CN113253224A - Passive distributed radar target detection method based on approximate message transfer algorithm - Google Patents

Passive distributed radar target detection method based on approximate message transfer algorithm Download PDF

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CN113253224A
CN113253224A CN202110365173.3A CN202110365173A CN113253224A CN 113253224 A CN113253224 A CN 113253224A CN 202110365173 A CN202110365173 A CN 202110365173A CN 113253224 A CN113253224 A CN 113253224A
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CN113253224B (en
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李军
鲍志宇
朱世翔
许京伟
朱圣棋
付琳
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/411—Identification of targets based on measurements of radar reflectivity
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/04—Systems determining presence of a target

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Abstract

The invention provides a passive distributed radar centralized target detection method based on approximate message transfer, aiming at a received signal after sparse representation of a passive distributed radar, an uncertain region possibly existing in a target is determined based on target time delay and target Doppler frequency; establishing a probability density function by using a received signal to obtain a corresponding likelihood ratio detection function, and performing sparse recovery on unknown parameters in the likelihood ratio detection function by using an improved approximate message transfer algorithm to obtain determined parameters after sparse recovery; introducing the determined parameters after sparse recovery into a likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT; and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target. The invention can reduce the complexity of target detection under the condition that the sampling modes of all radar base stations are different, and has good stability and effectiveness.

Description

Passive distributed radar target detection method based on approximate message transfer algorithm
Technical Field
The invention belongs to the technical field of radar target detection, and particularly relates to a passive distributed radar target detection method based on an approximate message transfer algorithm.
Background
In a passive distributed radar system, a passive radar receiver employs spatial or temporal filtering to isolate direct wave signals (i.e., transmitter to receiver) and target transmit signals (i.e., transmitter to target to receiver) into a reference channel and a monitor channel, respectively, where the reference channel provides an estimate of the unknown signal.
Detection algorithms in passive distributed radar can be divided into two broad categories: a detection algorithm that utilizes a reference channel and a detection algorithm that does not utilize a reference channel. The detection algorithm using the reference channel uses the reference channel as a matched signal for an approximate matched filter, similar to active radar, and then applies constant false alarm detection when calculating the ambiguity function between the reference channel and the monitor channel. High quality direct path signals may not be available for a number of reasons, such as: the directional pattern of the transmitting antenna or the blocking of the path between the radiation Signal source and the receiving radar leads to low Signal-to-Noise Ratio (SNR) of the direct wave Signal, severe complex multipath environment, and the influence caused by the rotation of the transmitting antenna. Using the direct wave signal in this case may significantly degrade the target detection performance of the blur function based process. Aiming at the passive MIMO radar system under the condition, detection algorithm detection without a reference channel is provided, namely a generalized likelihood ratio detection algorithm for centralized target detection under the condition of not using a direct wave reference signal, and the method needs to acquire information of a plurality of base stations with higher complexity.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a passive distributed radar target detection method based on an approximate message passing algorithm. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides a passive distributed radar target detection method based on an approximate message transfer algorithm, which is applied to a fusion center communicating with a passive distributed radar system and comprises the following steps:
step 1: receiving a compressed signal sent by a passive distributed radar system;
the compressed signal is a signal obtained by compressing an observed received signal by a radar base station in a passive distributed radar system;
step 2: determining an uncertain region in which the target may exist based on the target time delay and the target Doppler frequency;
wherein the uncertainty region comprises a plurality of small cells;
and step 3: comparing a first probability density function established based on the compressed signal with a second probability density function to obtain a likelihood ratio detection function;
the first probability density function is a probability density function established based on a compressed signal in the presence of noise, the second probability density function is a probability density function established based on a compressed signal in the presence of both a target echo signal and noise, and the second probability density function comprises a plurality of unknown parameters which represent sparse vectors fusing all radar base station information;
and 4, step 4: carrying out sparse recovery on unknown parameters in the likelihood ratio detection function by using an approximate message transfer algorithm to obtain determined parameters after sparse recovery;
and 5: introducing the determined parameters after the sparse recovery into the likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT;
step 6: and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target.
Optionally, the radar base station observes a received signal;
and compressing the observed received signal at a preset sampling rate to obtain a compressed signal.
Optionally, step 2 includes:
setting a plurality of target time delays and a plurality of target Doppler frequencies;
and aiming at a target time delay and a target Doppler frequency, determining an uncertain area of the target based on the relation between the radar base station and the position where the target possibly appears.
