CN112363151B - Self-adaptive target detection method of frequency diversity array multi-input multi-output radar - Google Patents

Self-adaptive target detection method of frequency diversity array multi-input multi-output radar Download PDF

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CN112363151B
CN112363151B CN202011221803.1A CN202011221803A CN112363151B CN 112363151 B CN112363151 B CN 112363151B CN 202011221803 A CN202011221803 A CN 202011221803A CN 112363151 B CN112363151 B CN 112363151B
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CN112363151A (en
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兰岚
祁佳炜
廖桂生
许京伟
朱圣棋
赵英海
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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
    • 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
    • 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
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Abstract

The invention discloses a self-adaptive target detection method of a frequency diversity array multi-input multi-output radar, which mainly solves the problem that the existing frequency diversity array multi-input multi-output radar cannot realize self-adaptive target detection. The method comprises the following implementation steps: 1) constructing an equivalent receiving signal of a frequency diversity array multi-input multi-output radar; 2) constructing a binary hypothesis test problem and generalized likelihood ratio test detection statistics according to the received signals; 3) optimizing and solving the test statistic in the step 2) by adopting an improved interval searching method of a quasi-Newton method to obtain improved interval searching generalized likelihood ratio detection statistic based on the quasi-Newton method; 4) and setting a detection threshold according to the actual situation, and comparing the improved interval search generalized likelihood ratio detection statistic based on the Newton-like method with the detection threshold to obtain a detection result. The invention can realize the self-adaptive detection of the target, improves the target detection performance of the radar, and can be used for the target identification of the frequency diversity array multi-input multi-output radar.

Description

Self-adaptive target detection method of frequency diversity array multi-input multi-output radar
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a design method for self-adaptive target detection, which can be used for target detection of frequency diversity array multiple-input multiple-output FDA-MIMO radars.
Background
With the development of radar technology, the resolution of a radar system is continuously improved, and the performance of a detected target is also continuously enhanced, so that the radar target detection faces many challenges. Existing radar systems include synthetic aperture radar, pulse doppler radar, phased array radar, multiple input multiple output radar, and the like. With the upgrading of radar systems, the multi-channel signal detection theory is continuously upgraded. The frequency diversity array multiple-input multiple-output FDA-MIMO radar in the multiple-input multiple-output radar has higher signal processing dimensionality and can acquire more comprehensive clutter and target information, so that the self-adaptive target detection performance is improved.
Yu Zhu et al preliminarily studied the Target Detection of FDA-MIMO Radar with frequency diversity array under Gaussian white noise background in its published paper "Target Detection Performance Analysis of FDA-MIMO Radar", and an important prerequisite of the Detection model is the prior information of known Target distance and interference covariance matrix. In practice, however, the target information and the interference covariance matrix are not known, as evidenced in the numerous publications of target detection, these assumptions take into account the unknown parameters possible with target or interference statistics.
Currently, common adaptive target detector design methods include a Generalized Likelihood Ratio Test (GLRT), a Rao detector, a Wald detector, and the like, wherein the GLRT criterion is used to design the adaptive target detector for the most extensive application. However, the self-adaptive design of the existing detector based on the GLRT criterion is established on the basis of the traditional radar system, and the radar of the traditional system has the characteristic of waveform diversity, so that the target detection performance is poor. The frequency diversity array multiple-input multiple-output FDA-MIMO radar has higher system controllable degree of freedom due to the introduction of a distance dimension, but the current target detection method based on the frequency diversity array multiple-input multiple-output FDA-MIMO radar cannot use a likelihood ratio criterion to check LRT and calculate unknown parameters due to the fact that the target information, an interference covariance matrix and other unknown parameters are not considered, and cannot realize the self-adaptive target detection of the frequency diversity array multiple-input multiple-output FDA-MIMO radar.
Disclosure of Invention
The invention aims to provide a self-adaptive target detection method of a frequency diversity array multiple-input multiple-output radar aiming at the defects of the prior art, so as to construct frequency diversity array multiple-input multiple-output FDA-MIMO radar self-adaptive target detection statistics designed by a generalized likelihood ratio test GLRT criterion, and realize the self-adaptive detection of a target.
