An information geometry based adaptive detection method for MIMO radar extended targets

Abstract

The application provides a MIMO radar extended target adaptive detection method based on information geometry, and belongs to the technical field of radar target detection. Firstly, the statistics of three kinds of adaptive detectors are derived based on GLRT, Wald and Rao detection criteria under the condition that the clutter covariance matrix is known; then, the information geometry theory is used to model the clutter covariance matrix estimation problem on the matrix manifold; secondly, based on a geometric measure with rotational invariance, an optimization solution method is designed to obtain the clutter covariance matrix estimation result; finally, the clutter covariance estimation value is substituted into the GLRT, Wald and Rao detection statistics to obtain the adaptive detector, which is compared with the threshold to make a judgment, so that target detection is realized. The application depends on less auxiliary data, can effectively realize target detection under non-Gaussian clutter, and is suitable for practical application.

Description

Technical Field

[0001] This invention belongs to the field of radar target detection technology, and in particular relates to a method for extended target detection in MIMO radar under non-Gaussian clutter environments. Background Technology

[0002] Compared to phased array radar, multiple-input multiple-output (MIMO) radar has potential advantages in improving parameter estimation accuracy, angular resolution, clutter suppression, and detection performance. Distributed MIMO radar, due to the large spacing between antenna elements, can detect targets from different angles, thereby obtaining spatial diversity gain and geometric diversity gain, significantly improving target detection performance in cluttered environments. Radar detection performance is mainly limited by clutter, noise, and other interference. Especially for high-resolution radar systems, the statistical characteristics of clutter deviate from a Gaussian distribution, exhibiting significant non-Gaussian characteristics. Furthermore, when the radar's range resolution cell is smaller than the target size, the target echo signal occupies multiple range cells; this situation is called distributed target or extended target. For extended targets, traditional point target detection methods suffer from the shielding effect of adjacent range cells and the inability to effectively accumulate energy from multiple range cells, leading to performance degradation or even complete failure. Therefore, improving the radar's extended target detection performance under non-Gaussian clutter is crucial.

[0003] Many research institutions both domestically and internationally have conducted research on radar extended target detection methods under non-Gaussian clutter conditions. For composite Gaussian clutter models, the University of Naples Federico II in Italy proposed a detection method based on the generalized likelihood ratio detection (GLRT) criterion (E. Conte, A. De Maio, G. Ricci. "GLRT-based adaptive detection algorithms for range-spread targets," IEEE Trans. Signal Process., vol. 49, no. 7, pp. 1336-1348, 2001.). Although the GLRT method has a theoretical basis, it lacks optimality due to the absence of a uniform maximum potential. Therefore, some researchers have designed detection methods with better detection performance and robustness based on other criteria. For example, the University of Electronic Science and Technology of China designed a detection method based on the Rao and Wald detection criteria and achieved good detection performance (G. Cui, L. Kong, X. Yang, and J. Yang, “The Rao and Wald tests designed for distributed targets with polarization MIMO radar in compound Gaussianclutter,” Circuits Syst. Signal Process., vol. 31, pp. 237-254, 2012.). The above detection method has sufficient auxiliary data for clutter covariance matrix estimation. Commonly used clutter covariance matrix estimation methods include sample covariance matrix (SCM), normalized sample covariance matrix estimation (NSCM), and approximate maximum likelihood estimation (AML). These estimation methods achieve good performance when the number of auxiliary units is greater than the matrix dimension. In practical scenarios, the application of these methods is limited when the above conditions are not met. Therefore, research on clutter covariance matrix estimation under conditions of small auxiliary data samples, and subsequent design of adaptive detectors, is of significant value in the field of radar target detection. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a class of adaptive target detection methods for MIMO radar based on information geometry, applicable to non-Gaussian clutter environments. First, given the clutter covariance matrix, statistics for three adaptive detectors are derived based on GLRT, Wald, and Rao detection criteria. Then, using information geometry theory, the clutter covariance matrix estimation problem is modeled on a matrix manifold. Next, based on a rotationally invariant geometric measure (TBD), an optimization solution method is designed to obtain the clutter covariance matrix estimation result. Finally, the estimated clutter covariance value is substituted into the GLRT, Wald, and Rao detection statistics to obtain the adaptive detector, which is then compared with a threshold for decision-making, thereby achieving target detection.

[0005] The technical solution of this invention is as follows:

[0006] An adaptive target detection method for MIMO radar based on information geometry is proposed. The application scenario is a distributed MIMO radar with antennas configured far apart at the transmitting and receiving ends. The transmitting end has M transmitting array elements and the receiving end has K receiving array elements, that is, there are MK paths from the transmitting end to the receiving end. Each antenna transmits L pulses in one coherent processing interval, and each antenna at the transmitting end transmits mutually orthogonal waveforms.

