CN115685081B - GLRT-based method for detecting distance expansion target in interference plus noise background - Google Patents
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Abstract
The invention belongs to the technical field of radar signal processing, and particularly relates to a GLRT-based method for detecting a distance expansion target under an interference and noise background. Modeling both the target and the disturbance as signals having unknown coordinates within a known subspace, and the target signal subspace is contained within the disturbance signal subspace; and estimating an interference covariance matrix by using a group of auxiliary data containing interference and noise, transforming an interference matrix structure by adopting a square root decomposition method, further solving maximum likelihood estimation of the interference coordinate covariance matrix, noise power and target signal coordinates, and establishing a generalized likelihood ratio detection detector based on a one-step design strategy to perform distance expansion target detection. Simulation analysis shows that the invention can effectively restrain subspace interference signals with different powers under the background of interference related to target signals and unknown noise.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a GLRT-based method for detecting a distance expansion target under an interference and noise background.
Background
The high-range resolution radar has the advantages of large bandwidth, high range resolution, obvious advantages in the aspects of accurate detection, imaging, target recognition and the like, and has become an important direction of the development of modern radars. The target echo signal of the traditional low-range resolution radar often occupies only one range unit and is often treated as a 'point target'. Unlike "point targets", the echo signals of common high range resolution radar targets do not occupy only one range bin, but are distributed among different radial range bins, forming a "range expansion target". With the wide application of broadband technology in the radar field, the problem of adaptive detection of a distance-extended target is receiving more and more attention, and becomes one of hot spots and difficult problems in the radar signal processing field in recent years.
The research of distance expansion target detection in Gaussian noise background is relatively extensive, a target detection method based on the detection criteria of generalized likelihood ratio (generalized likelihood ratio test, GLRT), rao, wald and the like has been formed, and some improved methods have been further developed. For example, to make full use of prior information of the density distribution of scattering points of the target, GLRT detectors based on spatial scattering density are proposed; for distance extended target detection in a gaussian noise background with an unknown covariance matrix, part of the literature derives a modified (modified generalized likelihood ratio test, MGLRT) detector and analyzes the detector for bounded constant false alarm rate (constant false alarm rate, CFAR) characteristics. Such background modeling of gaussian noise for radar receivers has become a fundamental assumption of target detection problems.
The electronic interference measures are widely valued and applied in modern war, and the design research heat of the high-performance distance expansion target detector under the interference background is further improved. Researchers develop a series of research works aiming at the design of a distance expansion target detector under noise plus interference background from the aspects of one-step or two-step design strategy, different covariance matrix structure analysis, known or unknown noise power, known or unknown interference matrix 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 by using a priori information of the interference matrix and noise.
But the actual interference information and noise power are often unknown and vary in real time, making it difficult to obtain their accurate a priori information and corresponding target detectors. Thus, going back to the study, the structured subspace interference problem is presented, i.e. modeling interference and objects as subspace signals and confining them to known subspaces, but object detection problems in case the subspace coordinates are unknown. Structured subspace interference can be divided into two cases, namely interference which is irrelevant to the target signal and interference which is relevant to the target signal according to the correlation degree of the interference signal and the target signal. The interference caused by unintentional communication signals, sidelobe targets, multipath multi-angle interference and the like on the target signals is generally classified as interference irrelevant to the target signals, and the research attention of the target detection problem under the interference background is higher from the public literature. The interference caused by the back scattering of the obstacle in the illuminated area on the target signal is classified as the background of the interference related to the target signal compared with the interference unrelated to the target signal, and the problem of detecting the target related to the target signal is highly focused and studied.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a GLRT-based method for detecting a distance expansion target under an interference plus noise background.