The technical scheme of the invention is as follows: firstly, obtaining the difference delta tau between the actual target delay and the sampling value in each distance unit through the receiving, matching and filtering processing of the frequency diversity array multi-input multi-output FDA-MIMO radar; constructing a binary hypothesis test problem under the background of Gaussian noise; constructing detection statistics according to GLRT criterion, and obtaining H by utilizing an algorithm for improving interval search by Newton-like method 1 The maximum likelihood estimation under the hypothesis test comprises the following specific implementation steps:
(1) performing matched filtering processing on the signal of each channel of the frequency diversity array multiple-input multiple-output FDA-MIMO radar in a mode of synchronous digital mixing and matched filtering;
(2) constructing an emission guide vector a (delta tau) related to the target increment distance, and constructing an emission guide vector d (theta tau) related to the target angle 0 ) Constructing a transmitting guide vector a of the frequency diversity array multi-input multi-output FDA-MIMO radar T (θ 0 Δ τ), where Δ τ is the difference between the sample time and the actual delay of the target in each range bin, θ 0 Is the angle of the far field target;
(3) constructing a reception steering vector b (theta) related to an angle 0 )；
(4) Constructing virtual transmit-receive steering vector s (theta) of target of frequency diversity array multi-input multi-output FDA-MIMO radar 0 Δ τ); based on the guide vector s (theta) 0 Delta tau) to construct the equivalent total received signal y of the FDA-MIMO radar target of the frequency diversity array S ；
(5) Adopting the GLRT criterion of the generalized likelihood ratio test of the frequency diversity array multiple-input multiple-output FDA-MIMO radar to construct the statistic Λ of the generalized likelihood ratio test GLRT ：
(5a) Let a set of training samples be z q Q is 1,2, K is equal to or greater than MN, wherein z is C ∈ MN Representing echo vectors from the unit to be detected, K-tableIndicating the number of pulses, wherein M is the number of transmitting array elements, N is the number of receiving array elements,
Figure BDA0002762291100000021
a complex vector space is maintained for MN; the detection problem is converted into the following binary hypothesis testing problem according to the training sample:
Figure BDA0002762291100000022
wherein H 0 Hypothesis that target is absent, H 1 The hypothesis that the target is present in the cell to be detected, n and n q ∈C MN In order to satisfy the zero-mean complex Gaussian noise with independent and same distribution condition,
Figure BDA0002762291100000023
β 1 complex echo power after digital mixing;
(5b) respectively calculating the joint probability density function under two assumptions to obtain the probability density function at H 0 The joint probability density function under the assumption is g (z, z) 1 ,…,z K ∣M；H 0 ) In H 1 The joint probability density function under the assumption is g (z, z) 1 ,…,z K ∣β 1 ,Δτ,M；H 1 ) Wherein
Figure BDA0002762291100000024
Is a positive-definite clutter covariance matrix,
Figure BDA0002762291100000025
a complex matrix set is constructed by MN multiplied by MN;
(5c) the statistics of the generalized likelihood ratio test GLRT are constructed as follows:
Figure BDA0002762291100000026
wherein the content of the first and second substances,
Figure BDA0002762291100000027
represents a tight set containing all possible values of the variable Δ τ;
(6) constructing improved interval search GLRT detection statistics based on a Newton-like method:
(6a) constructing a statistic φ (Δ τ) containing the unknown parameter Δ τ:
testing statistic Λ for generalized likelihood ratio GLRT The numerator and denominator of (c) are maximized with respect to M, resulting in a test rule:
Figure BDA0002762291100000031
wherein the content of the first and second substances,
Figure BDA0002762291100000032
Figure BDA0002762291100000033
represents a conjugate transpose operation;
denominator of checking rule with respect to beta 1 Minimization, the test rule is equivalent to:
Figure BDA0002762291100000034
wherein the content of the first and second substances,
Figure BDA0002762291100000035
for the detection statistics based on the interval search,
Figure BDA0002762291100000036
Figure BDA0002762291100000037
C(θ 0 )＝diag{c(θ 0 )}，c(θ 0 )＝R T d(θ 0 )，
Figure BDA0002762291100000038
Figure BDA0002762291100000039
is a matrix S -1 The (l, k) -th block-blocked matrix of (l, k), which indicates a Hardmard product operation of Hadamard,
Figure BDA00027622911000000310
is a set of M multiplied by M wiener matrix,
Figure BDA00027622911000000311
is a set of complex matrices of dimension M x M,
Figure BDA00027622911000000312
is a set of complex matrices of dimension M x N,
Figure BDA00027622911000000313
is an M-dimensional complex vector space;
(6b) according to newton's method, let F (Δ τ) be ln Φ (Δ τ) at a given point
Figure BDA00027622911000000314
Nearby, approximating the taylor expansion for the first derivative of F (Δ τ) with respect to Δ τ is:
Figure BDA00027622911000000315
wherein
Figure BDA00027622911000000316
And
Figure BDA00027622911000000317
are each F (. DELTA.tau.) in
Figure BDA00027622911000000318
The first and second derivatives of (d); let F Δτ (Δ τ) ═ 0, found about
Figure BDA00027622911000000319
The estimation of (d) is:
Figure BDA00027622911000000320
(6c) dividing the whole search interval
Figure BDA00027622911000000321
Divided into Q sub-intervals, wherein each sub-interval constructed is of length
Figure BDA00027622911000000322
The midpoint of each subinterval is Δ τ i ；
(6d) At the midpoint of each subinterval Δ τ i As a given point
Figure BDA00027622911000000335
Obtaining a preliminary estimation value thereof according to (6b)
Figure BDA00027622911000000323
And judge
Figure BDA00027622911000000324
Whether or not within a sub-interval, i.e.
