CN115685081A

CN115685081A - GLRT-based distance extension target detection method under interference plus noise background

Info

Publication number: CN115685081A
Application number: CN202211404265.9A
Authority: CN
Inventors: 魏广芬; 刘旭; 简涛; 周战; 田华飞; 罗沅; 朱智林
Original assignee: Shandong Technology and Business University
Current assignee: Shandong Technology and Business University
Priority date: 2022-11-10
Filing date: 2022-11-10
Publication date: 2023-02-03
Anticipated expiration: 2042-11-10
Also published as: CN115685081B

Abstract

The invention belongs to the technical field of radar signal processing, and particularly relates to a method for detecting a distance extension target under an interference plus noise background based on GLRT. Modeling both the target and the interference as signals with unknown coordinates in a known subspace, and the target signal subspace being contained in the interference signal subspace; estimating an interference covariance matrix by utilizing a group of auxiliary data containing interference and noise, transforming an interference matrix structure by adopting a square root decomposition method, further solving a maximum likelihood estimation of the interference coordinate covariance matrix, noise power and a target signal coordinate, and establishing a generalized likelihood ratio test detector for distance extension target detection based on a one-step method design strategy. Simulation analysis shows that the method can effectively inhibit subspace interference signals with different powers under the background of interference and unknown noise related to target signals.

Description

GLRT-based distance extension target detection method under interference plus noise background

Technical Field

The invention belongs to the technical field of radar signal processing, and particularly relates to a method for detecting a distance extension target under an interference plus noise background based on GLRT.

Background

The high-range-resolution radar has the advantages of large bandwidth, high range resolution, and obvious advantages in the aspects of accurate detection, imaging, target identification and the like, and becomes an important direction of the development of modern radars. The target echo signal of the traditional low range resolution radar only occupies one range unit and is often treated as a 'point target'. Unlike "point targets," the echo signals of a common high range resolution radar target not only occupy only one range bin, but are distributed among different radial range bins, forming "range extension targets. With the wide application of the broadband technology in the radar field, the problem of adaptive detection of a range-extended target is receiving more and more attention, and becomes one of the hot spots and difficult problems in the radar signal processing field in recent years.

The distance extended target detection research under the background of gaussian noise is relatively extensive, a target detection method based on the detection criteria of Generalized Likelihood Ratio Test (GLRT), rao, wald and the like has been formed, and some improved methods have been further developed. For example, to fully utilize prior information of the density distribution of target scattering points, a GLRT detector based on spatial scattering density is provided; for range-extended target detection on gaussian noise background with unknown covariance matrix, some documents derive a Modified (MGLRT) detector, and analyze that the detector has a bounded Constant False Alarm Rate (CFAR) characteristic. Such modeling of gaussian noise background for radar receivers has become a fundamental assumption for the problem of target detection.

The wide attention and application of electronic interference measures in modern wars further promote the design and research heat of high-performance distance extension target detectors under the interference background. Researchers develop a series of research works aiming at the design of a distance expansion target detector under the noise plus interference background from the aspects of one-step or two-step design strategies, different covariance matrix structure analysis, known or unknown noise power conditions, known or unknown interference matrixes and the like, and obtain modeling strategies and detection methods of various backgrounds. These studies also fully demonstrate that the accuracy of the range-extended target detector can be effectively improved using the prior information of the interference matrix and noise.

However, the actual interference information and noise power are usually unknown and vary in real time, and it is difficult to obtain accurate a priori information of the actual interference information and the noise power and corresponding target detectors. Therefore, a further study is undertaken to address the problem of structured subspace interference, i.e. the problem of target detection where the interference and target are modeled as subspace signals and constrained to be in a known subspace, but with unknown subspace coordinates. The structured subspace interference can be divided into two cases, interference not related to the target signal and interference related to the target signal, according to the degree of correlation between the interference signal and the target signal. The interference caused by the target signal by the unconscious communication signal, the sidelobe target, the multi-path multi-angle interference and the like is generally classified as the interference irrelevant to the target signal, and the research attention of the target detection problem under the background of the interference is high from the published literature. The interference situation caused by backscattering of obstacles in the irradiation region on the target signal is classified as the background of interference related to the target signal compared with interference unrelated to the target signal, and the target detection problem of such interference related to the target signal needs to be further paid attention and researched.

