CN107271978B - Target detection method based on Rao detection under multiple heterogeneous satellites - Google Patents

Target detection method based on Rao detection under multiple heterogeneous satellites Download PDF

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CN107271978B
CN107271978B CN201710354357.3A CN201710354357A CN107271978B CN 107271978 B CN107271978 B CN 107271978B CN 201710354357 A CN201710354357 A CN 201710354357A CN 107271978 B CN107271978 B CN 107271978B
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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
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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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 Rao detection under a plurality of heterogeneous satellites, which comprises the following steps: separating direct wave signals of the reference channel and using the direct wave signals as local reference signals; establishing a binary hypothesis model and probability density functions of signals under two hypotheses according to the local reference signals and the signals of the monitoring channel; estimating hypothesis H in two cases by maximum likelihood estimation method0Unknown parameters of the following; constructing detection statistics based on Rao detection in two cases; and setting detection thresholds under two conditions, and comparing and judging the detection thresholds with the detection statistics under the two conditions so as to detect the target. The invention effectively realizes the detection of moving targets under a plurality of heterogeneous satellite radiation sources, and can be used for low-penetration target detection and air early warning; the parametric data were simulated in 2000 monte carlo experiments.

Description

Target detection method based on Rao detection 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 Rao detection under multiple heterogeneous satellites.
Background
Aiming at the problem that a traditional time-frequency two-dimensional coherent detection method is sensitive to noise of a reference channel, 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. Liu J, Liu W and Chen B provide a target detection algorithm based on Rao detection, and compared with generalized likelihood ratio detection, the algorithm only needs to estimate hypothesis H0The following unknown parameters are small in calculated amount and low in complexity, so that the method is relatively easy to implement, and the detection reliability is low when echo signals are detected under a single radiation source. (Liu J, Liu W, Chen B, et]IEEEtransactions on Signal Processing,2015,64(3): 1-1). Jun Liu, Bo Chen, Hong weiLiu derived Rao-based detectionAnd giving the false alarm probability and the expression of the detection probability to obtain the Rao detection with constant false alarm characteristic. But also under a single satellite external radiation source. (Jun Liu; Bo Chen; Hong Wei Liu; Wei jian Liu. "Performance analysis of a modified Rao test for adaptive subspace detection," 2016IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Pages: 2926-. Liu J, Li H, Himed et al derive expressions for generalized likelihood ratio detection when the monitored channel has multiple receivers, and give expressions for detection probability and false alarm probability, but the derivation under the conditions of no interfering echoes and known noise variance is inconsistent with the actual scenario. (Liu J, Li H, high B.two Target Detection Algorithms for Passive multistatic Radar [ J].IEEE Transactions on Signal Processing,2014, 62(22):5930-5939)
In summary, the problems of the prior art are as follows: the traditional time-frequency two-dimensional coherent detection method has the defects of low detection reliability, derivation under the conditions of no interference echo and known noise variance, and inconsistency with an actual scene.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a target detection method based on Rao detection under a plurality of heterogeneous satellites.
The invention is realized in such a way that a target detection method based on Rao detection under a plurality of heterogeneous satellites comprises the following steps: separating direct wave signals of the reference channel and using the direct wave signals as local reference signals; establishing a binary hypothesis model and probability density functions of signals under two hypotheses according to the local reference signals and the signals of the monitoring channel; estimating hypothesis H in two cases by maximum likelihood estimation method0Unknown parameters of the following; constructing detection statistics based on Rao detection in two cases; and setting detection thresholds under two conditions, and comparing and judging the detection thresholds with the detection statistics under the two conditions so as to detect the target.
Further, the target detection method based on Rao detection 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 signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
step three, estimating the hypothesis H by utilizing a maximum likelihood estimation method0Lower unknown parameter c when the noise variance is unknownη,k，σ2And unknown parameters when the noise variance is unknown and an interfering target is present
Figure BDA0001298708530000021
cη,k，σ2；
Constructing detection statistics based on Rao detection under two conditions;
and step five, setting detection thresholds under two conditions, and comparing and judging the detection thresholds with the detection statistics under the two conditions so as to detect the target.