Figure BDA00027622911000000325
If yes, then estimate the value
Figure BDA00027622911000000326
If not, then estimate value
Figure BDA00027622911000000327
(6e) Respectively dividing the estimated values of Q sub-intervals
Figure BDA00027622911000000328
i 1, 2.. Q substitutes into the detection statistic
Figure BDA00027622911000000329
Calculating the function value and taking the value
Figure BDA00027622911000000330
Maximum function value
Figure BDA00027622911000000331
As an optimal solution;
(6f) according to the optimal solution
Figure BDA00027622911000000332
Obtaining the optimal objective function value
Figure BDA00027622911000000333
According to the optimal objective function value t NB And obtaining an improved interval search GLRT detection statistic y based on a Newton-like method:
Figure BDA00027622911000000334
(7) setting a detection threshold xi according to the actual situation, and comparing the detection statistic y with the detection threshold xi:
if upsilon > xi, the target is judged to exist, otherwise, the target is judged not to be detected.
Compared with the prior art, the invention has the following advantages:
firstly, the invention adopts the GLRT criterion of the generalized likelihood ratio test of the frequency diversity array multiple-input multiple-output FDA-MIMO radar to construct the statistic Λ of the generalized likelihood ratio test GLRT Thus, can be at a complex echo power beta 1 And realizing the self-adaptive detection of the target under the condition that the difference delta tau between the sampling time in each distance unit and the actual delay of the target and the clutter covariance matrix M are unknown.
Secondly, the invention adopts a frequency diversity array multiple-input multiple-output FDA-MIMO radar system, and compared with the self-adaptive target detection method of the radar of the traditional system, the target detection performance of the radar is effectively improved.
Thirdly, the invention improves the GLRT detection statistic based on the interval search by adopting the Newton method, thereby avoiding the detection performance loss caused by overlarge search interval span.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 shows the detection probability P of the present invention under different array element numbers d A plot against a plot of the variation of the signal to noise ratio SINR.
Detailed Description
The embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, constructing a signal y received by a frequency diversity array multiple-input multiple-output FDA-MIMO radar nth array element n (t,θ 0 )。
(1.1) for the frequency diversity array multiple-input multiple-output FDA-MIMO radar with the number of transmitting array elements being M and the number of receiving array elements being N, constructing the complex envelope of the signal received by the nth array element and transmitted by the mth array element as follows:
Figure BDA0002762291100000041
where E is the emitted electric field energy, T p For radar pulse duration, x m (t) is the transmit waveform of the mth array element, f m ＝f 0 + (M-1) Δ f, M is 1,2, …, M is carrier frequency of M-th array element, f 0 Is a reference carrier frequency, delta f is a frequency increment, j represents an imaginary number symbol, and e represents an exponential operation taking a base 2.7 as a base;
(1.2) results according to (1.1) at θ for an angle 0 A distance of R 0 The complex envelope of the signal received by the nth array element and transmitted by the mth array element is constructed as follows:
Figure BDA0002762291100000042
wherein the content of the first and second substances,
Figure BDA0002762291100000051
is the time delay of the back-and-forth propagation, beta is the complex echo power considering the transmission amplitude, phase, target reflectivity and channel propagation effect, d is the array element spacing, c is the lightAt the speed of the operation of the device,
Figure BDA0002762291100000052
actual time delay for the target;
(1.3) constructing a signal y received by the nth array element according to the result of (1.2) n (t,θ 0 ) Comprises the following steps:
Figure BDA0002762291100000053
wherein the content of the first and second substances,
Figure BDA0002762291100000054
is the reference carrier frequency.
And 2, constructing a frequency diversity array multi-input multi-output matching filter of the FDA-MIMO radar to obtain a sampling signal.