[0007] Let y mk,h Let mk be the received signal vector of the h-th range cell in the mk-th path; the radar extended target detection problem under non-Gaussian clutter is:

[0008]

[0009] Where H0 represents no target, H1 represents a target, H represents the number of range cells occupied by the target echo signal, and α mk,h This reflects the target scattering and channel propagation effects along the mk-th path, where mk represents the path from the m-th transmitting element to the k-th receiving element. mk The corresponding steering vector is represented as p. mk =[1,exp(j2πf mk T r ),…,exp(j2π(L-1)f mk T r )] T f mk For the target Doppler frequency shift, T r c is the pulse repetition time. mk,h The clutter vector is generally modeled using a composite Gaussian model, represented by a slowly varying component τ. mk,h and a fast variable component g mk,h The product of, i.e. g mk,hIt follows a complex Gaussian distribution with zero mean and Σ variance;

[0010] Step 1: Construct the detection statistic given the known clutter covariance matrix;

[0011] Step 2: Within the geometric framework, model the clutter covariance matrix estimation problem as follows:

[0012]

[0013] Among them, w n For normalized weights, d(R,R) n ) represents matrices R and R n The geometric measure on a matrix manifold, R n Let N be the clutter autocorrelation matrix of the nth auxiliary unit, where N represents the total number of auxiliary units, and the superscript is... The values ​​are 1 and 2, and R represents the covariance matrix of the unit to be detected; Represents a matrix manifold;

[0014] Step 3: Based on the TBD geometric measure on the matrix manifold, the optimization problem in Step 2 is transformed into a geometric measure minimization problem between the covariance matrix A of the auxiliary data on the matrix manifold and the matrix Q to be estimated. Then, the optimization problem is solved using the properties of the TBD measure.

[0015]

[0016] Where, d TBD (A,Q) denotes the TBD geometric measure, and the function F is a strictly convex function. It is the gradient of the function F, tr(·) denotes the trace of the matrix, and the conformal factor is expressed as...

[0017] Step 4: Construct an adaptive detector using the covariance matrix estimate from Step 3;

[0018] Step 5: Use the adaptive detector obtained in Step 4 to make a detection decision;

[0019] The test result is expressed as follows:

[0020]

[0021] The above GLRT, Rao, or Wald detection statistics are compared with the decision threshold. If the detection statistics are greater than the threshold, the target is determined to exist; otherwise, the target is determined to not exist.

[0022] Furthermore, the detection statistic in step 1 is T. G :

[0023]

[0024] Among them, y mk,h This represents the received signal vector of the mk-th path and the h-th distance cell. This represents the conjugate transpose operation;

[0025] Furthermore, the detection statistic in step 1 is T. R :

[0026]

[0027] Furthermore, the detection statistic in step 1 is T. W :

[0028]

[0029] Furthermore, the adaptive detection statistics in step 4 are as follows:

[0030]

[0031]

[0032]

[0033] This invention proposes an information geometry-based adaptive target detection method for MIMO radar. This method utilizes a two-stage design process. In the first stage, statistics for three types of adaptive detection algorithms are derived based on GLRT, Rao, and Wald detection criteria. In the second stage, using information geometry theory, the clutter covariance matrix estimation problem is transformed into a geometric problem on a matrix manifold within a geometric framework. A clutter covariance matrix estimation method is designed based on two types of geometric measures, thereby obtaining the adaptive detection statistics. Compared to the clutter covariance matrix estimation method mentioned in the background, this method requires less auxiliary data. Using detection probability as the performance evaluation index, simulation experiments show that this invention has higher detection performance than existing methods in non-Gaussian clutter environments, and still maintains performance advantages with limited auxiliary data, making it suitable for practical applications. Attached Figure Description

[0034] Figure 1 Configure for distributed MIMO radar.

[0035] Figure 2 The detection probability of the GLRT detector varies with the signal-to-noise ratio (N=10).

[0036] Figure 3 The detection probability of the Rao detector varies with the signal-to-noise ratio (N=10).

[0037] Figure 4The detection probability of the Wald detector varies with the signal-to-noise ratio (N=10).

[0038] Figure 5 The detection probability of the GLRT detector varies with the signal-to-noise ratio (N=16).

[0039] Figure 6 The detection probability of the Rao detector varies with the signal-to-noise ratio (N=16).

[0040] Figure 7 The detection probability of the Wald detector varies with the signal-to-noise ratio (N=16). Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0042] An adaptive target detection method for MIMO radar based on information geometry includes the following steps:

[0043] Step 1: Given the clutter covariance matrix, derive the GLRT, Wald, and Rao detection statistics.

