730000048
Figure GDA0002442694730000049
It shows the assumption H1Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimate of the amplitude of the direct wave signal corresponding to the satellite,
Figure GDA00024426947300000410
Figure GDA00024426947300000411
indicating the Mth echo signal amplitude αMIs estimated.
Figure GDA00024426947300000412
rssShowing the autocorrelation between echoes, [ r ]ss]Is a matrix of M, [ r [ ]ss]rηIs represented by rssIs represented as:
Figure GDA0002442694730000051
rscrepresenting the correlation of multipath and echo, [ r ]sc]Is a matrix of M, [ r [ ]sc]qηIs represented by rscIs represented as:
Figure GDA0002442694730000052
rxseach target echo signal representing a received signal of the monitor channel is represented by (n)r,Ωr) Cross correlation of [ r ]xs]Is a vector of M1, [ rxs]rIs represented by rxsIs represented as:
Figure GDA0002442694730000053
unknown parameters α when noise variance is unknownη，cη,k，σ2The maximum likelihood estimate of (c) is as follows:
αη，cη,kwith unknown parameters α when the noise variance is knownη，cη,kThe maximum likelihood estimates of (a) are consistent;
suppose H1Lower, variance of noise
Figure GDA0002442694730000054
Maximum likelihood estimation of
Figure GDA0002442694730000055
Comprises the following steps:
Figure GDA0002442694730000056
H0variance of noise
Figure GDA0002442694730000057
Maximum likelihood estimation of
Figure GDA0002442694730000058
Comprises the following steps:
Figure GDA0002442694730000059
unknown parameters α when noise variance is unknown and an interfering target is presentη，
Figure GDA00024426947300000510
cη,k，σ2The maximum likelihood estimate of (c) is as follows:
maximum likelihood estimation of unknown parameters is similar in principle to the previous method, assuming H0The following unknown parameters are as follows:
Figure GDA00024426947300000511
suppose H1The following unknown parameters are as follows:
Figure GDA0002442694730000061
wherein the content of the first and second substances,
Figure GDA0002442694730000062
Figure GDA0002442694730000063
Figure GDA0002442694730000064
presentation assumption HiUnknown parameter of
Figure GDA0002442694730000065
Is estimated by the estimation of (a) a,
Figure GDA0002442694730000066
Figure GDA0002442694730000067
it shows the assumption HiThe estimated value of the amplitude of the next b interference echo;
rtsrepresenting interfering target echo signals at
Figure GDA0002442694730000068
And the echo to be detected is at (n)η,Ωη) Correlation of [ r ]ts]Is a vector of M x K, [ rts]mrIs represented by rtsIs represented as:
Figure GDA0002442694730000069
Rtcindicating that the interfering target echo is at (n)η,Ωη) And a multipath signal in (n)q,s,Ωq,s) Correlation between [ R ]tc]Is a vector of K P, [ Rtc]smIs RtcIs represented as:
Figure GDA00024426947300000610
rxtrepresenting received signals and interfering target echo signals at
Figure GDA00024426947300000611
Correlation of [ r ]xt]Is a vector of K1, [ rxt]fIs rxtIs represented as:
Figure GDA00024426947300000612
Rttphase representing echoes of an interfering targetOff, [ R ]tt]Is a vector of K by K, [ R ]tt]fmIs RttThe elements of (a) are:
Figure GDA00024426947300000613
the maximum likelihood estimates of the noise variance under the two assumptions are:
Figure GDA0002442694730000071
further, in the fourth step, the detection statistics based on the generalized likelihood ratio under the three conditions are constructed as follows: detection statistic when noise variance is known:
Figure GDA0002442694730000072
detection statistic when noise variance is unknown:
Figure GDA0002442694730000073
wherein ξ', ηKWhich are the detection thresholds for the three cases, respectively.