(2.1) passing the received signal
Figure BDA0002762291100000055
After mixing, constructing M sets of matched filters to process the signal of each receive channel, wherein the matched filter for the ith transmit waveform is designed as:
Figure BDA0002762291100000056
wherein, is the conjugate transpose operation;
(2.2) constructing a received signal of the nth array element matched by the l filter, and using f for the signal s Sampling at the sampling frequency B to obtain a sampling signal
Figure BDA0002762291100000057
Comprises the following steps:
Figure BDA0002762291100000058
wherein the content of the first and second substances,
Figure BDA0002762291100000059
b is the bandwidth of the baseband radar of the detection wave, and Delta tau is the sampling time t ＊ Actual delay tau from target in each range unit 0 The difference, i.e. Δ τ ═ t ＊ -τ 0 ,
Figure BDA00027622911000000510
Step 3, constructing equivalent total received signal y of frequency diversity array multiple-input multiple-output FDA-MIMO radar S 。
(3.1) constructing an emission guide vector a (delta tau) related to the target increment distance, which is expressed as follows:
Figure BDA00027622911000000511
wherein the content of the first and second substances,
Figure BDA00027622911000000512
representing an M-dimensional complex vector space, T representing a transposition operation;
(3.2) constructing a transmission steering vector d (theta) related to the target angle 0 ) Expressed as follows:
Figure BDA00027622911000000513
(3.3) constructing a transmitting guide vector a of the frequency diversity array multiple-input multiple-output FDA-MIMO radar by the results of (3.1) and (3.2) T (θ 0 Δ τ) as follows:
a T (θ 0 ,Δτ)＝[R T d(θ 0 )]⊙a(Δτ)，
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00027622911000000514
indicating a matched filter output matrix,. indicates a Hardmard product operation of Hadamard, T is a transpose operation;
(3.4) constructing a reception steering vector b (theta) related to the angle 0 ) Expressed as follows:
Figure BDA0002762291100000061
(3.5) constructing a virtual transceiving steering vector s (theta) of a target of the FDA-MIMO radar of the frequency diversity array multiple input multiple output according to the results of (3.3) and (3.4) 0 Δ τ) as follows:
Figure BDA0002762291100000062
wherein the content of the first and second substances,
Figure BDA0002762291100000063
representing Kronecker product operation;
(3.6) constructing an equivalent total received signal y S Expressed as follows:
y S ＝β 1 s(θ 0 ,Δτ)，
wherein the content of the first and second substances,
Figure BDA0002762291100000064
for the complex echo power after digital mixing, beta is the complex echo power taking into account the transmission amplitude, phase, target reflectivity and channel propagation effects, f 0 In order to refer to the carrier frequency,
Figure BDA0002762291100000065
the target actual delay.
And 4, constructing a binary hypothesis test problem.
(4.1) let a set of training samples be z q Q is 1,2, K is more than or equal to MN, wherein z belongs to C MN Representing an echo vector from a unit to be detected, K representing the pulse number, M representing the number of transmitting array elements, and N representing the number of receiving array elements;
(4.2) converting the detection problem into the following binary hypothesis testing problem according to the training sample:
Figure BDA0002762291100000066
wherein H 0 Hypothesis that target is absent, H 1 The hypothesis that the target is present in the cell to be detected, n and n q ∈C MN In order to satisfy independent same distribution condition and have zero mean complex Gaussian noise,
Figure BDA0002762291100000067
beta is the complex echo power;
(4.3) calculation of H 0 And H 1 Joint probability density function under assumption:
(4.3.1) calculation of H 0 Joint probability density function under the assumption:
Figure BDA0002762291100000068
wherein the content of the first and second substances,
Figure BDA0002762291100000069
(4.3.2) calculation of H 1 Joint probability density function under assumption:
Figure BDA00027622911000000610
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00027622911000000611
step 5, adopting a generalized likelihood ratio test GLRT rule of the frequency diversity array multiple-input multiple-output FDA-MIMO radar to construct a statistic Λ of the generalized likelihood ratio test GLRT 。
The optimal detector for the binary hypothesis testing problem in step 4 is the likelihood ratio test LRT, i.e. H, according to the Neyman-Pearson criterion 1 Likelihood function and H of data under hypothesis test 0 The ratio of the likelihood functions under the hypothesis test is compared to the detection threshold. However, fromAt complex echo power beta 1 The clutter covariance matrix M and the difference delta tau between the sampling time in each range unit and the actual delay of the target are unknown in practice, then the likelihood ratio test LRT can not be calculated, the generalized likelihood ratio test GLRT obtains the estimated value of the unknown parameter according to the maximum likelihood estimation on the basis of the likelihood ratio test LRT, and the problem that the target detection can not be carried out due to the unknown parameter can be solved.