Disclosure of Invention

In order to overcome the problems in the prior art, the invention provides a method for detecting a distance extension target under an interference plus noise background based on GLRT.

The technical scheme for solving the technical problems is as follows:

a method for detecting a distance extension target under an interference plus noise background based on GLRT comprises the following steps:

step 1, acquiring data to be detected from K distance units to be detected as main data, and acquiring M observation data without target signals from a target-free distance unit adjacent to the detected unit as auxiliary data; performing subspace modeling on a target signal and an interference signal, modeling noise into complex Gaussian distribution with unknown noise power, and establishing a binary hypothesis test model, wherein the target signal subspace is contained in an interference signal subspace; constructing a joint probability density function of the main data and the auxiliary data based on a binary hypothesis test model;

step 2, carrying out maximum likelihood estimation on unknown parameters in the joint probability density function, and constructing detection statistics lambda of a distance expansion target subspace detector under an interference plus noise background based on a GLRT (generalized likelihood ratio test) test criterion _SRD-GLRT ；

Step 3, setting a detection threshold T according to the preset false alarm probability _G (ii) a Will detect the statistic lambda _SRD-GLRT And a detection threshold T _G Making a comparison if λ _SRD-GLRT ≥T _G Judging that distance expansion targets exist in the current K distance units to be detected; otherwise if lambda is _SRD-GLRT <T _G And judging that the current K distance units to be detected have no distance expansion targets.

Further, the step 1 performs subspace modeling on the target signal and the interference signal, models noise as complex gaussian distribution with unknown noise power, and establishes a binary hypothesis test model, which specifically includes:

wherein H ₀ Representing the assumption that there is no target signal, H ₁ Representing an assumption of a target signal; the main data to be detected is represented as x ₁ ,x ₂ ,…,x _k ,…,x _K ]M observations are denoted by [ y ] ₁ ,y ₂ ,…,y _m ,…,y _M ]；

For the target signal of the kth range bin, S is a known N x p-dimensional column full-rank complex matrix, p _k Is an unknown p × 1-dimensional signal coordinate vector;

j is a full-rank complex matrix of Nxq dimension columns, q is an interference signal of the kth distance unit _k Is an unknown q x 1-dimensional interference coordinate vector, p is a target signal subspace dimension, and q is an interference subspace dimension; n is _k As noise component, noise component n _k Independently and equally distributed among different distance units; jq _m Interference signals for M auxiliary data, n _m Is the noise component of M auxiliary data, where q _m 、n _m Are each independently of q _k 、n _k Independently and equally distributed.

Further, in step 1, based on a binary hypothesis testing model, a joint probability density function of the main data and the auxiliary data is constructed:

wherein i =0,1 corresponds to the hypothesis H without the target signal, respectively ₀ And hypothesis H with target signal ₁ Sigma is an unknown qxq dimensional interference coordinate covariance matrix; c is a dry noise covariance matrix, J is an interference matrix, σ ² For unknown noise power, I _N Representing an N-dimensional identity matrix; tr represents the trace of the matrix; | represents the determinant of the matrix, (-) ^H The representation represents the conjugate transpose of the matrix.

Further, the step 2 specifically includes the following steps:

step 2-1: transforming the interference matrix J structure by adopting a square root decomposition method, and carrying out logarithm operation on the transformed joint probability density function to obtain a joint probability density function in a logarithm form;

step 2-2: carrying out maximum likelihood estimation on an interference coordinate covariance matrix, noise power and a target coordinate in a combined probability density function in a logarithmic form;

step 2-3: the maximum likelihood estimator of the target coordinate, the converted interference coordinate covariance estimator and the estimator of the noise power are substituted back to the joint probability density function to obtain the detection system of the distance extension target subspace detector under the interference plus noise backgroundMeasuring lambda _SRD-GLRT 。

Further, in the step 2-1, a square root decomposition method is adopted to transform the structure of the interference matrix J, and the method specifically comprises the following steps:

J ^H J＝LL ^H

wherein L is J ^H The q × q dimension of J is a lower triangular matrix.