Wherein the first probability density function is:
Figure BDA0003006670230000031
the second probability density function is:
Figure BDA0003006670230000032
the likelihood ratio detection function is:
Figure BDA0003006670230000033
wherein the content of the first and second substances,
Figure BDA0003006670230000034
α＝[α1 ... αK]Tx represents a projection vector of a baseband signal s obtained by adding Q IO signal sources after target reflection on a frequency domain, and alpha represents a channel correlation coefficient, wherein the two are unknown parameters; c ═ pi σ2)-MRepresents a normalization constant, and M ═ M1+...+MK，||·||2Represents the square of the two-norm of the vector, ykSize of M for compressed sensingkAn observation vector of x 1; a. thekA sensing matrix with the size of M for the k-th receiving radar base station to compress the sensing processkxN, and satisfies Ak HAkI is a unit array; alpha is alphakThe channel correlation coefficient of a target reflection signal received by the kth receiving radar base station is related to the gain of an antenna, energy attenuation, the scattering characteristic of a target and phase cancellation among different receiving radars; noise obedience distribution in radar received signals
Figure BDA0003006670230000035
σ2Representing noise power, and K represents the number of static distributed receiving radar base stations; l0(y) represents simplified p0(y)，
Figure BDA0003006670230000036
l1(α, x | y) represents simplified p1(y|α,x)，
Figure BDA0003006670230000041
Figure BDA0003006670230000042
Indicating that the function is maximized over the unknown parameters a, x.
Optionally, the generalized likelihood ratio detection GLRT for passive distributed radar target detection is:
Figure BDA0003006670230000043
the AMP-GLRT test statistic of the passive distributed radar target detection is as follows:
Figure BDA0003006670230000044
wherein the content of the first and second substances,
Figure BDA0003006670230000045
shows the determined parameters after sparse recovery is carried out on the sparse vector fusing all the radar base station information by using an improved approximate message transfer algorithm,
Figure BDA0003006670230000046
indicating that the target echo signal and noise are present at the same time,
Figure BDA0003006670230000047
only noise is present and gamma represents the detection threshold.
Optionally, step 4 includes:
step 41: fusing two unknown parameters of a sparse vector and a channel correlation coefficient in a likelihood ratio detection function;
step 42: calculating a residual error item of each radar base station and a threshold of a soft threshold function based on the fused unknown parameters;
step 43: performing soft threshold function processing on the residual error item and the threshold to obtain an estimated value of an unknown parameter after sparse recovery;
step 44: and converging the approximate message transfer algorithm through repeated iteration, and determining the estimated value of the estimated unknown parameter of the converged approximate message transfer algorithm as the determined value of the unknown parameter to obtain the determined parameter.
Optionally, step 6 includes:
determining a detection threshold according to the false alarm probability by using a plurality of Monte Carlo tests;
when the test statistic is larger than a detection threshold, determining that the small unit has a target;
and when the test statistic is not greater than the detection threshold, determining that the target does not exist in the small unit.
The invention provides a passive distributed radar centralized target detection method based on approximate message transfer, aiming at a received signal after sparse representation of a passive distributed radar, an uncertain region possibly existing in a target is determined based on target time delay and target Doppler frequency; establishing a probability density function by using a received signal to obtain a corresponding likelihood ratio detection function, and performing sparse recovery on unknown parameters in the likelihood ratio detection function by using an improved approximate message transfer algorithm to obtain determined parameters after sparse recovery; introducing the determined parameters after sparse recovery into a likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT; and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target. The invention can reduce the complexity of target detection under the condition that the sampling modes of all radar base stations are different, and has good stability and effectiveness.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of a passive distributed radar target detection method based on an approximate message passing algorithm according to the present invention;
FIG. 2 is a schematic structural diagram of a multi-static passive distributed radar system provided by the present invention;
FIG. 3 is a schematic diagram of centralized target detection provided by the present invention;
FIG. 4 shows the detection probability P provided by the present inventiondSNR with average Signal-to-noise ratioavgA graph of variation of (d);
FIG. 5 is a graph of the number of iterations of convergence versus average SNR provided by the present inventionavgGraph of the variation of (c).
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
As shown in fig. 1, the passive distributed radar target detection method based on approximate message passing algorithm provided by the present invention is applied to a fusion center communicating with a passive distributed radar system, and includes:
referring to fig. 2, the multi-static passive distributed radar system shown in fig. 2 includes Q third-party opportunistic signal sources (IO) and K static distributed reception radar base stations, where the positions of the IO signal sources are unknown and the positions of the distributed reception radar base stations are known.