The example tests GLRT criterion based on generalized likelihood ratio, according to (4.3.2) H 1 Joint probability density function g (z, z) under assumption 1 ,…,z K ∣β 1 ,Δτ,M；H 1 ) And (4.3.1) H 0 Joint probability density function g (z, z) under assumption 1 ,…,z K ∣M；H 0 ) The maximum likelihood ratio of (A), constructing a generalized likelihood ratio test statistic Λ GLRT Is represented as follows:
Figure BDA0002762291100000071
wherein the content of the first and second substances,
Figure BDA0002762291100000072
representing a tight set of all possible values that comprise the variable delta tau.
And 6, constructing improved interval search GLRT detection statistics based on a Newton-like method.
(6.1) constructing a statistic φ (Δ τ) containing the unknown parameter Δ τ:
(6.1.1) test statistic Λ for generalized likelihood ratio GLRT The numerator and denominator of (c) are maximized with respect to M, resulting in a test rule:
Figure BDA0002762291100000073
wherein the content of the first and second substances,
Figure BDA0002762291100000074
Figure BDA0002762291100000075
a complex matrix set is maintained for MN x MN,
Figure BDA0002762291100000076
represents a conjugate transpose operation;
(6.1.2) denominator of the checking rule with respect to the complex echo power β 1 Minimization, the test rule is equivalent to:
Figure BDA0002762291100000077
wherein the content of the first and second substances,
Figure BDA0002762291100000078
(6.1.3) the molecules of φ (Δ τ) are further expressed:
Figure BDA0002762291100000079
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00027622911000000710
c(θ 0 )＝R T d(θ 0 )；
(6.1.4) the denominator of φ (Δ τ) is further expressed as follows:
Figure BDA00027622911000000711
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002762291100000081
C(θ 0 )＝diag{c(θ 0 )}，
Figure BDA0002762291100000082
Figure BDA0002762291100000083
is a matrix S -1 (l, k) th block division of (C)The matrix of the blocks is a matrix of blocks,
Figure BDA0002762291100000084
is a set of M multiplied by M wierie matrices,
Figure BDA0002762291100000085
a M multiplied by M dimension complex matrix set is obtained;
(6.1.5) construct the statistic φ (Δ τ) according to (6.1.3) and (6.1.4):
Figure BDA0002762291100000086
(6.2) according to Newton's method, let F (Delta tau) be ln phi (Delta tau), at a given point
Figure BDA0002762291100000087
In the vicinity, the first derivative approximation taylor expansion of F (Δ τ) with respect to Δ τ is:
Figure BDA0002762291100000088
wherein
Figure BDA0002762291100000089
And
Figure BDA00027622911000000810
are each F (. DELTA.t) in
Figure BDA00027622911000000811
The first and second derivatives of (d); let F Δτ (Δ τ) ═ 0, found about
Figure BDA00027622911000000812
The estimation of (d) is:
Figure BDA00027622911000000813
(6.3) dividing the entire search space
Figure BDA00027622911000000814
Divided into Q sub-intervals, whichEach subinterval of the structure of (1) has a length of
Figure BDA00027622911000000815
The midpoint of each subinterval is Δ τ i ，
Figure BDA00027622911000000816
i＝1,…,Q，f s Is the sampling frequency;
(6.4) at the midpoint of each subinterval, Δ τ i As a given point
Figure BDA00027622911000000817
Obtaining a preliminary estimate thereof according to (6.2)
Figure BDA00027622911000000818
And make a judgment on
Figure BDA00027622911000000819
Whether or not to lie in a sub-interval
Figure BDA00027622911000000820
Internal:
if yes, then estimate the value
Figure BDA00027622911000000821
If not, then estimate the value
Figure BDA00027622911000000822
(6.5) separately estimating the Q sub-intervals
Figure BDA00027622911000000823
Substituting i-1, 2, Q into the detection statistic
Figure BDA00027622911000000824
Calculating the function value and taking the value
Figure BDA00027622911000000825
Maximum function value
Figure BDA00027622911000000826
As an optimal solution;
(6.6) according to the optimal solution
Figure BDA00027622911000000827
Obtaining the optimal objective function value
Figure BDA00027622911000000828
(6.7) based on the optimal objective function value t NB The modified interval search GLRT detection statistic y based on newton-like method was obtained, and is represented as follows:
Figure BDA00027622911000000829
wherein the content of the first and second substances,
Figure BDA00027622911000000830
z∈C MN representing an echo vector from a unit to be detected;
step 7, setting a detection threshold xi according to the actual situation, and comparing the detection statistic γ with the detection threshold xi:
if γ > ξ, the target is judged to be present, otherwise, the target is judged not to be detected.
The effect of the present invention will be further described with reference to the simulation diagram.