Further, the detection statistic λ of the distance-extended target subspace detector under the interference plus noise background in the step 2-3 _SRD-GLRT ：

In the above formula, the first and second carbon atoms are,

compared with the prior art, the invention has the following technical effects:

(1) The invention assumes that a target signal subspace is contained in an interference signal subspace, thereby representing the correlation between a target signal and an interference signal and establishing a subspace-based distance extension target signal model under the condition of interference plus unknown noise;

(2) Based on GLRT criterion, the constant false alarm rate characteristic is ensured, and meanwhile, a square root decomposition method is adopted, so that the parameter estimation process is simplified, the detector construction efficiency is improved, and the method has wide potential popularization and application values.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions and advantages of the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is a schematic diagram of the CFAR characteristics of the SRD-GLRT detector of the present invention;

fig. 3 is a diagram illustrating the SRD-GLRT detection performance with respect to the target signal matrix dimension and the interference signal matrix dimension q when N =8, k =8, m =8, inr = 10db;

fig. 4 is a graph showing the relationship between the detection performance of the SRD-GLRT detector and the SINR and INR when N =8, k =8, p =2, q =3, and m = 16;

FIG. 5 is a graph showing the detection performance of the SRD-GLRT detector for different amounts of auxiliary data when N =8, p =2, q =3, and INR = 10dB;

fig. 6 is a graph showing comparison between the detection performance of the SRD-GLRT detector and that of the other detectors when K =8, p =2, inr =10 db.

Detailed Description

To further explain the technical means and effects of the present invention adopted to achieve the predetermined objects, the following detailed description of the embodiments, structures, features and effects of the technical solutions according to the present invention will be given with reference to the accompanying drawings and preferred embodiments. In the following description, different references to "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

Referring to fig. 1, the invention provides a method for detecting a distance extended target under an interference plus noise background based on GLRT, comprising the following steps:

step 1, acquiring data to be detected from K distance units to be detected as main data, and acquiring M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; performing subspace modeling on a target signal and an interference signal, modeling noise into complex Gaussian distribution with unknown noise power, and establishing a binary hypothesis test model, wherein the target signal subspace is contained in the interference signal subspace; constructing a joint probability density function of the main data and the auxiliary data based on a binary hypothesis test model;

step 2, carrying out maximum likelihood estimation on unknown parameters in the joint probability density function, and constructing detection statistics lambda of a distance expansion target subspace detector under an interference plus noise background based on a GLRT (generalized likelihood ratio test) criterion _SRD-GLRT ；

Step 3, setting a detection threshold T according to the preset false alarm probability _G (ii) a Comparing the detection statistic lambda with a detection threshold T _G Making a comparison as to λ _SRD-GLRT ≥T _G Judging that distance expansion targets exist in the current K distance units to be detected; otherwise if lambda is _SRD-GLRT <T _G And judging that the current K distance units to be detected have no distance expansion targets.

The following steps are detailed:

step 1, acquiring data to be detected from K distance units to be detected as main data, and acquiring M observation data without target signals from a target-free distance unit adjacent to the detected unit as auxiliary data; performing subspace modeling on a target signal, an interference signal and noise, and establishing a binary hypothesis test model, wherein the target signal is contained in the interference signal; and constructing a joint probability density function of the main data and the auxiliary data based on a binary hypothesis test model.