Step 1: receiving a compressed signal sent by a passive distributed radar system;
the compressed signal is a signal obtained by compressing an observed received signal by a radar base station in a passive distributed radar system;
when a target exists in the detection range, y 'is used for the signal of the kth receiving radar base station'k(t) represents:
Figure BDA0003006670230000061
wherein, s'q(t) a baseband signal generated for the qth IO, assuming that the signal is approximately sparse or locally sparse in the frequency domain; tau isqkIs from the first toq IOs and the kth receiving radar base station reach the target by two-way time delay; alpha's'qkThe channel coefficient of the q IO received from the kth receiving radar after being reflected by the target is related to the reflection coefficient of the target, the antenna gain and the channel attenuation; f. ofkAnd receiving the target Doppler frequency in the signal for the kth receiving radar base station. Omega'k(t) is white Gaussian noise in the received signal, obeying the distribution
Figure BDA0003006670230000062
Assuming noise power σ2Are known.
Adding Q IO reflected signals received by the kth receiving radar into a sum signal alphakAnd s (t), taking the signal as a final signal of the kth receiving radar base station of the PMR sensor networking system, wherein the above formula is simplified into the following form:
Figure BDA0003006670230000071
wherein alpha iskRepresenting the sum signal reflection coefficient, τ, from the kth receiving radar base station to the targetkAnd the time delay from the kth receiving radar base station to the target is obtained. It is assumed that the signal is still sparse in the frequency domain at this time.
Assume that the acquired baseband signal is a column vector s with length N, i.e., T ═ NTs. Similarly, mixing y'k(t)、s(t)、ω′k(t) N sample points are written in column vector form y 'of Nx 1'kS, ω'. The formula is expressed on the digital signal as:
y′k＝αkD(fkTs)THD(-τkfs/N)Ts+ω′k
wherein f issFor the sampling frequency, D (f)kTs)、D(-τkfs/N) with respect to the parameter delay τkAnd Doppler frequency fkThe correlation matrix of (a) is calculated,
Figure BDA0003006670230000072
diag (k) is the vector
Figure BDA0003006670230000073
A diagonalized N square matrix.
Figure BDA0003006670230000074
Is an N-point discrete Fourier transform matrix, and (·)HIndicating that the matrix is conjugate transposed.
To simplify the formula, use
Figure BDA0003006670230000075
Replacing factor D (f) in formulakTs)THD(-τkfsT,/N), then the signal is:
Figure BDA0003006670230000076
compressed sensing theory (CS) proves that as long as yk(t) sparseness in a transform domain, data can be collected by sub-sampling much less than twice the highest frequency of the signal, while ensuring that the main information of the signal is preserved, the transformation is represented by a transform matrix ψ, and the projection vector of the baseband signal s in the frequency domain is represented by a column vector x of length N, which is referred to herein as a sparse vector. The N-dimensional discrete signal x can be represented by a set of linear combinations of the transformation matrix ψ:
s＝ψx
wherein, the sparse vector x only has few non-zero elements, and the number of the non-zero elements is set as
Figure BDA0003006670230000077
Then define its relative sparsity as
Figure BDA0003006670230000078
And ρ < N.
After sparse representation, the CS sub-sampling signal compression process is carried out. Obtaining M by CS sub-samplingkA sampling point corresponding to yk(t)、ωk(t) sampling Point set write MkX 1 column vector form yk、ωkDefining the sampling rate of the kth radar base station CS as deltak＝Mkand/N. Likewise, the sub-sampling process may use a size of MkxN matrix form
Figure BDA0003006670230000081
Express, define
Figure BDA0003006670230000082
To observe the matrix, it may act as a projection of the high-dimensional signal s into the low-dimensional space yk。
Figure BDA0003006670230000083
An appropriate observation vector is selected, and the selected observation vector is not correlated with the transformation matrix. Using the observation vector
Figure BDA0003006670230000084
The process of linear mapping the signal s is mathematically represented as:
Figure BDA0003006670230000085
the whole CS measurement process of the kth receiving radar in the passive distributed radar can be obtained as follows:
Figure BDA0003006670230000086
wherein, ykSize of M for compressed sensingkAn observation vector of x 1;
Figure BDA0003006670230000087
a sensing matrix with the size of M for the k-th receiving radar base station to compress the sensing processkxN, and satisfies Ak HAkI is a unit array; alpha is alphakFor the kth receiving radar base station to receiveThe channel correlation coefficient of the reflected signal to the target is related to the gain of the antenna, energy attenuation, the scattering characteristic of the target and phase cancellation among different receiving radars;
Figure BDA0003006670230000088
for the sum time delay tau in the target reflected signal received by the kth receiving radar base stationkDoppler frequency fkA correlation matrix of (a); x represents a projection vector x of a baseband signal s obtained by adding Q IO signal sources after target reflection on a frequency domain; omegakIs white Gaussian noise and obeys the distribution
Figure BDA0003006670230000089
Assuming noise power σ2Are known. It should be noted that in CS processing, the sensing matrix AkAn equal distance constraint characteristic needs to be satisfied to obtain a vector y from the observation vectorkAnd recovering the sparse signal.
