Robust DOA tracking method based on zero memory nonlinear transformation

Abstract

The invention provides a robust DOA tracking method based on zero-memory nonlinear transformation, which can effectively suppress burst non-Gaussian noise under the condition that noise of a complex electromagnetic environment where a radiation source signal is located lacks priori knowledge, and suppression is based on zero-memory nonlinear adaptive soft threshold amplitude limiting. And the defect of a hard threshold is avoided. Therefore, the adverse effect of the non-Gaussian noise on the real-time tracking estimation of the DOA of the multi-radiation source target is remarkably reduced, and the method has good electromagnetic noise environment adaptability to the tracking of the DOA of the multi-radiation source target, is high in robustness, low in calculation complexity and good in flexibility, and can meet the application requirements in a complex electromagnetic environment scene in actual engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a robust DOA tracking method based on zero-memory nonlinear transformation. Background Art

[0002] Direction of Arrival (DOA) tracking is to obtain important intelligence information such as the angle and position of multiple radiator targets by processing the radio signals received by the antenna array. It is the main means of electronic warfare support measures, so it has received great attention in the application of many systems such as radar, sonar and wireless communication. Traditionally, many methods for DOA estimation, such as Maximum Likelihood, Subspace Fitting, Multiple Signal Classification, Estimation of Signal Parameters via Rotational Invariance Technology, etc., are all based on the Gaussian white noise background assumption. Many methods for tracking signal subspace, such as PAST, PASTd, YAST, FAPI, etc., are also based on the Gaussian white noise background assumption.

[0003] This seriously restricts the progress of such methods from theory to practical engineering application, because in the electromagnetic environment of many systems such as radar, sonar and wireless communication, the widely existing atmospheric environmental noise, sea clutter, ground clutter and radar backscatter echo, as well as the electromagnetic environmental noise in urban mobile radio channels, all show short-time pulse characteristics in the time domain and thick tail characteristics in the probability density function. These electromagnetic noises that are significantly different from the characteristics of Gaussian white noise, that is, non-Gaussian noise, are ubiquitous. When non-Gaussian noise appears, the tracking error of the signal subspace will immediately increase, which will cause the real-time DOA estimation to fail. The traditional method cannot be applied to the real-time tracking and estimation of DOA of actual multi-radiator targets. Summary of the invention

[0004] In view of the above problems, the present invention proposes a robust DOA tracking method based on zero-memory nonlinear transformation to significantly reduce the performance deterioration effect of non-Gaussian noise on the real-time tracking estimation of DOA of multi-radiation source targets. This method has good adaptability to electromagnetic noise environment for tracking estimation of signal subspace, strong robustness and low computational complexity, and can meet the application requirements of many systems in complex electromagnetic environment scenarios in actual engineering.

[0005] The technical solution adopted by the present invention is:

[0006] The present invention adopts a zero-memory nonlinear transformation based on the residual vector composed of the signal energy residuals of the antenna array receiving data at adjacent moments. According to the characteristics of the transformation function, when the signal energy residual vector is small, the zero-memory nonlinear transformation is in the linear region, and the current useful signal information is well retained; when the signal energy residual vector is large, the zero-memory nonlinear transformation is in the nonlinear region, and the non-Gaussian noise is adaptively soft-thresholded, which significantly reduces the adverse effects of the non-Gaussian noise. The method is based on the fast data projection algorithm (FDPM). When the incoming signal is interfered by non-Gaussian noise, the data projection method will lose the ability to track the signal subspace. By changing the step size of the signal subspace during iterative update through the zero-memory nonlinear transformation of the signal energy residual vector, when non-Gaussian noise appears, the weight coefficient of the step size will be significantly reduced, which can reduce the adverse effects on the tracking accuracy of the signal subspace caused by the non-Gaussian noise. At the same time, the adjustment of the weight coefficient of the step size is based on the adaptive soft threshold mode, which is very flexible.

[0007] Assuming that the number of antenna array elements is M, the number of spatial radiation signal sources is L, and the number of sampling points is T, the mathematical model of the observed data at the tth time is:

[0008]

[0009] in, is the time-varying array flow pattern, is the radiation signal, The following Gaussian mixture model is used, and its probability density function is:

[0010]

[0011] The first term on the right side of the equation is a standard Gaussian distribution, that is, it obeys x~N(0,1), and the second term obeys x~N(μ,σ 2 ) with a Gaussian distribution with mean μ>>0 and variance σ 2 >>1, ε is a value slightly greater than 0, and the sum of the two according to the ratio (1-ε):ε forms a typical Gaussian mixture model.

[0012] In the signal subspace tracking method based on the fast data projection algorithm (FDPM), the signal subspace D0=eye(M,L) is initialized first, and the update iteration step s is set. The core of the zero-memory nonlinear transformation proposed in the present invention is to perform adaptive soft threshold limiting on the fixed update iteration step. The actual signal subspace tracking iteration step s(t) is determined by the following formula (s0 is the initialization update iteration step):

[0013]

[0014] The denominator ω(t) in the above formula is the weight factor, which is obtained by performing a zero-memory nonlinear transformation on the signal energy residual:

[0015]

[0016] λ and β are adaptive parameters for controlling the robustness of the algorithm, and the signal energy residual

[0017] The robust DOA tracking method for multiple radiation source targets of the present invention comprises the following steps:

[0018] S1, initialize the signal subspace D0 = eye(M, L), initialize the update iteration step s0, and the robustness adaptive parameters λ0, β0;

[0019] S2. Calculate the following parameters during the nth iteration:

[0020]

[0021] where y n is the projection of the observed data x(n), m n is the signal energy residual, and then a zero-memory nonlinear transformation is used to adaptively limit the update iteration step size with a soft threshold. Specifically, the weight factor ω is first calculated. n :

[0022]

[0023] Then calculate the iteration step size s n :

[0024]

[0025] Calculate the intermediate variable z n , g n and q n :

[0026] z n =D n-1 y n

[0027]

[0028] S3, finally get the tracking signal subspace D at time n n for:

[0029]

[0030] S4. Based on the data obtained in S3, the DOA parameters at time n are finally estimated by using the rotational invariance technique based on the total least squares method to estimate the signals of each radiation source.