In some embodiments, this step may include the following sub-steps:

step 1-1: acquiring data to be detected from K distance units to be detected as main data, acquiring M observation data from a non-target distance unit adjacent to the detected unit as auxiliary data, performing subspace modeling on target signals and interference, and establishing a binary hypothesis test model, wherein the target signals are contained in the interference signals;

assuming that the receiver adopts a uniform linear array of N array elements and the target distance extension range is K distance units, the main data to be detected can be expressed as [ x ] ₁ ,x ₂ ,…,x _k ,…,x _K ]Wherein K =1,2, ·, K; selecting M observation data [ y ] without target signal in adjacent range unit ₁ ,y ₂ ,…,y _m ,…,y _M ]As auxiliary data, M =1, 2.., M, observation vectors of different range bins are statistically independent of each other. x is a radical of a fluorine atom _k And y _m All are Nx 1-dimensional complex vectors, and N represents the number of channels processed by the system; the target signal of the kth distance cell is denoted as Sp _k Is a known N x p dimension column full rank complex matrix, p _k Is an unknown p × 1-dimensional signal coordinate vector; the interference signal of the kth range bin is denoted as Jq _k J is an N × q dimensional column full-rank complex matrix, q _k Is an unknown q x 1-dimensional interference coordinate vector, assuming p + q ≦ N, and q _k Obeying complex Gaussian distribution with unknown mean value as a zero covariance matrix as sigma, wherein the sigma is an unknown q multiplied by q dimensional interference coordinate covariance matrix, p is a target signal subspace dimension, and q is an interference subspace dimension; noise component n _k Are independently and identically distributed among different distance units, and the covariance matrix subject to mean value being zero is sigma ² I _N In which I is _N Representing an N-dimensional identity matrix, σ ² Unknown noise power.

Assume that M auxiliary data [ y ] are employed ₁ ,y ₂ ,…,y _m ,…,y _M ]Containing interference signals Jq _m And noise n _m Wherein q is _m 、n _m Are each independently of q _k 、n _k Independently and equally distributed.

Assuming a target signal subspace<S>Involving in interfering subspaces<J>In, is marked as

The corresponding matrix dimension satisfies the relation p ≦ q, so as to represent the correlation between the target signal and the interference signal.

According to the above assumptions, the problem of detecting a distance extended target in a subspace interference plus unknown noise environment can be expressed as a binary hypothesis test for determining whether a target exists in data to be detected:

wherein H ₀ Indicating the assumption that there is no target signal, H ₁ Indicating the assumption of the presence of the target signal.

From the above description, the noise power σ ² Target coordinate p _k The interference coordinate covariance matrix Σ is unknown, and the interference signals and noise in different range cells are independent of each other.

Step 1-2: constructing a joint probability density function of the main data and the auxiliary data based on a binary hypothesis test model;

assuming that interference signals and noises between the K range cells are independent of each other, the frequency of the interference signals and noises are H ₀ And H ₁ Two assumptions the joint Probability Density Function (PDF) of the main and auxiliary data is expressed as:

wherein i =0,1 corresponds to the hypothesis H, respectively ₀ And H ₁ The symbol "H" denotes the conjugate transpose of the matrix, and the dry-noise covariance C is C = J Σ J ^H +σ ² I _N And | C | represents the determinant of C, C ^-1 Represents the inverse of C. According to the conversion relation y of vector inner product and matrix trace ^H C ^-1 y＝tr(C ^-1 yy ^H ) Let us order

T _i ＝S _i +S _M ,i＝0,1 (5)

The joint PDF of the main data and the auxiliary data shown in equation (2) is simplified as:

thus, the unknown noise power σ ² Distance extension target GLRT detection statistic lambda under condition of covariance matrix sigma of sum interference coordinates _SRD-GLRT Can be expressed as:

in the formula, T _G Is the detection threshold for a given false alarm probability.

Step 2, carrying out maximum likelihood estimation on unknown parameters in the joint probability density function, and constructing detection statistics lambda of the distance expansion target subspace detector under the interference plus noise background _SRD-GLRT ；

As shown in step 1, the unknown parameters in the joint probability density function include: noise power σ ² Target coordinate p _k The interference co-ordinate covariance matrix sigma, and thus the noise power σ in said joint probability density function ² Target coordinate p _k And performing maximum likelihood estimation on the interference coordinate covariance matrix sigma.