[0044] Distributed MIMO radar: The transmitting end has M transmitting elements, and the receiving end has K receiving elements, meaning there are MK paths from the transmitting end to the receiving end. Each antenna transmits L pulses within one coherent processing interval, and the waveforms transmitted by each antenna at the transmitting end are mutually orthogonal.

[0045] Assuming the target echo signal occupies H range cells, let y mk,h Let represent the received signal vector of the mk-th path and the h-th range cell. Without loss of generality, the radar extended target detection problem under non-Gaussian clutter is expressed as:

[0046]

[0047] Where α mk,h This reflects the target scattering and channel propagation effects along the mk-th path, p mk The corresponding steering vector is represented as p. mk =[1,exp(j2πf mk T r ),…,exp(j2π(L-1)f mk T r )] T ,(·)T is the transpose operation, f mk For the target Doppler frequency shift, T r c is the pulse repetition time. mk,h The clutter vector is generally modeled using a composite Gaussian model, represented by a slowly varying component τ. mk,hand a fast variable component g mk,h The product of, i.e. Where g mk,h It follows a complex Gaussian distribution with zero mean and Σ variance.

[0048] In practice, the scattering coefficient α of the target signal mk The texture component τ of clutter mk The covariance matrix of the clutter component is unknown. First, assume the clutter covariance matrix is ​​known, while the scattering coefficient of the target signal and the texture component of the clutter are unknown. For range-extended targets in a distributed MIMO radar, the GLRT detection criterion is expressed as:

[0049]

[0050] The scattering coefficient of the target signal and the texture component of clutter are estimated using the maximum likelihood estimation method, and the detection statistic T is obtained. G , represented as

[0051]

[0052] When the scattering coefficient of the target signal and the texture components of clutter are unknown, the Rao detection criterion is expressed as follows:

[0053]

[0054] Where θ r θ represents a useful parameter when the covariance matrix Σ is known. r =[α 111 ,…,α mkh ,…α MKH ] T It is an MKH-dimensional vector. This represents the logarithmic probability density function with respect to θ. r The first-order partial derivative. J(θ)=J(θ) r ,θ s ) is the Fisher information matrix, represented as a block matrix;

[0055]

[0056]

[0057] Furthermore, the detection statistic T R Represented as

[0058]

[0059] When the scattering coefficient of the target signal and the texture component of clutter are unknown, the Wald detection criterion is expressed as follows:

[0060]

[0061] in

[0062] The detection statistic T was calculated. W Represented as

[0063]

[0064] Step 2: Model the clutter covariance matrix estimation problem within a geometric framework.

[0065] Let R1, R2, ..., R N Let be a set of HPD matrices on the matrix manifold P(m), which are the autocorrelation matrices of the auxiliary cell data. The clutter covariance matrix estimation problem is modeled as follows:

[0066]

[0067] Where w n For normalized weights, d(R,R) n R represents the geometric measure of two matrices on a matrix manifold. n Let be the clutter autocorrelation matrix of the nth auxiliary unit.

[0068] Step 3: Design an optimized solution method based on TBD geometric measures.

[0069] The TBD geometric measure on the matrix manifold is chosen to measure the difference between two matrices, denoted as:

[0070]

[0071] in It is the gradient of the convex function F, tr(·) denotes the trace of the matrix, and the conformal factor is expressed as...

[0072] It is worth noting that the TBD measure depends on the generating function F. In practical applications, any convex function can be chosen as the generating function, such as F = xlogx - x.

[0073] Step 4: Construct an adaptive detector using the covariance matrix estimate from Step 3.

[0074] Detection statistic T G1 for:

[0075]

[0076] Detection statistic T R1 for:

[0077]

[0078] Detection statistic T W1 for:

[0079]

[0080] Step 5: Use the adaptive detector obtained in Step 4 to make a detection decision.

[0081]

[0082] Where η is the decision threshold. Based on the false alarm probability P... fa Size, execute 100 / P fa In this experiment, the detection statistics for the case without a target were calculated and sorted in descending order. The 100th detection statistic was taken as the decision threshold. The detection statistic T was compared with the decision threshold η. If the detection statistic T was greater than the threshold, it was determined that a target existed in the current detection unit; otherwise, it was determined that the target did not exist.

[0083] Parameter settings: such as Figure 1 As shown, a specific embodiment of the present invention is executed in a distributed MIMO radar system. It is assumed that both the number of transmitting antenna array elements and the number of receiving antenna array elements are 2, where the angles between the two transmitting antennas and the target are 0° and 65°, and the angles between the two receiving antennas and the target are -30° and 40°. It is assumed that the number of pulses transmitted within a coherent processing interval is M = 10, the transmit pulse repetition frequency is 500Hz, the carrier frequency is set to 1GHz, and the speed of the target is 108km / h. The clutter amplitude statistical characteristics are modeled as a K-distribution, the texture component follows a gamma distribution, and the speckle component follows a zero-mean covariance matrix Σ = Σ0 + I. M The complex Gaussian distribution is Σ0, and Σ0 is modeled in exponential form.