Further, the signals of the channels in the first step are represented as:
Figure RE-GDA0001348944380000022
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,αηRespectively, the delay, doppler shift, and amplitude of the echo signal, and when k is 1, c isη,kIs the amplitude of the direct wave signal, and when k is 2,3, …, P,
Figure RE-GDA0001348944380000031
cη,kis the Doppler shift, time delay, amplitude of the multipath signal, K represents the number of the interference targets,
Figure RE-GDA0001348944380000032
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 BDA0001298708530000033
Figure BDA0001298708530000034
suppose H0X [ n ] of]The probability density function of (a) is:
Figure BDA0001298708530000035
suppose H1X [ n ] of]The probability density function of (a) is:
Figure RE-GDA0001348944380000036
further, the third step specifically includes:
H0unknown parameter c ofη,kThe maximum likelihood estimate of (c) is:
Figure BDA0001298708530000037
wherein
Figure BDA0001298708530000038
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 BDA0001298708530000041
representing received signals and direct waves in the monitoring channel and multipath signals in
Figure BDA0001298708530000042
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure BDA0001298708530000043
suppose H0Variance of noise
Figure BDA0001298708530000044
Maximum likelihood estimation of
Figure BDA0001298708530000045
Comprises the following steps:
Figure BDA0001298708530000046
hypothesis H when noise variance is unknown and interference targets are present0Unknown parameter of
Figure BDA0001298708530000047
The maximum likelihood estimate of (c) is as follows:
suppose H0The following unknown parameters are estimated as follows:
Figure BDA0001298708530000048
wherein the content of the first and second substances,
Figure BDA0001298708530000049
is that the amplitude of the b-th interfering echo is at the hypothesis H0Estimating; 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 BDA00012987085300000410
rxtrepresenting received signals and interfering target echo signals at
Figure BDA00012987085300000411
Correlation of rxtIs a vector of K1, [ rxt]Is rxtIs represented as:
Figure BDA0001298708530000051
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 BDA0001298708530000052
suppose H0The maximum likelihood estimates of the noise variance are:
Figure BDA0001298708530000053
where x is the hypothesis H0Signal of rssShowing the autocorrelation between echoes, [ r ]ss]Is M*Matrix of M, [ r ]ss]rηIs represented by rssIs represented as:
Figure BDA0001298708530000057
further, in the fourth step:
detection statistic when noise variance is unknown:
Figure BDA0001298708530000054
detection statistics when noise variance is unknown and interfering targets are present:
Figure BDA0001298708530000055
where λ, λ' are the thresholds corresponding to the respective detectors.
Further, in the fifth step:
decision threshold of the detector when the noise variance is unknown ψ:
Figure BDA0001298708530000056
decision threshold ψ of the detector when the noise variance is unknown and an interference target is present:
Figure BDA0001298708530000061
the invention has the advantages and positive effects that: the invention effectively realizes the detection of moving targets under a plurality of heterogeneous satellite radiation sources, and can be used for low-penetration target detection and air early warning; the parameter data were subjected to 2000 Monte Carlo experimental simulations to obtain the detection performance as shown in FIG. 2.
Drawings
Fig. 1 is a flowchart of a target detection method based on Rao detection 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 target detection method based on Rao detection under multiple heterogeneous satellites according to an embodiment of the present invention includes the following steps:
s101: separating direct wave signals of the reference channel and using the direct wave signals as local reference signals;
s102: establishing a binary hypothesis model and probability density functions of signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
s103: respectively estimating unknown parameters under the assumption H0 under two conditions by utilizing a maximum likelihood estimation method;
s104: constructing detection statistics based on Rao detection in two cases;
s105: and setting detection thresholds under two conditions, and comparing and judging the detection thresholds with the detection statistics under the two conditions so as to detect the target.