1. The simulation parameters are shown in table 1:
TABLE 1 FDA-MIMO Radar System simulation parameters
Figure BDA0002762291100000091
2. Simulation conditions
The interference is set to be zero mean value complex Gaussian distribution, and the cyclic symmetry characteristic is met;
let the interference covariance matrix be
Figure BDA0002762291100000092
Wherein, C m,n ＝0.9 |m-n| ，
Figure BDA0002762291100000093
And
Figure BDA0002762291100000094
respectively noise and clutter power, and I is a unit array;
let the noise-to-noise ratio CNR be calculated as
Figure BDA0002762291100000095
Probability of false alarm P fa Is equal to 10 -4 In accordance with the need
Figure BDA0002762291100000096
Setting a threshold by a sub-Monte Carlo experiment;
targeting a signal to interference and noise ratio of
Figure BDA0002762291100000097
Calculating the detection probability P by using 1000 Monte Carlo experiments d ；
After the target distance information is confirmed, namely under the condition that the difference delta tau between the sampling time in each distance unit and the actual delay of the target is a confirmed parameter, the statistic lambda of the standard detection method is constructed ben Comprises the following steps:
Figure BDA0002762291100000098
where a (Δ τ) is the emission guide vector associated with the target incremental distance,
Figure BDA0002762291100000099
z∈C MN representing an echo vector from a unit to be detected;
Figure BDA00027622911000000910
Figure BDA00027622911000000911
C(θ 0 )＝diag{c(θ 0 )}，c(θ 0 )＝R T d(θ 0 )，
Figure BDA00027622911000000912
is a matrix S -1 The (l, k) -th block partitioning matrix of (a),
Figure BDA00027622911000000913
is a set of M multiplied by M wiener matrix,
Figure BDA00027622911000000914
is a set of complex matrices of dimension M x M,
Figure BDA00027622911000000915
is a set of complex matrices of dimension M x N,
Figure BDA00027622911000000916
is an M-dimensional complex vector space, and is,
Figure BDA00027622911000000917
representing a conjugate transpose operation.
3. Simulation content and result analysis:
under the simulation parameters and the simulation conditions, the detection method and the standard detection method of the invention are compared in a simulation mode, and the result is shown in fig. 2.
The results from fig. 2 show that: probability of detection P d Increases as the target signal to interference plus noise ratio SINR increases. With the increase of the number of the array elements, the detection performance of the detection method based on the Newton-like method for improving the interval search is improved. The detection performance of the detection method based on the Newton-like method for improving the interval search is consistent with that of a standard detection method. The simulation result highlights that the detection method provided by the invention has better target detection effect.

Claims (10)

1. An adaptive target detection method for a frequency diversity array MIMO radar, comprising:
(1) performing matched filtering processing on the signal of each channel of the frequency diversity array multiple-input multiple-output FDA-MIMO radar in a mode of synchronous digital mixing and matched filtering;
(2) constructing an emission guide vector a (delta tau) related to the target increment distance, and constructing an emission guide vector d (theta tau) related to the target angle 0 ) Constructing a transmitting guide vector a of the frequency diversity array multi-input multi-output FDA-MIMO radar T (θ 0 Δ τ), where Δ τ is the difference between the sample time and the actual delay of the target in each range bin, θ 0 Is the angle of the far field target;
(3) constructing a reception steering vector b (theta) related to an angle 0 )；
(4) Constructing virtual transmit-receive steering vector s (theta) of target of frequency diversity array multi-input multi-output FDA-MIMO radar 0 Δ τ); according to the guide vector s (theta) 0 Delta tau) to construct the equivalent total received signal y of the frequency diversity array multiple-input multiple-output FDA-MIMO radar target S ；
(5) Adopting the GLRT criterion of the generalized likelihood ratio test of the frequency diversity array multiple-input multiple-output FDA-MIMO radar to construct the statistic Λ of the generalized likelihood ratio test GLRT ：
(5a) Let a set of training samples be z q Q 1, 2.. K, where z e C MN Representing the echo vector from the unit to be detected, K representing the pulse number, K being more than or equal to MN, M being the number of transmitting array elements, N being the number of receiving array elements,
Figure FDA0003734785450000015