Step 2: determining an uncertain region in which the target may exist based on the target time delay and the target Doppler frequency;
wherein the uncertainty region includes a plurality of small cells.
As an optional implementation manner of the present invention, the radar base station observes a received signal;
and compressing the observed received signal at a preset sampling rate to obtain a compressed signal.
As an optional embodiment of the present invention, the step 2 includes:
step a: setting a plurality of target time delays and a plurality of target Doppler frequencies;
step b: and aiming at a target time delay and a target Doppler frequency, determining an uncertain area of the target based on the relation between the radar base station and the position where the target possibly appears.
When the radar echo is subjected to target detection, the uncertain region of target time delay and target Doppler frequency is generally decomposed into a plurality of small units
Figure BDA0003006670230000091
Wherein p and
Figure BDA0003006670230000092
are the location and doppler frequency parameters of the corresponding cell. When the signal model of the established passive distributed radar is aimed at the detection unit
Figure BDA0003006670230000093
Figure BDA0003006670230000094
When the centralized target detection is carried out, the information of each receiving radar is transmitted to the fusion center and then the subsequent signal processing process is carried out, and at the moment, the information obtained by the fusion center is expressed in a matrix form as follows:
Figure BDA0003006670230000095
let y be [ y1...yK]TThe schematic diagram of the centralized target detection is shown in fig. 3.
And step 3: comparing a first probability density function established based on the compressed signal with a second probability density function to obtain a likelihood ratio detection function;
the first probability density function is a probability density function established based on a compressed signal in the presence of noise, the second probability density function is a probability density function established based on a compressed signal in the presence of both a target echo signal and noise, the second probability density function comprises a plurality of unknown parameters, and the unknown parameters represent sparse vectors fusing all radar base station information;
and 4, step 4: carrying out sparse recovery on unknown parameters in the likelihood ratio detection function by using an approximate message transfer algorithm to obtain determined parameters after sparse recovery;
as an optional embodiment of the present invention, step 4 includes:
step 41: fusing two unknown parameters of a sparse vector and a channel correlation coefficient in a likelihood ratio detection function;
step 42: calculating a residual error item of each radar base station and a threshold of a soft threshold function based on the fused unknown parameters;
step 43: performing soft threshold function processing on the residual error item and the threshold to obtain an estimated value of an unknown parameter after sparse recovery;
step 44: and converging the approximate message transfer algorithm through repeated iteration, and determining the estimated value of the estimated unknown parameter of the converged approximate message transfer algorithm as the determined value of the unknown parameter to obtain the determined parameter.
And 5: introducing the determined parameters after the sparse recovery into the likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT;
step 6: and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target.
As an alternative embodiment of the present invention, step 6 includes:
step 61: determining a detection threshold according to the false alarm probability by using a plurality of Monte Carlo tests;
step 62: when the test statistic is larger than a detection threshold, determining that the small unit has a target;
and step 63: and when the test statistic is not greater than the detection threshold, determining that the target does not exist in the small unit.