The technical scheme for solving the technical problems is as follows:
a GLRT-based method for detecting a distance expansion target under interference plus noise background comprises the following steps:
step 1, obtaining data to be detected from K distance units to be detected as main data, and obtaining M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; carrying out 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 testing 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 statistic lambda of a distance expansion target subspace detector under interference plus noise background based on GLRT (global noise reduction) test criterion SRD-GLRT ；
Step 3, setting a detection threshold T according to the preset false alarm probability G The method comprises the steps of carrying out a first treatment on the surface of the Will detect statistic lambda SRD-GLRT And a detection threshold T G Comparing if lambda SRD-GLRT ≥T G Judging that the current K distance units to be detected have distance expansion targets; on the contrary if lambda 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 testing model, which specifically includes:
wherein H is 0 Indicating the assumption of no target signal, H 1 A hypothesis representing the target signal; the main data to be detected is expressed as [ x ] 1 ,x 2 ,…,x k ,…,x K ]M observations are represented as [ y ] 1 ,y 2 ,…,y m ,…,y M ]；For the target signal of the kth distance unit, S is a known N x p-dimensional column-full rank complex matrix, p k Is an unknown p x 1 dimensional signal coordinate vector; />For the interference signal of the kth distance unit, J is N×q-dimensional column-full-rank complex matrix, q k The method is an unknown q multiplied by 1-dimensional interference coordinate vector, p is the subspace dimension of the target signal, and q is the interference subspace dimension; n is n k As the noise component, noise component n k The units with different distances are independently distributed in the same way; jq m Interference signals for M auxiliary data, n m Noise component for M auxiliary data, where q m 、n m Respectively with q k 、n k Are independently distributed in the same way.
Further, in the 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 assumption H that there is no target signal, respectively 0 And hypothesis H with target signal 1 Sigma is an unknown q×q-dimensional interference coordinate covariance matrix; c (C)For the interference 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; i·| represents the determinant of the matrix, (·) H Representing the conjugate transpose of the representation 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 logarithmic operation on the transformed joint probability density function to obtain a joint probability density function in a logarithmic form;
step 2-2: carrying out maximum likelihood estimation on a disturbance coordinate covariance matrix, noise power and a target coordinate in a logarithmic combined probability density function;
step 2-3: substituting the maximum likelihood estimator of the target coordinates, the converted interference coordinate covariance estimator and the estimator of the noise power back into a joint probability density function to obtain the detection statistic lambda of the distance-expanded target subspace detector under the interference plus noise background SRD-GLRT 。
Further, in step 2-1, the interference matrix J structure is transformed by adopting a square root decomposition method, specifically:
J H J＝LL H
wherein L is J H Q×q-dimensional lower triangular matrix of J.
Further, the detection statistic lambda of the distance expansion target subspace detector in the interference plus noise background in the step 2-3 SRD-GLRT ：
In the above-mentioned method, the step of,
compared with the prior art, the invention has the following technical effects:
(1) The invention assumes that the target signal subspace is contained in the interference signal subspace, so as to represent the correlation between the target signal and the interference signal, and establishes a subspace-based distance expansion target signal model under the condition of interference and unknown noise;
(2) Based on GLRT criterion, the square root decomposition method is adopted while ensuring the constant false alarm rate characteristic, so that the parameter estimation process is simplified, the construction efficiency of the detector is improved, and the method has wide potential popularization and application values.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions and advantages of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic representation of the CFAR characteristics of the SRD-GLRT detector of the present invention;
fig. 3 is a schematic diagram of the relation between the SRD-GLRT detection performance and the target signal matrix dimension and the interference signal matrix dimension q when n= 8,K =8, m=8, inr=10 dB;
fig. 4 is a diagram showing the relation 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 schematic diagram of the detection performance of the SRD-GLRT detector for different auxiliary data amounts when n= 8,p =2, q=3, inr=10 dB;
fig. 6 is a graph showing the comparison of detection performance of the SRD-GLRT detector with other detectors when k= 8,p =2 and inr=10 dB.
Detailed Description
In order to further describe the technical means and effects adopted by the present invention to achieve the preset purpose, the following detailed description is given below of the specific implementation, structure, features and effects of the technical solution according to the present invention with reference to the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" means that the embodiments are not necessarily the same. Furthermore, the particular features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.
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 expansion target in interference plus noise background based on GLRT, comprising the following steps:
step 1, obtaining data to be detected from K distance units to be detected as main data, and obtaining M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; carrying out 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 testing 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 statistic lambda of a distance expansion target subspace detector under interference and noise background based on GLRT criterion SRD-GLRT ；
Step 3, setting a detection threshold T according to the preset false alarm probability G The method comprises the steps of carrying out a first treatment on the surface of the The detection statistic lambda is compared with the detection threshold T G Proceeding withComparing, if lambda SRD-GLRT ≥T G Judging that the current K distance units to be detected have distance expansion targets; on the contrary if lambda SRD-GLRT <T G And judging that the current K distance units to be detected have no distance expansion targets.