In some embodiments, this step may include the following sub-steps:

step 2-1: transforming the interference matrix structure by adopting a square root decomposition method, and carrying out logarithm operation on the transformed joint probability density function to obtain a joint probability density function in a logarithm form;

due to N>And q, the interference matrix J is a rectangular matrix, and an inverse matrix does not exist, so that the subsequent solving process is complicated, and the solved unknown parameter estimator is complex in form. In order to reduce the calculated amount of solving the maximum unknown parameters, a square root decomposition method is introduced, and J is ^H The J matrix is represented as LL by square root decomposition ^H Wherein L is J ^H The q × q dimension of J is a lower triangular matrix, i.e. J ^H J＝LL ^H . The square root decomposition is also called Cholesky decomposition, and the inverse of the matrix is easier to solve directly by using the decomposed small matrix, so that the matrix calculation amount is simplified, and the calculation amount for solving and maximizing unknown parameters is reduced.

By means of square root decomposition, an unknown parameter matrix Q = sigma is defined ^-2 L ^H Σ L, the corresponding covariance matrix Σ obeyed by the interference coordinates may be expressed as Σ = σ ² (L ^H ) ^-1 QL ^-1 . According to

Determinant re-expression of the interference covariance matrix C as

|C|＝σ ^2N |J(L ^H ) ^-1 QL ^-1 J ^H +I _N |＝σ ^2N |QL ^-1 J ^H J(L ^H ) ^-1 +I _q |＝σ ^2N |I _q +Q| (8)

Wherein, | I _N +A _N×q B _q×N |＝|I _q +B _q×N A _N×q In the formula, J (L) ^H ) ^-1 ＝A，QL ^-1 J ^H ＝B；J(L ^H ) ^-1 Is an Nxq dimensional matrix, QL ^-1 J ^H Is a q x N dimensional matrix.

The inverse of the interference covariance matrix C is transformed and then re-expressed as

In the formula, P _J ^⊥ ＝I _N -P _J ，P _J ＝J(J ^H J) ^-1 J ^H Representing a projection matrix on the interference subspace. Accordingly, related to C in formula (6) ^-1 The following can be simplified:

in the formula, Z _i ＝L ^-1 J ^H T _i J(L ^H ) ^-1 ，i＝0,1。

Further, since the target signal subspace is contained within the interference signal subspace, i.e., exists

In the above formula

Can be simplified as follows:

from the above equation, under the assumption that the target signal subspace is covered by the interference signal subspace, there is

The expression (8), the expression (9) and the expression (10) are substituted for the expression (6), and the logarithm operation is further performed to obtain

Step 2-2: for Q and noise power sigma in combined probability density function of logarithm form ² And target coordinates p _k Carrying out maximum likelihood estimation;

according to the equation (12), Q is solved for H by the maximum likelihood estimation method ₀ And H ₁ Assumed maximum likelihood estimation

And with

And noise power σ ² At H ₀ And H ₁ Assumed maximum likelihood estimation

And with

As can be seen from formula (11), in formula (13)

This may indicate that the noise power is independent of the design of the detector. The estimated value to be solved

And noise power estimate

Can be substituted by the formula (7) to obtain

And simplifying the formula, and solving the maximum likelihood estimation value of the target parameter.