Further, in the fifth step:
the decision threshold ψ of the detector when the noise variance is known is:
Figure GDA0002442694730000074
the detector decision threshold when the noise variance is unknown ψ is:
Figure GDA0002442694730000075
the decision threshold ψ of the detector when the noise variance is unknown and an interference target is present is:
Figure GDA0002442694730000081
wherein the content of the first and second substances,
Figure GDA0002442694730000082
is distributed in the central chi-square
Figure GDA0002442694730000083
Probability of right tail, PfaIs the false alarm probability.
The invention has the advantages and positive effects that: the parameter data is subjected to 2000 Monte Carlo experimental simulations to obtain the detection performance shown in FIG. 2, which proves that the invention can effectively realize the detection of the moving target under a plurality of heterogeneous satellite radiation sources.
Drawings
Fig. 1 is a flowchart of a target detection method based on GLRT under multiple heterogeneous satellites according to an embodiment of the present invention.
Fig. 2 is a comparison diagram of target detection performance under different conditions according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, a method for detecting a target based on GLRT under multiple heterogeneous satellites according to an embodiment of the present invention includes the following steps:
s101: modeling the received signals of the reference channel and the monitoring channel, separating the reference channel signals, and substituting the reference channel signals into the monitoring channel signals;
s102: establishing a binary hypothesis according to the received signals of the monitoring channel, and giving probability density functions of the signals under the two hypotheses;
s103: estimating the maximum likelihood estimation of the unknown parameters under two assumptions by using a maximum likelihood estimation method according to the two probability density functions;
s104: obtaining detection statistics based on the generalized likelihood ratio according to the maximum likelihood estimation of the unknown parameters to obtain a detector;
s105: and obtaining the optimal detection threshold of the detector according to the probability distribution of the detection statistics, and judging to detect the target.
The target detection method based on GLRT under a plurality of heterogeneous satellites provided by the embodiment of the invention specifically comprises the following steps:
separating a plurality of direct wave signals of a reference channel and using the signals as local reference signals;
secondly, establishing a binary hypothesis model and probability density functions of the signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
step three, estimating the unknown parameters α when the noise variance is known under two assumptions by using a maximum likelihood estimation methodη，cη,kUnknown parameters α when the noise variance is unknownη，cη,k，σ2And unknown parameters α when the noise variance is unknown and an interfering target is presentη，
Figure GDA0002442694730000091
cη,k，σ2；
Step four, constructing detection statistics based on the generalized likelihood ratio under three conditions;
and step five, setting detection thresholds under three conditions, and comparing and judging with the detection statistics under the three conditions, thereby detecting the target.
In the first step, a plurality of direct wave signals of a reference channel are separated and used as local reference signals to be processed according to the following steps:
the expression for the reference channel signal z (t) is:
Figure GDA0002442694730000092
wherein lηIs the amplitude, n, of the direct wave signal of the reference channelr(t) is the noise of the reference channel, and M is the number of satellite radiation sources.
Because the reference channel receives direct wave signals of a plurality of different satellites, the direct wave signals are different in frequency, a band-pass filter can be designed to separate the direct wave signals, and after the direct wave signals are separated by the band-pass filter, the signals in the reference channel can be expressed as follows:
yη(t)＝bηsη(t)+nη(t)0≤t＜T η＝1,2…M；
wherein, bηIs the amplitude, n, of the direct wave signal of the reference channelη(t) is the noise in the single direct wave signal after separation.
The signal of the monitoring channel is represented as:
Figure GDA0002442694730000101
where N is 0,1, … N-1, M represents the number of satellites, P is the number of multipath paths under a single satellite signal, Nη,Ωη,αηTime delay, doppler shift, and amplitude of the echo signal, respectively, and when k is 1, c isη,kIs the amplitude of the direct wave signal, and when k is 2,3, …, P,
Figure GDA0002442694730000102
cη,kis the Doppler shift, time delay, amplitude of the multipath signal, K represents the number of the interference targets,
Figure GDA0002442694730000103
respectively representing the Doppler shift, delay, amplitude, n of the interfering echo signals(t) is white Gaussian noise.