Wherein the first probability density function is:
Figure BDA0003006670230000101
the second probability density function is:
Figure BDA0003006670230000102
the likelihood ratio detection function is:
Figure BDA0003006670230000111
wherein the content of the first and second substances,
Figure BDA0003006670230000112
α＝[α1 ... αK]Tx represents a projection vector of a baseband signal s obtained by adding Q IO signal sources after target reflection on a frequency domain, alpha represents a channel correlation coefficient, the two are unknown parameters, and c is (pi sigma)2)-MRepresents a normalization constant, and M ═ M1+...+MK，
Figure BDA0003006670230000113
α＝[α1...αK]T，||·||2Represents the square of the two-norm of the vector, ykSize of M for compressed sensingkAn observation vector of x 1; a. thekA sensing matrix with the size of M for the k-th receiving radar base station to compress the sensing processkxN, and satisfies Ak HAkI is a unit array; alpha is alphakThe channel correlation coefficient of a target reflection signal received by the kth receiving radar base station is related to the gain of an antenna, energy attenuation, the scattering characteristic of a target and phase cancellation among different receiving radars; noise obeying distribution in radar base station received signal
Figure BDA0003006670230000114
σ2Which is indicative of the power of the noise,
Figure BDA0003006670230000115
expressing the function maximization on unknown parameters alpha and x, K expresses the number of static distributed receiving radar base stations, and l0(y) represents simplified p0(y)，
Figure BDA0003006670230000116
l1(α, x | y) represents simplified p1(y|α,x)，
Figure BDA0003006670230000117
The generalized likelihood ratio detection GLRT for the passive distributed radar target detection is as follows:
Figure BDA0003006670230000118
the AMP-GLRT test statistic of the passive distributed radar target detection is as follows:
Figure BDA0003006670230000119
wherein the content of the first and second substances,
Figure BDA00030066702300001110
in order to determine parameters after sparse recovery of sparse vectors fusing all radar base station information by using an improved approximate message transfer algorithm,
Figure BDA00030066702300001111
indicating that the target echo signal and noise are present at the same time,
Figure BDA00030066702300001112
only noise is present and gamma represents the detection threshold.
According to the fact that the noise of each receiving radar is mutually independent and identically distributed
Figure BDA00030066702300001113
Wherein sigma2Known as the noise power. Then the assumption that the target echo signal and noise are present simultaneously
Figure BDA0003006670230000121
Assumption of only noise present
Figure BDA0003006670230000122
The following PDFs are:
Figure BDA0003006670230000123
Figure BDA0003006670230000124
here, the sparse vector x, the channel correlation coefficient α are considered as unknown parameters. c ═ pi σ2)-MRepresents a normalization constant, and M ═ M1+...+MK，||·||2Representing the square of the two-norm of the vector. After the above formula is logarithmized and constant terms are omitted, the formula can be simplified as follows:
Figure BDA0003006670230000125
Figure BDA0003006670230000126
then GLRT for passive distributed radar target detection is:
Figure BDA0003006670230000127
wherein the content of the first and second substances,
Figure BDA0003006670230000128
indicating that the function is maximized over the unknown parameters α, x.
First derive assumptions
Figure BDA0003006670230000129
The maximum likelihood estimation function of (1). From hypothesis
Figure BDA00030066702300001210
Can easily deduce the time alphakThe Maximum Likelihood Estimate (MLE) of (a) is:
Figure BDA00030066702300001211
wherein, (.)HIndicating that the matrix is conjugate transposed. Can find alphakIs about unknown parametersA function of the number x. Then the unknown parameters of the likelihood function at this time leave only the sparse vector x:
Figure BDA00030066702300001212
wherein the content of the first and second substances,
Figure BDA00030066702300001213
indicating that the function is maximized over the unknown parameter x.
Then minimizing the signal reconstruction error by using the sparse property of x can convert the above equation into the following optimization problem:
Figure BDA0003006670230000131
wherein the content of the first and second substances,
Figure BDA0003006670230000132
the regularization parameter λ represents a trade-off between the previous term allowable error and the next term sparsity in the optimization problem. In order to solve the optimization problem, an AMP method is used as a reference to carry out sparse recovery algorithm derivation, and then test statistics are obtained.
Defining a joint density function with respect to a sparse vector x:
Figure BDA0003006670230000133
obviously, this is one concern
Figure BDA0003006670230000134
αk_MLEAnd beta. Similarly, when β → ∞ μ will concentrate around the final solution. And it can be found that the difference from the distribution function established by the AMP-based algorithm is the addition of the factor alphak_MLE. When the edge density function of the distribution function is solved by using a factor graph and a product algorithm, under the conditions of N → ∞, β → ∞ the elimination can be writtenIterative form of information transfer:
Figure BDA0003006670230000135
Figure BDA0003006670230000136
with the greatest computational effort
Figure BDA0003006670230000137
The following formula can be used for estimation:
Figure BDA0003006670230000138
Figure BDA0003006670230000139
wherein
Figure BDA00030066702300001310
Are respectively as
Figure BDA00030066702300001311
Mean and variance of. According to Ak HAkCan be obtained as I
Figure BDA00030066702300001312
And when N is sufficiently large,
Figure BDA00030066702300001313
available tautApproximate substitution, here can be simplified as:
Figure BDA0003006670230000141
brought into
Figure BDA0003006670230000142
The following can be obtained:
Figure BDA0003006670230000143
then
Figure BDA0003006670230000144
The mean and variance of (a) are:
Figure BDA0003006670230000145
due to AkAre orthogonal to each other, so
Figure BDA0003006670230000146
And let η (·) be a soft threshold function, whose first derivative is η' (·), then:
Figure BDA0003006670230000147
and obtaining an AMP-GLRT algorithm iteration process by using the Taylor first-order expansion formula as follows:
Figure BDA0003006670230000148
Figure BDA0003006670230000149
Figure BDA00030066702300001410
it can be found that the sparse vector estimation x of the baseband signal of each node cannot be directly obtained in the t +1 th iterationt+1But rather obtains an estimate incorporating all node information
Figure BDA00030066702300001411
Compared to the basic iterative algorithm of AMP, the key point is α for the t +1 th iterationt+1Derivation of the calculation formula (c).