Let J _L ＝J(L ^H ) ^-1 Then | L ^-1 J ^H T _i J(L ^H ) ^-1 L can be simplified as:

the formula is further simplified as follows:

wherein W = J _L (J _L ^H S _M J _L ) ^-1 J _L ^H ，J _L ＝J(L ^H ) ^-1 . By substituting equations (15) and (16) back to equation (14), an expression in which only the target coordinate parameter is unknown can be obtained:

p in the denominator part within the ln function is corrected according to equation (17) _k Obtaining an extreme value to obtain a target coordinate p _k The maximum likelihood estimate of (c) is:

step 2-3: estimating maximum likelihood of target coordinate

Transformed interference coordinate covariance estimator

Estimation of noise power

The combined probability density function (2) is substituted back to obtain the detection statistic lambda of the SRD-GLRT detector based on the GLRT criterion _SRD-GLRT

Wherein, the first and the second end of the pipe are connected with each other,

step 3, setting a detection threshold T according to the preset false alarm probability _G (ii) a Will detect the statistic lambda _SRD-GLRT And a detection threshold T _G Making a comparison if λ _SRD-GLRT ≥T _G Judging that distance expansion targets exist in the current K distance units to be detected; whereas if lambda is _SRD-GLRT <T _G And judging that the current K distance units to be detected have no distance expansion targets.

The CFAR characteristic of the SRD-GLRT detector on the joint covariance matrix C of the interference signal and the noise is proved to be as follows:

for ease of analysis, define:

can obtain X _J And Y _J The distribution of (A) is as follows:

wherein R = J ^H And (CJ). Order to

Detecting λ in statistics ₁ ,λ ₂ Can be rewritten as:

proving of lambda _SRD-GLRT At H ₀ Assuming that R has CFAR characteristics, it needs to be verified

And

independent of the transformed dry noise covariance R.

(1) Authentication

At H ₀ Is assumed to be independent of R

By taking advantage of the nature of the whitening transformation,

can be written as:

in the formula, X _RJ ＝R ^-1/2 X _J ，Y _RJ ＝R ^-1/2 Y _J ；

Pair of representations

The whitening transformation of (2). Further, X can be obtained _RJ Covariance matrix of (2):

from the above formula, in H ₀ Suppose lower X _RJ Each column in (a) is subject to a zero mean covariance matrix of I _q A complex gaussian vector of (a). At the same time, G ₀ Obeying the degree of freedom as M and the covariance matrix as I _q The N-dimensional complex center weixate distribution of (a). In this way, it can be seen that,

at H ₀ Let it be independent of R.

(2) Authentication

At H ₀ Is assumed to be independent of R

First is to

Performing a whitening transformation may result in:

in the formula

Further doing unitary transformation to the above equation can get:

in the formula, UU ^H ＝I _N U denotes a unitary matrix; x _URJ ＝U ^H X _RJ 、G＝U ^H G ₀ U represents X respectively _RJ 、G ₀ A matrix after unitary transformation; in addition, the first and second substrates are,

description of the preferred embodiments _UR Independent of the transformed covariance matrix R. From equation (27), it can be found that, under the assumption, X _URJ And X _RJ G and G ₀ Are statistically equivalent, so X _URJ G in H ₀ Provided that it is independent of R.

General analysis, H ₀ Let us assume lower λ _SRD-GLRT I.e., C, i.e., the SRD-GLRT detector has CFAR properties on the joint covariance matrix C of the interfering signal and noise.

According to the invention, the situation of target signal mismatch exists according to an actual target detection scene, the interference situation is complex, the relation between the interference situation and the target signal is not only expressed as orthogonality and equality, but also expressed as general correlation interference with the signal, therefore, the target signal subspace is assumed to be<S>Included in an interference subspace<J>In, is marked as

The corresponding matrix dimension satisfies the relation p<And q, representing the correlation between the target signal and the interference signal, and establishing a subspace-based distance extension target signal model under the interference plus unknown noise. Based on GLRT criterion, the distance extended target detection of the distance extended target subspace detector under the interference plus noise background is deduced, the constant false alarm rate characteristic is ensured, meanwhile, the square root decomposition method is adopted, the parameter estimation process is simplified, the detector construction efficiency is improved, and the method has wide potential popularization and application values.