In the second step, a binary hypothesis model is established according to the local reference signal and the signal of the monitoring channel, and the probability density function of the signal under two hypotheses is carried out as follows:
the binary hypothesis model is represented as:
Figure GDA0002442694730000104
Figure GDA0002442694730000105
suppose H0X [ n ] of]The probability density function of (a) is:
Figure GDA0002442694730000106
suppose H1X [ n ] of]The probability density function of (a) is:
Figure GDA0002442694730000111
in step three, the maximum likelihood estimation method is used to estimate the unknown parameters α under two assumptions when the noise variance is knownη，cη,kUnknown parameters α when the noise variance is unknownη，cη,k，σ2And unknown parameters α when the noise variance is unknown and an interfering target is presentη，
Figure GDA0002442694730000112
cη,k，σ2The method comprises the following steps:
number of unknown parameters α when the variance of the noise is knownη，cη,kThe maximum likelihood estimate of (c) is as follows:
H0the maximum likelihood estimate of the unknown parameters of:
Figure GDA0002442694730000113
wherein
Figure GDA0002442694730000114
Figure GDA0002442694730000115
It shows the assumption H0Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimate of the amplitude of the direct wave signal corresponding to the satellite.
RcRepresenting the correlation of multipath signals, RcIs a matrix of P, [ Rc]skIs RcIs represented as:
Figure GDA0002442694730000116
rxcrepresenting received signals and direct waves in the monitoring channel and multipath signals in
Figure GDA0002442694730000117
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure GDA0002442694730000118
H1the maximum likelihood estimate of the unknown parameters of:
Figure GDA0002442694730000119
wherein
Figure GDA0002442694730000121
Figure GDA0002442694730000122
It shows the assumption H1Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimate of the amplitude of the direct wave signal corresponding to the satellite,
Figure GDA0002442694730000123
Figure GDA0002442694730000124
indicating the Mth echo signal amplitude αMIs estimatedAnd (6) counting.
Figure GDA0002442694730000125
rssShowing the autocorrelation between echoes, [ r ]ss]Is a matrix of M, [ r [ ]ss]rηIs represented by rssIs represented as:
Figure GDA0002442694730000126
rscrepresenting the correlation of multipath and echo, [ r ]sc]Is a matrix of M, [ r [ ]sc]qηIs represented by rscIs represented as:
Figure GDA0002442694730000127
rxseach target echo signal representing a received signal of the monitor channel is represented by (n)r,Ωr) Cross correlation of [ r ]xs]Is a vector of M1, [ rxs]rIs represented by rxsIs represented as:
Figure GDA0002442694730000128
unknown parameters α when noise variance is unknownη，cη,k，σ2The maximum likelihood estimate of (c) is as follows:
αη，cη,kwith unknown parameters α when the noise variance is knownη，cη,kThe maximum likelihood estimates of (a) are consistent.
Suppose H1Lower, variance of noise
Figure GDA0002442694730000129
Maximum likelihood estimation of
Figure GDA00024426947300001210
Comprises the following steps:
Figure GDA0002442694730000131
H0variance of noise
Figure GDA0002442694730000132
Maximum likelihood estimation of
Figure GDA0002442694730000133
Comprises the following steps:
Figure GDA0002442694730000134
unknown parameters α when noise variance is unknown and an interfering target is presentη，
Figure GDA0002442694730000135
cη,k，σ2The maximum likelihood estimate of (c) is as follows:
maximum likelihood estimation of unknown parameters is similar in principle to the previous method, assuming H0The following unknown parameters are as follows:
Figure GDA0002442694730000136
suppose H1The following unknown parameters are as follows:
Figure GDA0002442694730000137
wherein the content of the first and second substances,
Figure GDA0002442694730000138
Figure GDA0002442694730000139
Figure GDA00024426947300001310
presentation assumption HiUnknown parameter of
Figure GDA00024426947300001311
Is estimated by the estimation of (a) a,
Figure GDA00024426947300001312
Figure GDA00024426947300001313
it shows the assumption HiThe estimate of the amplitude of the lower b-th disturbing echo.