The target detection method based on Rao detection 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 signals under two hypotheses according to the local reference signals and the signals of the monitoring channel;
step three, estimating the hypothesis H by utilizing a maximum likelihood estimation method0Lower unknown parameter c when the noise variance is unknownη,k，σ2And unknown parameters when the noise variance is unknown and an interfering target is present
Figure BDA0001298708530000071
cη,k，σ2；
Constructing detection statistics based on Rao detection under two conditions;
and step five, setting detection thresholds under two conditions, and comparing and judging the detection thresholds with the detection statistics under the two conditions so as to detect 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 as follows:
the expression for the reference channel signal z (t) is:
Figure BDA0001298708530000072
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 direct wave signals of a plurality of different satellites are received by the reference channel, 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 RE-GDA0001348944380000073
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,αηRespectively, the delay, doppler shift, and amplitude of the echo signal, and when k is 1, c isη,kIs the amplitude of the direct wave signal, and when k is 2,3, …, P,
Figure RE-GDA0001348944380000081
cη,kis the Doppler shift, time delay, amplitude of the multipath signal, K represents the number of the interference targets,
Figure RE-GDA0001348944380000082
respectively representing the Doppler shift, delay, amplitude, n of the interfering echo signals(t) is white Gaussian noise.
In the second step, the 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 the two hypotheses is performed as follows:
the binary hypothesis model is represented as:
Figure BDA0001298708530000083
Figure BDA0001298708530000084
suppose H0X [ n ] of]The probability density function of (a) is:
Figure BDA0001298708530000085
suppose H1X [ n ] of]The probability density function of (a) is:
Figure RE-GDA0001348944380000086
in the third step, the maximum likelihood estimation method is used to estimate the hypothesis H0Lower unknown parameter c when the noise variance is unknownη,k，σ2And unknown parameters when the noise variance is unknown and an interfering target is present
Figure BDA0001298708530000087
cη,k，σ2The method comprises the following steps:
hypothesis H when noise variance is unknown0Number of unknown parameters cη,k，σ2The maximum likelihood estimate of (c) is as follows:
H0unknown parameter c ofη,kThe maximum likelihood estimate of (c) is:
Figure BDA0001298708530000091
wherein
Figure BDA0001298708530000092
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 BDA0001298708530000093
representing received signals and direct waves in the monitoring channel and multipath signals in
Figure BDA0001298708530000094
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure BDA0001298708530000095
suppose H0Variance of noise
Figure BDA0001298708530000096
Maximum likelihood estimation of
Figure BDA0001298708530000097
Comprises the following steps:
Figure BDA0001298708530000098
hypothesis H when noise variance is unknown and interference targets are present0Unknown parameter of
Figure BDA0001298708530000099
The maximum likelihood estimate of (c) is as follows:
suppose H0The following unknown parameters are estimated as follows:
Figure BDA00012987085300000910
wherein the content of the first and second substances,
Figure BDA00012987085300000911
is that the amplitude of the b-th interfering echo is at the hypothesis H0The following estimation is performed. 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 BDA0001298708530000101
rxtrepresenting received signals and interfering target echo signals at
Figure BDA0001298708530000102
Correlation of rxtIs a vector of K1, [ rxt]Is rxtIs represented as:
Figure BDA0001298708530000103
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 BDA0001298708530000104
suppose H0The maximum likelihood estimates of the noise variance are:
Figure BDA0001298708530000105
where x is the hypothesis H0Signal of rssShowing the autocorrelation between echoes, [ r ]ss]Is a matrix of M x M, [ rss]rηIs represented by rssIs represented as:
Figure BDA0001298708530000106
in step four, the detection statistics based on the Rao detection in the two cases of construction are performed as follows:
detection statistic when noise variance is unknown:
Figure BDA0001298708530000107
detection statistics when noise variance is unknown and interfering targets are present:
Figure BDA0001298708530000108
where λ, λ' are the thresholds corresponding to the respective detectors.
In the fifth step, the detection thresholds under the two conditions are set and compared with the detection statistical quantities under the two conditions for judgment, so that the detection of the target is carried out according to the following steps:
decision threshold of the detector when the noise variance is unknown ψ:
Figure BDA0001298708530000111
decision threshold ψ of the detector when the noise variance is unknown and an interference target is present:
Figure BDA0001298708530000112
the application effect of the present invention will be described in detail with reference to the simulation.