The effect of the invention can be illustrated by the following simulation experiments:

and (3) analyzing an experimental result:

as can be seen from fig. 2, the interference coordinate covariance structure parameter γ is fixed, only the noise power level σ ² The false alarm probability under the same threshold value is basically unchanged, which shows that the false alarm probability of the SRD-GLRT detector is irrelevant to the noise power; fixed noise power level σ ² When only the interference coordinate covariance structure parameter gamma changes, the false alarm probability under the same threshold value is stable and unchanged, which indicates that the change of the interference coordinate covariance structure parameter does not affect the detection performance of the SRD-GLRT detector. The above results demonstrate that the SRD-GLRT detector operates on the noise power level σ ² And the interference coordinate covariance matrix sigma has the CFAR characteristic and is consistent with the theoretical analysis conclusion.

As can be seen from fig. 3, the target Signal subspace dimension p increases, and the detection probability decreases at the same Signal to Interference plus Noise Ratio (SINR); under the same signal subspace dimension, the interference subspace dimension q is increased, and the detection probability is reduced. This is because, in the design of the detector, the target signal subspace is included inside the interference signal subspace, and the interference signal subspace dimension becomes larger, which means that more target signal energy projected into the interference signal subspace is removed, thereby resulting in a decrease in the detection probability of the detector.

From fig. 4a, which is a relationship between the detection probability of the detector and the signal to Interference and Noise Ratio SINR under different dry Noise ratios, it can be seen that experimental detection performance curves are substantially overlapped, which indicates that the detection probability is slightly influenced by the dry Noise Ratio (INR). Fig. 4b shows the relationship between the detection probability and the dry-to-noise ratio INR at three low SINR values, and it can be seen that the detection probability of the detector is almost constant at different INRs with the same SINR. All the data show that the detection probability of the SRD-GLRT detector is less influenced by the power of the interference signal, that is, the detection performance of the SRD-GLRT is less influenced by interference environments with different intensities, and the detector has good anti-interference performance.

As can be seen from fig. 5, at the same SINR, the detection performance of the SRD-GLRT detector improves with the increase of the auxiliary data, which indicates that the increase of the auxiliary data improves the estimation accuracy of the covariance matrix R, so the detection probability increases and the detection performance is better. In addition, it can be seen that when M =8, the trend of increasing the detection probability is rapidly reduced as the auxiliary data is continuously added.

Fig. 6 tests the detection performance of the detector compared to the SRD-GLRT detector of the present invention under three parameter combinations of the amount of assistance data M, the system dimension N and the interference subspace dimension q. Under the combination of the three parameters of fig. 6a, fig. 6b and fig. 6c, the detection probability of the SRD-GLRT detector designed by the present invention is always better than that of the three contrast detectors under the same SINR, and the detection probability is less affected by the interference subspace dimension q. Comparing fig. 6a and fig. 6b, when the same amount of auxiliary data M, the system dimension N is increased, the detection performance of I-DMSD and II-DMSD is significantly improved, but the detection probability curve of the SRD-GLRT detector of the present invention and the detection probability curve of the S-GLRT detector in the comparison literature do not change much. Comparing fig. 6b and fig. 6c, with the same system dimension N, the detection performance of the SRD-GLRT detector and the S-GLRT detector is improved when the amount of the auxiliary data increases, but the improvement range is not large, and the detection probability curves of the I-DMSD and the II-DMSD are basically stable, because the two comparison detectors are not designed with auxiliary data.

The degree of influence of the detection probability on the interference subspace dimension represents the sensitivity degree of the detector on the interference signal dimension. The detection probabilities of the three contrast detectors in fig. 6 are all greatly influenced by the interference dimension q, while the detection probabilities of the SRD-GLRT detector of the present invention are very slightly influenced by the interference dimension q, indicating that the detector has better interference suppression performance under the same conditions.

The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present application and are intended to be included within the scope of the present application.