rtsRepresenting interfering target echo signals at
Figure GDA00024426947300001314
And the echo to be detected is at (n)η,Ωη) Correlation of [ r ]ts]Is a vector of M x K, [ rts]mrIs represented by rtsIs represented as:
Figure GDA00024426947300001315
Rtcindicating that the interfering target echo is at (n)η,Ωη) And a multipath signal in (n)q,s,Ωq,s) Correlation between [ R ]tc]Is a vector of K P, [ Rtc]smIs RtcIs represented as:
Figure GDA0002442694730000141
rxtrepresenting received signals and interfering target echo signals at
Figure GDA0002442694730000142
Correlation of [ r ]xt]Is a vector of K1, [ rxt]fIs rxtIs represented as:
Figure GDA0002442694730000143
Rttrepresenting the correlation of interfering target echoes, [ R ]tt]Is a vector of K by K, [ R ]tt]fmIs RttThe elements of (a) are:
Figure GDA0002442694730000144
the maximum likelihood estimates of the noise variance under the two assumptions are:
Figure GDA0002442694730000145
Figure GDA0002442694730000146
in the fourth step, the detection statistics based on the generalized likelihood ratio is constructed under three conditions as follows:
detection statistic when noise variance is known:
Figure GDA0002442694730000147
detection statistic when noise variance is unknown:
Figure GDA0002442694730000148
wherein ξ', ηKWhich are the detection thresholds for the three cases, respectively.
In the fifth step, the detection thresholds under the three conditions are set and compared with the detection statistics under the three conditions for judgment, so that the target detection is carried out according to the following steps: the decision threshold ψ of the detector when the noise variance is known is:
Figure GDA0002442694730000151
the detector decision threshold when the noise variance is unknown ψ is:
Figure GDA0002442694730000152
the decision threshold ψ of the detector when the noise variance is unknown and an interference target is present is:
Figure GDA0002442694730000153
wherein the content of the first and second substances,
Figure GDA0002442694730000154
is distributed in the central chi-square
Figure GDA0002442694730000155
Probability of right tail, PfaIs the false alarm probability.
The application effect of the present invention will be described in detail with reference to the simulation.
Simulation experiment: and performing simulation verification on the echo detection performance based on the generalized likelihood ratio under the three conditions, and performing simulation experiments by using three satellite signals including GPS, DVB-S and inmarsat. The carrier frequencies of the three signals are respectively: f. ofG＝1.57GHz,fD＝12.38GHz,fiAssuming that the time delays of three echo signals are 1 μ s,2 μ s and 3 μ s respectively, the doppler shifts are 100Hz,150Hz and 200Hz respectively, and the intensities of three direct signal waves are: 130.1dBw-111.83 dBw-120.61 dBw, the difference between the power of the direct wave and the corresponding echo is 40dB, and the number of sampling points is 105And performing simulation by using matlab. The above parameter data was subjected to 2000 monte carlo experimental simulations to obtain the detection performance of fig. 2.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (5)

1. A target detection method based on GLRT under a plurality of heterogeneous satellites is characterized by comprising the following steps: modeling the received signals of the reference channel and the monitoring channel, separating the reference channel signals, and substituting the reference channel signals into the monitoring channel signals; establishing a binary hypothesis according to the received signals of the monitoring channel, and giving probability density functions of the signals under the two hypotheses; estimating the maximum likelihood estimation of the unknown parameters under two assumptions by using a maximum likelihood estimation method according to the two probability density functions; obtaining detection statistics based on the generalized likelihood ratio according to the maximum likelihood estimation of the unknown parameters to obtain a detector; obtaining the optimal detection threshold of the detector according to the probability distribution of the detection statistics, and judging to detect the target;
the target detection method based on GLRT under a plurality of heterogeneous satellites comprises the following steps:
separating a plurality of direct wave signals of a reference channel and using the signals as local reference signals;
secondly, establishing a binary hypothesis model and probability density functions of the signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
step three, estimating the unknown parameters α when the noise variance is known under two assumptions by using a maximum likelihood estimation methodη，cη,kUnknown parameters α when the noise variance is unknownη，cη,k，σ2And unknown parameters α when the noise variance is unknown and an interfering target is presentη，
Figure FDA0002442694720000011
cη,k，σ2；
Step four, constructing detection statistics based on the generalized likelihood ratio under three conditions;
and step five, setting detection thresholds under three conditions, and comparing and judging with the detection statistics under the three conditions to detect the target.