First of all utilize
Figure BDA00030066702300001412
Obtaining an intermediate variable
Figure BDA00030066702300001413
Figure BDA00030066702300001414
Then to the obtained
Figure BDA0003006670230000151
Needs to be normalized
Figure BDA0003006670230000152
Of the t +1 th iteration
Figure BDA0003006670230000153
The calculation formula is as follows:
Figure BDA0003006670230000154
wherein the content of the first and second substances,
Figure BDA0003006670230000155
Figure BDA0003006670230000156
accordingly, the constraint condition is satisfied
Figure BDA0003006670230000157
While the factor alpha can be reducedtxtBy using
Figure BDA0003006670230000158
And (3) replacing:
Figure BDA0003006670230000159
Figure BDA00030066702300001510
since α need not be known separately in the t +1 th iterationt+1、xt+1Is known instead
Figure BDA00030066702300001511
That is, the iterative process can be further simplified. In summary, the iterative process of the AMP-GLRT algorithm can be simplified as follows:
Figure BDA00030066702300001512
Figure BDA00030066702300001513
Figure BDA00030066702300001514
it should be noted that the algorithm iterates at this time
Figure BDA00030066702300001515
The vector is not a sparse variable corresponding to the baseband signal, but a vector fused with all node information, namely information needed in target detection.
Compared with AMP basic algorithm flow, the key point of the algorithm is that a variable alpha is addedkOf the iterative operation ofWith the addition of the calculated amount, the algorithm flow is further simplified below.
Intermediate variables
Figure BDA00030066702300001516
Brought into
Figure BDA00030066702300001517
It is possible to obtain:
Figure BDA00030066702300001518
wherein the content of the first and second substances,
Figure BDA0003006670230000161
due to the fact that
Figure BDA0003006670230000162
Therefore, it is not only easy to use
Figure BDA0003006670230000163
And can thus be converted into:
Figure BDA0003006670230000164
Figure BDA0003006670230000165
from the derived iterative formula, it can be found that the iterative process at this time is with the respective node
Figure BDA0003006670230000166
Irrelevant, only with the fusion of all node information alphatIt is related. More importantly alphatIs coupled to x, which means atThe iterative operation with x can be used
Figure BDA00030066702300001612
One factor can be replaced, thereby simplifyingAnd (5) performing an operation process.
It is assumed that the above-described AMP-GLRT algorithm has converged after T iterations. Let the sparse vector fusing all node information obtained at this time be
Figure BDA0003006670230000167
Corresponding to
Figure BDA0003006670230000168
Figure BDA0003006670230000169
Figure BDA00030066702300001610
Brought into1In (α, x | y), we obtain:
Figure BDA00030066702300001611
wherein, c1、c2Respectively as follows:
Figure BDA0003006670230000171
Figure BDA0003006670230000172
from the above formula, c1+c 20, while being based on (α)1-MLE)2+...+(αK-MLE)2And K, the AMP-GLRT test statistic of the target detection of the passive distributed radar is as follows:
Figure BDA0003006670230000173
the test statistic in the formula can be regarded as the ratio of the sum of the power of signals contained in all nodes in the whole passive distributed radar system to the noise power, namely the output signal-to-noise ratio.
The invention provides a passive distributed radar centralized target detection method based on approximate message transfer, aiming at a received signal after passive distributed radar sparse representation, an uncertain region of a target is determined based on target time delay and target Doppler frequency; detecting a target in a plurality of small units by using a probability density function to obtain a likelihood ratio detection function; carrying out sparse recovery on unknown parameters in the likelihood ratio detection function by using an improved approximate message transfer algorithm to obtain determined parameters after sparse recovery; introducing the determined parameters after sparse recovery into a likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT; and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target. The invention can reduce the complexity of target detection under the condition that the sampling modes of all radar base stations are different, and has good stability and effectiveness.