Claims

1. A method for detecting a distance extension target under an interference plus noise background based on GLRT is characterized by comprising the following steps:

step 1, acquiring data to be detected from K distance units to be detected as main data, and acquiring M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; performing subspace modeling on a target signal and an interference signal, modeling noise into complex Gaussian distribution with unknown noise power, and establishing a binary hypothesis test model, wherein the target signal subspace is contained in an interference signal subspace; constructing a joint probability density function of the main data and the auxiliary data based on a binary hypothesis test model;

step 2, carrying out maximum likelihood estimation on unknown parameters in the joint probability density function, and constructing a detection statistic lambda of the distance extension target subspace detector under the interference plus noise background based on GLRT test _SRD-GLRT ；

Step 3, setting a detection threshold T according to the preset false alarm probability _G Will detect the statistic λ _SRD-GLRT And a detection threshold value T _G Making a comparison as to λ _SRD-GLRT ≥T _G Judging that distance expansion targets exist in the current K distance units to be detected; whereas if lambda is _SRD-GLRT <T _G Then, it is judged that the currentAnd no distance extension target exists in the K distance units to be detected.

2. The method according to claim 1, wherein the step 1 performs subspace modeling on the target signal and the interference signal, models noise as complex gaussian distribution with unknown noise power, and establishes a binary hypothesis testing model, specifically comprising:

wherein H ₀ Representing the assumption that there is no target signal, H ₁ Representing an assumption of a target signal; the main data to be detected is represented as x ₁ ,x ₂ ,…,x _k ,…,x _K ]And M observed data are expressed as [ y ] ₁ ,y ₂ ,…,y _m ,…,y _M ]；Sp _k For the target signal of the kth range bin, S is a known N x p dimensional column full rank complex matrix, p _k Is an unknown p × 1 dimensional signal coordinate vector; jp _k J is N × q dimension column full rank complex matrix, q is the interference signal of k-th range unit _k Is an unknown q x 1-dimensional interference coordinate vector, p is a target signal subspace dimension, and q is an interference subspace dimension; n is a radical of an alkyl radical _k As noise component, noise component n _k The units with different distances are independently and equally distributed; jq (joint Jq) _m Interference signals for M auxiliary data, n _m For the noise component of M auxiliary data, where q _m 、n _m Are each independently of q _k 、n _k Independently and equally distributed.

3. The method for detecting the distance-extended target under the interference-plus-noise background based on the GLRT as claimed in claim 2, wherein the joint probability density function of the main data and the auxiliary data is constructed based on a binary hypothesis testing model in step 1 of claim 1:

wherein i =0,1 corresponds to the hypothesis H without the target signal, respectively ₀ And hypothesis H with target signal ₁ The sigma is an unknown q multiplied by q dimensional interference coordinate covariance matrix; c is the dry noise covariance matrix, J is the interference matrix, σ ² For unknown noise power, I _N Representing an N-dimensional identity matrix; tr represents the trace of the matrix; | represents the determinant of the matrix, (-) ^H The representation represents the conjugate transpose of the matrix.

4. The method for detecting the range-extended target under the interference plus noise background based on the GLRT as claimed in claim 3, wherein the step 2 of claim 1 specifically comprises the following steps:

step 2-3: the maximum likelihood estimator of the target coordinate, the converted interference coordinate covariance estimator and the estimator of the noise power are substituted back to the joint probability density function to obtain the detection statistic lambda of the distance extension target subspace detector under the interference plus noise background _SRD-GLRT 。

5. The method for detecting the distance-extended target under the interference-plus-noise background based on the GLRT according to the claim 4, wherein the interference matrix J structure is transformed by a square root decomposition method in the step 2-1, specifically:

J ^H J＝LL ^H

wherein L is J ^H The q × q dimension of J is a lower triangular matrix.

6. A process as claimed in claim 5The method for detecting the distance extended target under the interference plus noise background based on the GLRT is characterized in that the detection statistic lambda of the distance extended target subspace detector under the interference plus noise background in the step 2-3 _SRD-GLRT

In the above formula, the first and second carbon atoms are,

W＝J _L (J _L ^H S _M J _L ) ^-1 J _L ^H

J _L ＝J(L ^H ) ^-1 。