2. The method for GLRT-based target detection under multiple heterogeneous satellites as claimed in claim 1, wherein the step one channel signal is represented as:
Figure FDA0002442694720000012
where N is 0,1, … N-1, M represents the number of satellites, P is the number of multipath paths under a single satellite signal, Nη,Ωη,αηTime delay, doppler shift, and amplitude of the echo signal, respectively, and when k is 1, c isη,kIs the amplitude of the direct wave signal, and when k is 2,3, …, P,
Figure FDA0002442694720000021
cη,kis the Doppler shift, time delay, amplitude of the multipath signal, K represents the number of the interference targets,
Figure FDA0002442694720000022
respectively representing the Doppler shift, delay, amplitude, n of the interfering echo signals[n]Is gaussian white noise; y isηFor the received signal in the reference channel, ymIs an interfering target echo signal.
3. The method for GLRT-based target detection under multiple heterogeneous satellites as claimed in claim 1, wherein in the second step:
the binary hypothesis model is represented as:
Figure FDA0002442694720000023
Figure FDA0002442694720000024
H0x [ n ] of]The probability density function of (a) is:
Figure FDA0002442694720000025
H1x [ n ] of]The probability density function of (a) is:
Figure FDA0002442694720000026
yηfor the received signal in the reference channel, ymIs an interfering target echo signal.
4. The method for GLRT-based target detection under multiple heterogeneous satellites as claimed in claim 1, wherein the third step is the unknown parameter α when the variance of the noise is knownη，cη,kThe maximum likelihood estimate of (c) is as follows:
H0the maximum likelihood estimate of the unknown parameters of:
Figure FDA0002442694720000027
wherein
Figure FDA0002442694720000031
Figure FDA0002442694720000032
It shows the assumption H0Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimated value of the amplitude of the direct wave signal corresponding to the satellite;
Rcrepresenting the correlation of multipath signals, RcIs a matrix of P, [ Rc]skIs RcIs represented as:
Figure FDA0002442694720000033
rxcrepresenting received signals and direct waves in the monitoring channel and multipath signals in
Figure FDA0002442694720000034
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure FDA0002442694720000035
H1the maximum likelihood estimate of the unknown parameters of:
Figure FDA0002442694720000036
wherein
Figure FDA0002442694720000037
Figure FDA0002442694720000038
It shows the assumption H1Amplitude c of kth multipath of the lower η th satellite signalη,kWhere k is 1, is an estimate of the amplitude of the direct wave signal corresponding to the satellite,
Figure FDA0002442694720000039
Figure FDA00024426947200000310
indicating the Mth echo signal amplitude αM(ii) an estimate of (d);
Figure FDA00024426947200000311
rssshowing the autocorrelation between echoes, [ r ]ss]Is a matrix of M, [ r [ ]ss]rηIs represented by rssIs represented as:
Figure FDA00024426947200000312
rscrepresenting the correlation of multipath and echo, [ r ]sc]Is a matrix of M, [ r [ ]sc]qηIs represented by rscIs represented as:
Figure FDA0002442694720000041
rxspresentation monitoringEach target echo signal of the channel received signal is in (n)r,Ωr) Cross correlation of [ r ]xs]Is a vector of M1, [ rxs]rIs represented by rxsIs represented as:
Figure FDA0002442694720000042
unknown parameters α when noise variance is unknownη，cη,k，σ2The maximum likelihood estimate of (c) is as follows:
αη，cη,kwith unknown parameters α when the noise variance is knownη，cη,kThe maximum likelihood estimates of (a) are consistent;