The following is a verification description of the beneficial effects of the present invention through simulation experiments.
(I) simulation experiment conditions
Baseband signal snN1.. N } is based on
Figure BDA0003006670230000181
Determining that s satisfies | | s | | non-woven calculation at the moment2N. Vector Ts＝[1...n/fs...N/fs]Is related to the sampling frequency fsA set of correlated sample time points. Let the sparsity of the baseband signal s in the frequency domain be p, i.e. zero in the corresponding sparse vector
Figure BDA0003006670230000182
Then define f as [0, fs]And randomly taking a vector consisting of rho frequency points.
Figure BDA0003006670230000183
It is necessary to select an appropriate observation vector,it is assumed that in the CS process,
Figure BDA0003006670230000184
is independently and identically distributed in zero mean and 1/M of variancekGaussian random variable composition. The simultaneous transformation matrix ψ can be represented using a discrete fourier transform change matrix of size N × N. Then the perception matrix
Figure BDA0003006670230000185
Size MkxN, satisfies Ak HAkI is a unit matrix. Added noise omegakIs of size MkX 1, and independently distributed in the same way
Figure BDA0003006670230000186
If not otherwise specified, the channel coefficient αkBy satisfying with respect to noise power σ2Desired SNR of 1avgThe values are randomly selected. Wherein the SNRavgIs defined as:
Figure BDA0003006670230000187
setting the sparse vector size N to 300, and receiving CS observation vector M of radar1＝M2＝…＝ MK0.1 × N, the total sampling rate Δ of the distributed radar system is defined as 0.1 × K. First use 104The sub-Monte Carlo test is determined under the hypothesis
Figure BDA0003006670230000188
Lower false alarm probability Pfa＝10-3The detection threshold gamma of time, then 104Sub-experiments determined at different SNRavgProbability of temporal detection PdAnd a variation curve of the convergence times.
(II) simulation experiment content and result analysis
In the whole simulation process, firstly, a decision threshold value corresponding to a specific false alarm probability is determined by a Monte Carlo experiment method, and then, a Monte card is also utilizedThe target detection performance results of the AMP-GLRT detector are determined by a Roman experiment. In order to research and analyze the target detection performance algorithm when the number of radar nodes is different, the detection probability P of the AMP-GLRT algorithm is adopted in the simulation resultdAnd number of convergence with average signal-to-noise ratio SNRavgIs shown by the change curve of (a).
Fig. 4 shows the detection probability P of the AMP-GLRT algorithm when the number K of radar nodes is 4, K is 8, and the sparsity ρ of the signal is 0.02dAs a function of SNRavgThe change curve of (2). Wherein the SNRavgThe variation range is (-30dB, 0dB), the solid line marked with "+" is the corresponding performance variation curve when the number K of radar base stations is 4, and the solid line marked with "+" is the performance variation curve when K is 8. It can be found that the final detection probability of the AMP-GLRT detector provided herein can reach 1 under the condition that the radar base station sensing matrixes are different from each other. And when the number K of radar base stations is 8, that is, the sampling rate is increased, the detection performance of the AMP-GLRT detector becomes better.
FIG. 5 shows the number of convergence iterations of the AMP-GLRT detector as a function of the average signal-to-noise ratio SNRavgThe change curve of (2). In both cases, the number of convergence iterations of the AMP-GLRT detector is a function of the average signal-to-noise ratio SNRavgBecomes larger, but requires a small number of iterations. And AMP-GLRT does not relate to a complex calculation formula, so that the time required by the operation can be greatly reduced. Meanwhile, as is apparent from the figure, when the number K of radar base stations is 8, the number of iterations required for convergence becomes smaller compared to K4, which shows that the number of iterations required for convergence of the AMP-GLRT detector decreases as the sampling rate increases.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (7)

1. A passive distributed radar target detection method based on approximate message transfer algorithm is applied to a fusion center communicating with a passive distributed radar system, and is characterized by comprising the following steps:
step 1: receiving a compressed signal sent by a passive distributed radar system;
the compressed signal is a signal obtained by compressing an observed received signal by a radar base station in a passive distributed radar system;
step 2: determining an uncertain region in which the target may exist based on the target time delay and the target Doppler frequency;
wherein the uncertainty region comprises a plurality of small cells;
and step 3: comparing a first probability density function established based on the compressed signal with a second probability density function to obtain a likelihood ratio detection function;
the first probability density function is a probability density function established based on a compressed signal in the presence of noise, the second probability density function is a probability density function established based on a compressed signal in the presence of both a target echo signal and noise, and the second probability density function comprises a plurality of unknown parameters which represent sparse vectors fusing all radar base station information;
and 4, step 4: carrying out sparse recovery on unknown parameters in the likelihood ratio detection function by using an approximate message transfer algorithm to obtain determined parameters after sparse recovery;
and 5: introducing the determined parameters after the sparse recovery into the likelihood ratio detection function to obtain test statistics corresponding to a centralized target detection algorithm AMP-GLRT;
step 6: and carrying out constant false alarm CFAR detection on the test statistic to determine whether the small unit has a target.