The following detailed development of each step is performed:
step 1, obtaining data to be detected from K distance units to be detected as main data, and obtaining M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; subspace modeling is carried out on a target signal, an interference signal and noise, and a binary hypothesis testing model is established, 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 the binary hypothesis test model.
In some embodiments, this step may include the sub-steps of:
step 1-1: obtaining data to be detected from K distance units to be detected as main data, obtaining M observation data from a non-target distance unit adjacent to a detected unit as auxiliary data, carrying out subspace modeling on a target signal and interference, and establishing a binary hypothesis testing model, wherein the target signal is contained in an interference signal;
assuming that the receiver adopts a uniform linear array of N array elements, and the target distance expansion 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 ] of adjacent distance units without target signals 1 ,y 2 ,…,y m ,…,y M ]As auxiliary data, where m=1, 2, M, the observation vectors of the different distance units are statistically independent from each other. X is x k And y m Are n×1-dimensional complex vectors, N represents the number of channels processed by the system; the target signal of the kth distance unit is denoted as Sp k Is a known N x p-dimensional column-full rank complex matrix, p k Is an unknown p x 1 dimensional signal coordinate vector; the interference signal of the kth distance unit is represented as Jq k J is N x q dimension column full rankComplex matrix, q k Is an unknown q multiplied by 1 dimensional interference coordinate vector, assuming that p+q is less than or equal to N, and q k Obeying complex Gaussian distribution with unknown mean value of zero covariance matrix of sigma, wherein sigma is unknown q multiplied by q dimension interference coordinate covariance matrix, p is the subspace dimension of the target signal, and q is the interference subspace dimension; noise component n k Are distributed independently and identically among different distance units, and obeys a mean value of zero covariance matrix to be sigma 2 I N Wherein I is N Representing an N-dimensional identity matrix, sigma 2 Is the unknown noise power.
Assume that M auxiliary data [ y ] are employed 1 ,y 2 ,…,y m ,…,y M ]Comprising an interference signal Jq m And noise n m Wherein q m 、n m Respectively with q k 、n k Are independently distributed in the same way.
Suppose a target signal subspace<S>Contained in interfering subspaces<J>In, recorded asThe corresponding matrix dimension satisfies the relation p.ltoreq.q, thereby representing the correlation of the target signal and the interference signal.
According to the above assumption, the problem of detecting the distance expansion target in the subspace interference plus unknown noise environment can be expressed as a binary hypothesis test for judging whether the target exists in the data to be detected:
wherein H is 0 Indicating the assumption of no target signal, H 1 Representing the hypothesis that there is a target signal.
From the above description, it can be seen that the noise power σ 2 Target coordinates p k The interference coordinate covariance matrix Σ is unknown, and the interference signals and noise in different distance units 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 the interference signal and noise between each distance unit are mutually independent in the K distance units, then in H 0 And H 1 The joint probability density function (probability density function, PDF) of the main data and the auxiliary data under two hypotheses is expressed as:
wherein i=0, 1 corresponds to the assumption H, respectively 0 And H 1 The symbol "H" represents the conjugate transpose of the matrix, with the dry noise covariance C being c=jΣj H +σ 2 I N The expression C represents the determinant of C, C -1 Representing the inverse of C. According to the conversion relation y of the vector inner product and the matrix trace H C -1 y＝tr(C -1 yy H ) Order-making
T i ＝S i +S M ,i＝0,1 (5)
The joint PDF of the main data and the auxiliary data shown in expression (2) is simplified as:
thus, the unknown noise power sigma 2 And distance-extended target GLRT detection statistic lambda under interference coordinate covariance matrix Sigma condition SRD-GLRT Can be expressed as:
wherein T is 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 statistic lambda of the distance expansion target subspace detector under interference and noise background SRD-GLRT ；
As can be seen from step 1, the unknown parameters in the joint probability density function include: noise power sigma 2 Target coordinates p k An interference coordinate covariance matrix Σ, thus, for the noise power σ in the joint probability density function 2 Target coordinates p k And carrying out maximum likelihood estimation on the interference coordinate covariance matrix sigma.