a complex vector space is maintained for MN; the detection problem is converted into the following binary hypothesis testing problem according to the training sample:
Figure FDA0003734785450000011
wherein H 0 Representing objectsHypothesis of absence, H 1 The hypothesis that the target is present in the cell to be detected, n and n q ∈C MN In order to satisfy the zero-mean complex Gaussian noise with independent and same distribution condition,
Figure FDA0003734785450000016
，β 1 complex echo power after digital mixing;
(5b) respectively calculating the joint probability density function under two assumptions to obtain the probability density function at H 0 The joint probability density function under the assumption is g (z, z) 1 ,…,z K ∣Σ；H 0 ) In H 1 The joint probability density function under the assumption is g (z, z) 1 ,…,z K ∣β 1 ,Δτ,Σ；H 1 ) Wherein
Figure FDA0003734785450000012
Is a positive-definite clutter covariance matrix,
Figure FDA0003734785450000013
a complex matrix set is constructed by MN multiplied by MN;
(5c) the statistics of the generalized likelihood ratio test GLRT are constructed as follows:
Figure FDA0003734785450000014
wherein the content of the first and second substances,
Figure FDA0003734785450000017
represents a tight set containing all possible values of the variable Δ τ;
(6) constructing improved interval search GLRT detection statistics based on a Newton-like method:
(6a) constructing a statistic φ (Δ τ) containing the unknown parameter Δ τ:
testing statistic Λ for generalized likelihood ratio GLRT The numerator and denominator of (c) are maximized with respect to M, resulting in a test rule:
Figure FDA0003734785450000021
wherein the content of the first and second substances,
Figure FDA0003734785450000022
represents a conjugate transpose operation;
denominator of checking rule with respect to beta 1 Minimization, the verification rule is equivalent to:
Figure FDA0003734785450000023
wherein the content of the first and second substances,
Figure FDA0003734785450000024
for the detection statistics to be based on an interval search,
Figure FDA0003734785450000025
Figure FDA0003734785450000026
C(θ 0 )＝diag{c(θ 0 )}，c(θ 0 )＝R T d(θ 0 )，
Figure FDA0003734785450000027
is a matrix S -1 The (l, k) th block blocking matrix of which indicates a hadamard product operation,
Figure FDA0003734785450000028
is a set of M multiplied by M wierie matrices,
Figure FDA0003734785450000029
is a set of complex matrices of dimension M x M,
Figure FDA00037347854500000210
is a M x N dimensional complex matrixIn the collection of the images, the image data is collected,
Figure FDA00037347854500000211
is an M-dimensional complex vector space;
(6b) according to newton's method, let F (Δ τ) be ln Φ (Δ τ) at a given point
Figure FDA00037347854500000212
In the vicinity, the first derivative approximation taylor expansion of F (Δ τ) with respect to Δ τ is:
Figure FDA00037347854500000213
wherein
Figure FDA00037347854500000214
And
Figure FDA00037347854500000215
are each F (. DELTA.t) in
Figure FDA00037347854500000216
The first and second derivatives of (a); let F Δτ (Δ τ) ═ 0, found about
Figure FDA00037347854500000217
The estimation of (d) is:
Figure FDA00037347854500000218
(6c) dividing the whole search interval
Figure FDA00037347854500000219
Divided into Q sub-intervals, wherein each sub-interval constructed is of length
Figure FDA00037347854500000220
The midpoint of each subinterval is Δ τ i ；
(6d) At the midpoint of each subinterval Δ τ i As a given point Δ τ, based on(6b) Obtaining a preliminary estimate thereof
Figure FDA00037347854500000221
And judge
Figure FDA00037347854500000222
Whether or not within a sub-interval, i.e.
Figure FDA00037347854500000223
If yes, then estimate the value
Figure FDA00037347854500000224
If not, then estimate the value
Figure FDA00037347854500000225
(6e) Respectively dividing the estimated values of Q sub-intervals
Figure FDA00037347854500000226
Substituting detection statistics
Figure FDA00037347854500000227
Calculating the function value and taking the value
Figure FDA00037347854500000228
Maximum function value
Figure FDA00037347854500000229
As an optimal solution;
(6f) according to the optimal solution
Figure FDA00037347854500000230
Obtaining the optimal objective function value
Figure FDA00037347854500000231
According to the optimal objective function value t NB Obtaining an improved interval search based on the Newton-like methodThe soglrt detection statistic γ:
Figure FDA00037347854500000232
(7) setting a detection threshold xi according to the actual situation, and comparing the detection statistic y with the detection threshold xi:
if γ > ξ, the target is judged to be present, otherwise, the target is judged not to be detected.