[0031] The beneficial effect of the present invention is that the present invention can solve the problem of effectively suppressing burst non-Gaussian noise in the complex electromagnetic environment noise in which multiple radiation source signals are located in the absence of prior knowledge, and the suppression is based on zero-memory nonlinear adaptive soft threshold limiting, which avoids the defects of the hard threshold and can effectively retain the useful information of the radiation source signal, and realizes accurate real-time tracking of the target angles of multiple radiation sources. The method has low computational complexity, good flexibility, strong robustness, and is suitable for application requirements in complex electromagnetic environment scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is the real angle trajectory diagram of the radiation source target;

[0033] Figure 2 It is the signal subspace estimation accuracy of the original algorithm under non-Gaussian noise conditions;

[0034] Figure 3 This is the DOA tracking result of the original algorithm under non-Gaussian noise;

[0035] Figure 4 The signal subspace estimation accuracy of the robust algorithm in the case of non-Gaussian noise;

[0036] Figure 5 The DOA tracking results of the robust algorithm under non-Gaussian noise conditions. DETAILED DESCRIPTION

[0037] The present invention is described in detail below with reference to the embodiments.

[0038] Example

[0039] In this example, Matlab is used to verify the above-mentioned robust DOA multi-radiator target tracking estimation method based on zero-memory nonlinear transformation using the fast data projection algorithm (FDPM) as the original framework. For the sake of simplicity, the following assumptions are made on the observation data model: the antenna array adopts a uniform linear array.

[0040] The effectiveness of the present invention is explained below with reference to the accompanying drawings and simulation examples.

[0041] Simulation conditions and parameters

[0042] Simulation environment:

[0043] The number of antenna elements is set to 9, the antenna array is equally spaced at half a wavelength, the number of radiation sources in the target space is 3, and the sampling period is 1000 seconds. The angle of target 1 changes from 60° to 80° during the sampling period, the angle of target 2 changes from 50° to 30° during the sampling period, and the angle of target 3 remains unchanged at 15° during the sampling period. At the same time, electromagnetic environmental noise based on the probability density function of the Gaussian mixture model is added in the sampling period [300,399], and its μ1 is set to 10. Set to 100; add electromagnetic environment noise based on Gaussian mixture model probability density function in the sampling period [500,599], and its μ2 is set to 20. Set to 200, add electromagnetic environment noise based on Gaussian mixture model probability density function in the sampling period [700,799], and set μ3 to 40. It is set to 400, and the probability density functions ε of the three Gaussian mixture models are all set to 0.2.

[0044] Simulation content and result analysis

[0045] Figure 1 The real DOA time-varying trajectories of the three radiation source targets are shown. Figure 2 It can be seen from the signal subspace estimation accuracy that in the sampling period with non-Gaussian noise, the signal subspace estimation accuracy of the original algorithm has seriously deviated from the real signal subspace, resulting in serious distortion of the DOA tracking results of each radiation source target in the sampling period with non-Gaussian noise, such as Figure 3 As shown. Figure 4 It can be seen from the signal subspace estimation accuracy that after the robustness modification of the original algorithm, that is, the adaptive soft threshold limit based on zero-memory nonlinear transformation is applied to the signal energy residual, the purpose of suppressing non-Gaussian noise is achieved, and the negative impact of non-Gaussian noise is significantly reduced. Even in the sampling period where non-Gaussian noise exists, the signal subspace estimation accuracy of the robust algorithm is very close to the real signal subspace, so that the DOA real-time tracking effect of each radiation source target can be achieved. Figure 5 As shown in the above description, it can be seen that the method proposed in the present invention has strong robustness, flexibility and adaptability to complex electromagnetic environments.

Claims

1. A robust DOA tracking method based on zero-memory nonlinear transformation, defining the number of antenna array elements as M, the number of spatial radiation signal sources as L, the number of sampling points as T, and mathematically modeling the observation data at the tth time as: in is the time-varying array flow pattern, is the radiation signal, The following Gaussian mixture model is used, and its probability density function is: The first term on the right side of the equal sign in the above formula is the standard Gaussian distribution, that is, it obeys x~N(0,1), and the second term obeys x~N(μ,σ 2 ) with a Gaussian distribution with mean μ>>0 and variance σ 2 >>1, ε is a value slightly greater than 0; It is characterized in that An improved fast data projection algorithm is used for DOA tracking, including: S1, initialize signal subspace D0 = eye(M, L), iteration step s0, robust adaptive parameters λ0, β0; S2. Calculate the following parameters during the nth iteration: where y n is the projection of the observed data x(n), m n is the signal energy residual, and then a zero-memory nonlinear transformation is used to adaptively limit the update iteration step size with a soft threshold. Specifically, the weight factor ω is first calculated. n : Then calculate the iteration step size s n : Calculate the intermediate variable z n , g n and q n : z n =D n-1 y n S3, finally get the tracking signal subspace D at time n n for: S4. Based on the data obtained in S3, the DOA parameters at time n are finally estimated by using the rotational invariance technique based on the total least squares method to estimate the signals of each radiation source.

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