In some embodiments, this step may include the sub-steps of:
step 2-1: transforming the interference matrix structure by adopting a square root decomposition method, and carrying out logarithmic operation on the transformed joint probability density function to obtain a joint probability density function in a logarithmic form;
due to N>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 estimation form is complex. To reduce the calculation amount of solving the maximized unknown parameters, a square root decomposition method is introduced, J H Square root decomposition of the J matrix is denoted as LL H Wherein L is J H Q x q-dimensional lower triangular matrix of J, i.e. J H J＝LL H . Square root decomposition, also known as Cholesky decomposition, simplifies the matrix computation by using small matrices after decomposition to more easily solve the inverse of the matrix directly, thereby reducing the computation to solve for maximizing the unknown parameters.
By means of square root decomposition, an unknown parameter matrix q=σ is defined -2 L H Σl, the corresponding interference coordinate-compliant covariance matrix Σ may be expressed as Σ=σ 2 (L H ) -1 QL -1 . According toThe determinant of the dry noise covariance matrix C is re-expressed 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 I in the above 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×n dimensional matrix.
The inverse of the dry noise covariance matrix C is transformed and re-expressed as
Wherein P is J ⊥ ＝I N -P J ，P J ＝J(J H J) -1 J H Representing the projection matrix on the interfering subspace. Correspondingly, in formula (6) C -1 Can be simplified as follows:
wherein Z is i ＝L -1 J H T i J(L H ) -1 ，i＝0,1。
Further, since the target signal subspace is contained inside the interfering signal subspace, i.e. presentTherefore +.>The method can be simplified as follows:
as can be seen from the above, under the assumption that the target signal subspace is covered by the interfering signal subspace, there areSubstituting formula (8), formula (9) and formula (10) back to formula (6), and further performing logarithmic operation
Step 2-2: for Q, noise power sigma in a logarithmic form of joint probability density function 2 And the target coordinate p k Performing maximum likelihood estimation;
according to equation (12), Q is solved for H by using the maximum likelihood estimation method 0 And H is 1 Maximum likelihood estimation value under assumptionAnd->Noise power sigma 2 At H 0 And H is 1 Maximum likelihood estimate under the assumption +.>And->
From the formula (11), the formula (13)It can thus be stated that the noise power is independent of the design of the detector. Estimated value to be solved +.>And noise power estimate->Substitute for the return type (7) to obtain
The above equation is then reduced to solve for the maximum likelihood estimates of the target parameters.
Let J L ＝J(L H ) -1 Then |L -1 J H T i J(L H ) -1 The i can be reduced to:
the above is further simplified into:
where w=j L (J L H S M J L ) -1 J L H ，J L ＝J(L H ) -1 . Substituting equations (15), (16) back to equation (14) can yield an expression with only the target coordinate parameters as unknowns:
according to equation (17), p in the denominator part within the ln function k Obtaining the extreme value to obtain the target coordinate p k The maximum likelihood estimate for (2) is:
step 2-3: maximum likelihood estimator for coordinates of a targetTransformed interference coordinate covariance estimator +.>Estimated amount of noise power->Substituting back the joint probability density function (2) to obtain the detection statistic lambda of the SRD-GLRT detector based on the GLRT criterion SRD-GLRT
Wherein, the liquid crystal display device comprises a liquid crystal display device,
step 3, setting a detection threshold T according to the preset false alarm probability G The method comprises the steps of carrying out a first treatment on the surface of the Will detect statistic lambda SRD-GLRT And a detection threshold T G Comparing if lambda SRD-GLRT ≥T G Judging that the current K distance units to be detected have distance expansion targets; on the contrary if lambda 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 combined covariance matrix C of the SRD-GLRT detector on the interference signal and the noise is proved, and the CFAR characteristic is specifically as follows:
for ease of analysis, define:
x can be obtained J And Y is equal to J The distribution of (2) is:
wherein r=j H CJ. Order theLambda in detection statistics 1 ,λ 2 Can be rewritten as:
proof lambda SRD-GLRT At H 0 Assuming that R has CFAR characteristics, it needs to be verifiedAnd->Independent of the transformed dry noise covariance R.
(1) VerificationAt H 0 Is not related to R under the assumption
By taking advantage of the nature of the whitening transformation,can be written as:
wherein X is RJ ＝R -1/2 X J ，Y RJ ＝R -1/2 Y J ；Representation pair->Is a whitening transformation of (a). Further, X can be obtained RJ Is a covariance matrix of (a):
from the above, it can be seen that in H 0 Under the assumption X RJ Is subject to zero mean covariance matrix as I q Is a complex gaussian vector of (c). Meanwhile, G 0 Is subject to the degree of freedom M covariance matrix I q Is a N-dimensional complex central weisate distribution. It can be seen from this that,at H 0 Let us assume that R is independent.