2. The method of claim 1, wherein the matched filtering process is performed on the signals of each channel of the frequency diversity array MIMO-FDA radar in (1) as follows:
(1a) the method comprises the following steps of constructing a complex envelope of a signal which is received by the nth array element of the frequency diversity array and transmitted by the mth array element of the FDA-MIMO radar:
Figure FDA0003734785450000031
where E is the emitted electric field energy, T p For radar pulse duration, x m (t) the transmit waveform of the m-th array element, f m ＝f 0 + (M-1) Δ f, M is 1,2, …, M is carrier frequency of M-th array element, f 0 The reference carrier frequency is delta f is frequency increment, j represents imaginary number symbol, pi represents circumference ratio, and e represents exponential operation taking 2.7 as base;
(1b) for an angle at theta 0 A distance of R 0 The complex envelope of the signal received by the nth array element and transmitted by the mth array element is constructed as follows:
Figure FDA0003734785450000032
wherein the content of the first and second substances,
Figure FDA0003734785450000033
is the time delay of the back-and-forth propagation, beta is the complex echo power considering the transmission amplitude, phase, target reflectivity and channel propagation effect, d is the array element spacing, c is the speed of light,
Figure FDA0003734785450000034
actual time delay for the target;
(1c) constructing a signal y received by the nth array element n (t,θ 0 ) Comprises the following steps:
Figure FDA0003734785450000035
wherein the content of the first and second substances,
Figure FDA0003734785450000036
is a reference carrier frequency;
(1d) after the received signal passes through
Figure FDA0003734785450000037
After mixing, constructing M sets of matched filters to process the signal of each receive channel, wherein the matched filter for the ith transmit waveform is designed as:
Figure FDA0003734785450000038
wherein, is a conjugate transpose operation;
(1e) constructing a received signal of the nth array element matched by the first filter, and using f for the signal s Sampling at the sampling frequency B to obtain a sampling signal
Figure FDA0003734785450000039
Comprises the following steps:
Figure FDA00037347854500000310
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00037347854500000311
b is the bandwidth of the baseband radar of the detection wave, and Delta tau is the sampling time t ★ Actual delay tau from target in each range unit 0 A difference of
Figure FDA00037347854500000312
3. The method of claim 1, wherein: (2) the emission guide vector a (Δ τ) related to the target increment distance constructed in (1) is expressed as follows:
Figure FDA0003734785450000041
where Δ f is the frequency increment, e represents the exponentiation with base 2.7, j represents the imaginary symbol, and T is the transposition operation.
4. The method of claim 1, wherein: (2) the emission guide vector d (theta) related to the target angle constructed in (A) 0 ) Expressed as follows:
Figure FDA0003734785450000042
wherein d is the array element spacing, c is the speed of light, f 0 In order to refer to the carrier frequency,
Figure FDA0003734785450000043
is the reference carrier frequency, e denotes the base 2.7 exponentiation, j denotes the imaginary symbol, and T is the transpose operation.
5. The method of claim 1, wherein: (2) the transmission steering vector a constructed in T (θ 0 Δ τ) as follows:
a T (θ 0 ,Δτ)＝[R T d(θ 0 )]⊙a(Δτ)，
wherein the content of the first and second substances,
Figure FDA0003734785450000044
indicating a matched filter output matrix,. indicates a hadmard product operation, T is a transpose operation.
6. The method of claim 1, wherein: (3) the received steering vector b (theta) related to the target angle constructed in (1) 0 ) Expressed as follows:
Figure FDA0003734785450000045
wherein d is the array element spacing, c is the speed of light,
Figure FDA0003734785450000046
is an N-dimensional complex vector space, f 0 In order to refer to the carrier frequency,
Figure FDA0003734785450000047
is the reference carrier frequency, e denotes the base 2.7 exponentiation, j denotes the imaginary symbol, and T is the transpose operation.
7. The method of claim 1, wherein: (4) virtual transmit-receive steering vector s (theta) constructed in (1) 0 Δ τ) as follows:
Figure FDA0003734785450000048
wherein the content of the first and second substances,
Figure FDA0003734785450000051
representing Kronecker product operation.
8. The method of claim 1, wherein: (4) the equivalent total received signal y constructed in S Expressed as follows:
y S ＝β 1 s(θ 0 ,Δτ)，
wherein the content of the first and second substances,
Figure FDA0003734785450000052
for the complex echo power after digital mixing, beta is the complex echo power taking into account the transmission amplitude, phase, target reflectivity and channel propagation effects, f 0 In order to refer to the carrier frequency,
Figure FDA0003734785450000053
to target the actual delay, e represents the base 2.7 exponential operation and j represents the imaginary symbol.
9. The method of claim 1, wherein: (5b) h constructed in 0 Joint probability density function g (z, z) under assumption 1 ,…,z K ∣M；H 0 ) Expressed as follows:
Figure FDA0003734785450000054
wherein the content of the first and second substances,
Figure FDA0003734785450000055
tr denotes a matrix trace-finding operation.
10. The method of claim 1, wherein: (5b) h constructed in 1 Joint probability density function g (z, z) under assumption 1 ,…,z K ∣β 1 ,Δτ,M；H 1 ) Expressed as follows:
Figure FDA0003734785450000056
wherein the content of the first and second substances,
Figure FDA0003734785450000057
tr denotes a matrix trace-finding operation.
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