[0084]

[0085] Where ρ is the first-order delay correlation coefficient of clutter, set to ρ = 0.9; For noise ratio, set to 10dB; f dc The normalized Doppler frequency for clutter is set to 0.05.

[0086] Example 1:

[0087] Assume the signal-to-noise ratio (SCR) is between -30 dB and 0 dB, and the false alarm probability is 0.001. Figure 2 , Figure 3 , Figure 4 The paper demonstrates how the detection probability of the existing GLRT, Rao, and Wald detection methods of this invention varies with SCR when the amount of auxiliary data N = M = 10. For example... Figure 2 , Figure 3 , Figure 4 As shown, some existing technologies are ineffective. In contrast, the technology of this invention has a higher detection probability and significantly improves the radar's extended target detection performance in non-Gaussian clutter environments.

[0088] Example 2:

[0089] Figure 5 , Figure 6 , Figure 7 The paper presents the detection probabilities of existing technologies and the GLRT, Rao, and Wald detection methods of this invention as a function of SCR when the amount of auxiliary data M < N = 16. The results show that the detection performance of all methods improves with increasing auxiliary data, especially at high SCR, where some existing technologies transition from being completely inoperable to functioning normally. However, the detection probabilities of this invention are significantly higher than those of existing technologies, and its performance is robust.

Claims

1. An adaptive target detection method for MIMO radar based on information geometry, applicable to a distributed MIMO radar system where the transmitter and receiver are configured with antennas spaced far apart. The transmitter has M transmitting elements, and the receiver has K receiving elements, meaning there are a total of [number missing] antennas from the transmitter to the receiver. There are L paths; each antenna transmits L pulses within a coherent processing interval, and each antenna at the transmitting end transmits mutually orthogonal waveforms; make Let mk be the received signal vector of the h-th range cell in the mk-th path; the radar extended target detection problem under non-Gaussian clutter is: ； in, This indicates that there is no goal. This indicates the presence of a target, where H represents the number of range cells occupied by the target echo signal. This reflects the target scattering and channel propagation effects along the mk-th path, where the mk-th path represents the path from the m-th transmitting element to the k-th receiving element. The corresponding guide vector is represented as , For the target Doppler frequency shift, The pulse repetition time; For clutter vectors, a composite Gaussian model is generally used to model them, representing them as a slowly varying component. and a fast variable component The product of, i.e. , To obey the following: the mean is zero and the variance is The complex Gaussian distribution; Step 1: Construct the detection statistic given the known clutter covariance matrix; Step 2: Within the geometric framework, model the clutter covariance matrix estimation problem as follows: : ； in, To normalize the weights, Representation matrix Geometric measure on a matrix manifold Let n be the clutter autocorrelation matrix of the nth auxiliary unit. Indicates the total number of auxiliary units, superscript The values ​​are 1 and 2. Represents the covariance matrix of the unit to be detected; Represents a matrix manifold; Step 3: Based on the TBD geometric measure on the matrix manifold, the optimization problem in Step 2 is transformed into the covariance matrix of auxiliary data on the matrix manifold. With the matrix to be estimated The problem is to minimize the geometric measure between the two sides, and then solve the optimization problem using the properties of the TBD measure. ； in, Represents the geometric measure of TBD, function It is a strictly convex function. It is the gradient of the function F. The trace of a matrix is ​​represented by the conformal factor. ; Step 4: Construct an adaptive detector using the covariance matrix estimate from Step 3; Step 5: Use the adaptive detector obtained in Step 4 to make a detection decision; The test result is expressed as follows: ； The detection statistics of GLRT, Rao, or Wald are compared with the decision threshold. If the detection statistics are greater than the threshold, the target is determined to exist; otherwise, the target is determined to not exist.

2. The MIMO radar extended target adaptive detection method based on information geometry as described in claim 1, characterized in that, The detection statistic in step 1 is: : ； in, This represents the received signal vector of the mk-th path and the h-th distance cell. This represents the conjugate transpose operation; The adaptive detector in step 4 is ; 。 3. The MIMO radar extended target adaptive detection method based on information geometry as described in claim 1, characterized in that, The detection statistic in step 1 is: : ； The adaptive detector in step 4 is : 。 4. The MIMO radar extended target adaptive detection method based on information geometry as described in claim 1, characterized in that, The detection statistic in step 1 is: : ； The adaptive detection statistics in step 4 are as follows: : 。

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