(2) VerificationAt H 0 Is not related to R under the assumption
First, toThe whitening transformation can be performed to obtain:
in the middle ofFurther unitary transformation of the above equation can be obtained:
in the formula, UU H ＝I N U represents a unitary matrix; x is X URJ ＝U H X RJ 、G＝U H G 0 U represents X RJ 、G 0 A unitary transformed matrix; in addition, in the case of the optical fiber,description P UR Independent of the transformed covariance matrix R. From equation (27), it follows that under the assumption, X URJ And X is RJ G and G 0 Statistically equivalent, so X URJ G is at H 0 Provided that it is independent of R.
Comprehensive analysis, H 0 Let lambda be SRD-GLRT Is independent of R, i.e. C, i.e. the SRD-GLRT detector has CFAR characteristics for the joint covariance matrix C of the interference signal and noise.
The invention has the advantages that the target signal mismatch condition exists according to the actual target detection scene, the interference condition is complex, the relation between the target signal and the target signal is not only orthogonal and equal, but also the relation is more related to the signal, thus, the target signal subspace is assumed<S>Contained in interfering subspaces<J>In, recorded asThe corresponding matrix dimensions satisfy the relation p<q, the correlation between the target signal and the interference signal is represented, and a subspace-based distance expansion target signal model under the condition of interference and unknown noise is established. Based on GLRT criterion, distance extension target detection of a distance extension target subspace detector under interference plus noise background is deduced, and a square root decomposition method is adopted while the constant false alarm rate characteristic is ensured, so that 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 experiment:
analysis of experimental results:
as can be seen from fig. 2, the fixed interference coordinate covariance structure parameter γ, the noise power level σ alone 2 The false alarm probability is basically unchanged under the same threshold value, which indicates the false alarm of the SRD-GLRT detectorThe probability is uncorrelated with the noise power; fixed noise power level sigma 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 influence the detection performance of the SRD-GLRT detector. The above results demonstrate that the SRD-GLRT detector is accurate for noise power level σ 2 The interference coordinate covariance matrix Σ has CFAR characteristics, which are 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 (Signal to Interference plus Noise Ratio, SINR); and 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 contained inside the interference signal subspace, and the interference signal subspace dimension becomes larger, meaning that more target signal energy projected to the interference signal subspace is removed, resulting in a reduced detection probability of the detector.
From fig. 4a, which shows the relationship between the detection probability of the detector and the SINR under different snr conditions, it can be seen that the experimental detection performance curves substantially coincide, which indicates that the detection probability is slightly affected by the snr (INR). Fig. 4b shows the relation between detection probability and the interference-to-noise ratio INR at three low SINR values, it can be seen that the detection probability of the detector is almost unchanged at the same SINR but different INR. These all show that the detection probability of the SRD-GLRT detector is less influenced by the power of the interference signal, that is, the interference environments with different intensities have little influence on the detection performance of the SRD-GLRT, and the detector has good anti-interference performance.
As can be seen from fig. 5, the detection performance of the SRD-GLRT detector improves with the increase of the auxiliary data at the same SINR, which means that the increase of the auxiliary data improves the estimation accuracy of the covariance matrix R, so that the detection probability increases and the detection performance is better. It can be seen that, when m=8, the auxiliary data continues to be added, and the tendency of the detection probability to rise rapidly decreases.
Fig. 6 shows the detection performance of a comparative detector with the SRD-GLRT detector of the present invention under three parameter combinations, auxiliary data quantity M, system dimension N and interference subspace dimension q. Under the condition of the same SINR in the three parameter combinations of fig. 6a, 6b and 6c, the detection probability of the SRD-GLRT detector designed by the invention is always better than that of three comparison detectors, and the detection probability is less influenced by the interference subspace dimension q. Comparing FIG. 6a with FIG. 6b, the system dimension N increases, the detection performance of I-DMSD and II-DMSD increases significantly, while the detection probability curve of the SRD-GLRT detector of the invention does not change much from that of the S-GLRT detector in the comparison document. Comparing fig. 6b and fig. 6c, the same system dimension N, the detection performance of the SRD-GLRT detector and the S-GLRT detector is improved when the amount of auxiliary data is increased, but the improvement amplitude is not large, and the I-DMSD and II-DMSD detection probability curves are basically stable, because the two comparison detectors are designed without auxiliary data.