2. The passive distributed radar target detection method of claim 1, wherein the radar base station observes a received signal;
and compressing the observed received signal at a preset sampling rate to obtain a compressed signal.
3. The passive distributed radar target detection method of claim 1, wherein the step 2 comprises:
setting a plurality of target time delays and a plurality of target Doppler frequencies;
and aiming at a target time delay and a target Doppler frequency, determining an uncertain area of the target based on the relation between the radar base station and the position where the target possibly appears.
4. The passive distributed radar target detection method of claim 1, wherein the first probability density function is:
Figure FDA0003006670220000021
the second probability density function is:
Figure FDA0003006670220000022
the likelihood ratio detection function is:
Figure FDA0003006670220000023
wherein the content of the first and second substances,
Figure FDA0003006670220000024
α＝[α1 ... αK]Tx represents a projection vector of a baseband signal s obtained by adding Q IO signal sources after target reflection on a frequency domain, and alpha represents a channel correlation coefficient, wherein the two are unknown parameters; c ═ pi σ2)-MRepresents a normalization constant, and M ═ M1+...+MK，||·||2Represents the square of the two-norm of the vector, ykSize of M for compressed sensingkAn observation vector of x 1; a. thekA sensing matrix with the size of M for the k-th receiving radar base station to compress the sensing processkxN, and satisfies Ak HAkI is a unit array; alpha is alphakChannel correlation coefficient for target reflected signal received by kth receiving radar station, andthe gain of the antenna, energy attenuation, scattering characteristics of the target and phase cancellation between different receiving radars are related; noise obedience distribution in radar received signals
Figure FDA0003006670220000025
σ2Representing noise power, and K represents the number of static distributed receiving radar base stations; l0(y) represents simplified p0(y)，
Figure FDA0003006670220000026
l1(α, x | y) represents simplified p1(y|α,x)，
Figure FDA0003006670220000027
Indicating that the function is maximized over the unknown parameters a, x.
5. The passive distributed radar target detection method of claim 4, wherein the generalized likelihood ratio detection (GLRT) for passive distributed radar target detection is:
Figure FDA0003006670220000031
the AMP-GLRT test statistic of the passive distributed radar target detection is as follows:
Figure FDA0003006670220000032
wherein the content of the first and second substances,
Figure FDA0003006670220000033
shows the determined parameters after sparse recovery is carried out on the sparse vector fusing all the radar base station information by using an improved approximate message transfer algorithm,
Figure FDA0003006670220000034
indicating that the target echo signal and noise are present at the same time,
Figure FDA0003006670220000035
only noise is present and gamma represents the detection threshold.
6. The passive distributed radar target detection method of claim 1, wherein step 4 comprises:
step 41: fusing two unknown parameters of a sparse vector and a channel correlation coefficient in a likelihood ratio detection function;
step 42: calculating a residual error item of each radar base station and a threshold of a soft threshold function based on the fused unknown parameters;
step 43: performing soft threshold function processing on the residual error item and the threshold to obtain an estimated value of an unknown parameter after sparse recovery;
step 44: and converging the approximate message transfer algorithm through repeated iteration, and determining the estimated value of the estimated unknown parameter of the converged approximate message transfer algorithm as the determined value of the unknown parameter to obtain the determined parameter.
7. The passive distributed radar target detection method of claim 1, wherein step 6 comprises:
determining a detection threshold according to the false alarm probability by using a plurality of Monte Carlo tests;
when the test statistic is larger than a detection threshold, determining that the small unit has a target;
and when the test statistic is not greater than the detection threshold, determining that the target does not exist in the small unit.
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