Simulation experiment: simulation verification is carried out on the echo detection performance based on the generalized likelihood ratio under the three conditions, and three satellite signals including GPS, DVB-S and inmarsat are adopted for simulationAnd (4) performing a true experiment. 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 waves of the signals are: 130.1 dBw-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 carrying out 2000 Monte Carlo experimental simulations on the parameter data to obtain the detection performance shown in the figure 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 (1)

1. A target detection method based on Rao detection under a plurality of heterogeneous satellites is characterized by comprising the following steps: separating direct wave signals of the reference channel and using the direct wave signals as local reference signals; establishing a binary hypothesis model and probability density functions of signals under two hypotheses according to the local reference signals and the signals of the monitoring channel; estimating hypothesis H by maximum likelihood estimation method0、H1Unknown parameters of the following; constructing detection statistics based on Rao detection in two cases; setting detection thresholds under two conditions, and comparing and judging the detection thresholds with detection statistics under the two conditions to detect a target;
the target detection method based on Rao detection 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 hypothesis H by utilizing a maximum likelihood estimation method0Unknown when there is no interference target when the noise variance is unknownParameter cη,k，σ2And unknown parameters when the noise variance is unknown and an interfering target is present
Figure FDA0002566025170000011
cη,k，σ2；
Constructing detection statistics based on Rao detection under two conditions;
step five, setting detection thresholds under two conditions, and comparing and judging the detection thresholds with detection statistics under the two conditions so as to detect a target;
the signals of the channels in the first step are expressed as:
Figure FDA0002566025170000021
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 FDA0002566025170000022
cη,kis the Doppler frequency shift, time delay and amplitude of the direct wave signal of the reference channel after separation, K represents the number of the interference targets,
Figure FDA0002566025170000023
respectively representing the Doppler shift, delay, amplitude, n of the interfering echo signals[n]Is gaussian white noise;
in the second step:
the binary hypothesis model is represented as:
Figure FDA0002566025170000024
Figure FDA0002566025170000025
suppose H0X [ n ] of]The probability density function of (a) is:
Figure FDA0002566025170000031
suppose H1X [ n ] of]The probability density function of (a) is:
Figure FDA0002566025170000032
the third step specifically comprises:
H0unknown parameter c ofη,kThe maximum likelihood estimate of (c) is:
Figure FDA0002566025170000041
wherein
Figure FDA0002566025170000042
Figure FDA0002566025170000043
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 FDA0002566025170000044
Figure FDA0002566025170000045
k,s＝1,2,…,P，rxcrepresenting received signals and direct waves in the monitoring channel and multipath signals in
Figure FDA0002566025170000046
Correlation of (a) with [ r ]xc]Is a matrix of P x M, representing [ rxc]qsIs represented as:
Figure FDA0002566025170000047
suppose H0Variance of noise
Figure FDA0002566025170000048
Maximum likelihood estimation of
Figure FDA0002566025170000049
Comprises the following steps:
Figure FDA00025660251700000410
hypothesis H when noise variance is unknown and interference targets are present0Unknown parameter of
Figure FDA00025660251700000411
cη,k,σ2The maximum likelihood estimate of (c) is as follows:
suppose H0The following unknown parameters are estimated as follows:
Figure FDA0002566025170000051
wherein the content of the first and second substances,
Figure FDA0002566025170000052
Figure FDA0002566025170000053
is that the amplitude of the b-th interfering echo is at the hypothesis H0Estimating; 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 FDA0002566025170000054
rxtrepresenting received signals and interfering target echo signals at
Figure FDA0002566025170000055
Correlation of rxtIs a vector of K1, [ rxt]Is rxtIs represented as:
Figure FDA0002566025170000056
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 FDA0002566025170000057
suppose H0The maximum likelihood estimates of the noise variance are:
Figure FDA0002566025170000058
where x is the hypothesis H0Signal of rssShowing the autocorrelation between echoes, [ r ]ss]Is a matrix of M, [ r [ ]ss]rηIs represented by rssIs represented as:
Figure FDA0002566025170000061
in the fourth step:
detection statistics when the noise variance is unknown and when there is no interfering target:
Figure FDA0002566025170000062
detection statistics when noise variance is unknown and an interfering target is present:
Figure FDA0002566025170000063
wherein λ, λ' are thresholds corresponding to respective detectors;
in the fifth step:
decision threshold ψ of the detector when the noise variance is unknown and no interference target is present:
Figure FDA0002566025170000064
decision threshold ψ of the detector when the noise variance is unknown and an interference target is present:
Figure FDA0002566025170000065
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