The degree to which the detection probability is affected by the dimension of the interfering subspace represents the sensitivity of the detector to the dimension of the interfering signal. The detection probability of the three comparison detectors in fig. 6 is greatly influenced by the interference dimension q, while the detection probability of the SRD-GLRT detector is very little influenced by the interference dimension q, which shows that the detector has better interference suppression performance under the same condition.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting thereof; 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 scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application.
Claims (5)
1. The method for detecting the distance expansion target under the interference plus noise background based on GLRT is characterized by comprising the following steps:
step 1, obtaining data to be detected from K distance units to be detected as main data, and obtaining M observation data without target signals from a non-target distance unit adjacent to the detected unit as auxiliary data; carrying out 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 testing 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 statistic lambda of a distance expansion target subspace detector under interference and noise background based on GLRT test SRD-GLRT ；
The step 2 specifically comprises the following steps:
step 2-1: transforming the interference matrix structure by adopting a square root decomposition method, and carrying out logarithmic operation on the transformed joint probability density function to obtain a joint probability density function in a logarithmic form;
step 2-2: carrying out maximum likelihood estimation on a disturbance coordinate covariance matrix, noise power and a target coordinate in a logarithmic combined probability density function;
step 2-3: substituting the maximum likelihood estimator of the target coordinates, the converted interference coordinate covariance estimator and the estimator of the noise power back into a joint probability density function to obtain the detection statistic lambda of the distance-expanded target subspace detector under the interference plus noise background SRD-GLRT ；
Step 3, setting a detection threshold T according to the preset false alarm probability G Will detect the statistic lambda SRD-GLRT And a detection threshold T G Comparing if lambda SRD-GLRT ≥T G Judging that the current K distance units to be detected have distance expansion targets; on the contrary if lambda SRD-GLRT <T G And judging that the current K distance units to be detected have no distance expansion targets.
2. The method for detecting a distance expansion target in a interference plus noise background based on GLRT according to claim 1, wherein the step 1 performs subspace modeling on a target signal and an interference signal, models noise as complex gaussian distribution with unknown noise power, and establishes a binary hypothesis testing model, and specifically comprises:
wherein H is 0 Indicating the assumption of no target signal, H 1 A hypothesis representing the target signal; the main data to be detected is expressed as [ x ] 1 ,x 2 ,…,x k ,…,x K ]M observations are represented as [ y ] 1 ,y 2 ,…,y m ,…,y M ]；Sp k For the target signal of the kth distance unit, S is a known N x p-dimensional column-full rank complex matrix, p k Is an unknown p x 1 dimensional signal coordinate vector; jp (joint mark) k For the interference signal of the kth distance unit, J is N×q-dimensional column-full-rank complex matrix, q k The method is an unknown q multiplied by 1-dimensional interference coordinate vector, p is the subspace dimension of the target signal, and q is the interference subspace dimension; n is n k As the noise component, noise component n k The units with different distances are independently distributed in the same way; jq m Interference signals for M auxiliary data, n m Noise component for M auxiliary data, where q m 、n m Respectively with q k 、n k Are independently distributed in the same way.
3. The method for detecting the distance expansion target in the interference plus noise background based on the GLRT according to claim 2, wherein in the 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 assumption H that there is no target signal, respectively 0 And hypothesis H with target signal 1 Sigma is an unknown q×q-dimensional interference coordinate covariance matrix; c is dry noiseCovariance matrix, J is interference matrix, σ 2 For unknown noise power, I N Representing an N-dimensional identity matrix; tr represents the trace of the matrix; i·| represents the determinant of the matrix, (·) H Representing the conjugate transpose of the representation matrix.
4. The method for detecting a distance expansion target in a GLRT-based interference plus noise background according to claim 3, wherein in step 2-1, an interference matrix J structure is transformed by a square root decomposition method, specifically:
J H J＝LL H
wherein L is J H Q×q-dimensional lower triangular matrix of J.
5. The method for detecting a distance-extended target in a GLRT-based interference-plus-noise background according to claim 4, wherein the detection statistics lambda of the distance-extended target subspace detector in the interference-plus-noise background in step 2-3 SRD-GLRT
In the above-mentioned method, the step of,
W＝J L (J L H S M J L ) -1 J L H
J L ＝J(L H ) -1 。
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