suppose H1Lower, variance of noise
Figure FDA0002442694720000043
Maximum likelihood estimation of
Figure FDA0002442694720000044
Comprises the following steps:
Figure FDA0002442694720000045
H0variance of noise
Figure FDA0002442694720000046
Maximum likelihood estimation of
Figure FDA0002442694720000047
Comprises the following steps:
Figure FDA0002442694720000048
unknown parameters α when noise variance is unknown and an interfering target is presentη，
Figure FDA0002442694720000049
cη,k，σ2The maximum likelihood estimate of (c) is as follows:
maximum likelihood estimation of unknown parameters is similar in principle to the previous method, assuming H0The following unknown parameters are as follows:
Figure FDA00024426947200000410
suppose H1The following unknown parameters are as follows:
Figure FDA0002442694720000051
wherein the content of the first and second substances,
Figure FDA0002442694720000052
Figure FDA0002442694720000053
Figure FDA0002442694720000054
presentation assumption HiUnknown parameter of
Figure FDA0002442694720000055
Is estimated by the estimation of (a) a,
Figure FDA0002442694720000056
Figure FDA0002442694720000057
it shows the assumption HiThe estimated value of the amplitude of the next b interference echo;
rtsrepresenting interfering target echo signals at
Figure FDA0002442694720000058
And the echo to be detected is at (n)η,Ωη) Correlation of [ r ]ts]Is a vector of M x K, [ rts]mrIs represented by rtsIs represented as:
Figure FDA0002442694720000059
Rtcindicating that the interfering target echo is at (n)η,Ωη) And a multipath signal in (n)q,s,Ωq,s) Correlation between [ R ]tc]Is a vector of K P, [ Rtc]smIs RtcIs represented as:
Figure FDA00024426947200000510
rxtrepresenting received signals and interfering target echo signals at
Figure FDA00024426947200000511
Correlation of [ r ]xt]Is a vector of K1, [ rxt]fIs rxtIs represented as:
Figure FDA00024426947200000512
Rttrepresenting the correlation of interfering target echoes, [ R ]tt]Is a vector of K by K, [ R ]tt]fmIs RttThe elements of (a) are:
Figure FDA00024426947200000513
the maximum likelihood estimates of the noise variance under the two assumptions are:
Figure FDA0002442694720000061
Figure FDA0002442694720000062
wherein the content of the first and second substances,
Figure FDA0002442694720000063
in the case of a multi-path signal,
Figure FDA0002442694720000064
in order to be able to delay the time of the multi-path signal,
Figure FDA0002442694720000065
for the purpose of the other echo signals,
Figure FDA0002442694720000066
for Doppler shift of multipath signals, nrAnd ΩrRespectively the time delay and the doppler shift of the target echo signal,
Figure FDA0002442694720000067
presentation assumption HiDirect wave and multipath signal amplitude c of each satelliteiIs estimated.
5. The method for GLRT-based target detection under multiple heterogeneous satellites as claimed in claim 1, wherein the step five comprises:
the decision threshold ψ of the detector when the noise variance is known is:
Figure FDA0002442694720000068
the detector decision threshold when the noise variance is unknown ψ is:
Figure FDA0002442694720000069
the decision threshold ψ of the detector when the noise variance is unknown and an interference target is present is:
Figure FDA00024426947200000610
wherein the content of the first and second substances,
Figure FDA00024426947200000611
is distributed in the central chi-square
Figure FDA00024426947200000612
Probability of right tail, PfaIs the false alarm probability.
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