A robust DOA tracking method based on zero-memory nonlinear transformation

Abstract

The application provides a robust DOA tracking method based on zero-memory nonlinear transformation, which can effectively suppress burst non-Gaussian noise under the condition that prior knowledge of a complex electromagnetic environment noise in which a radiation source signal is located is lacked, and the suppression is based on adaptive soft threshold limiting of zero-memory nonlinearity, so that defects of a hard threshold are avoided, thereby realizing significant reduction of adverse effects of non-Gaussian noise on real-time tracking estimation of a multi-radiation source target DOA, and the method has good electromagnetic noise environment adaptability, strong robustness, low calculation complexity and good flexibility in tracking of a multi-radiation source target DOA, and can meet application requirements in a complex electromagnetic environment scene in actual engineering.

Description

Technical Field

[0001] This invention belongs to the field of electronic countermeasures technology, specifically relating to a robust DOA tracking method based on zero-memory nonlinear transformation. Background Technology

[0002] Direction-of-arrival (DOA) tracking, through processing radio signals received by an antenna array, can obtain crucial intelligence information such as the angle and position of multiple radiation source targets. It is a primary means of electronic warfare support and is therefore highly valued in numerous systems, including radar, sonar, and wireless communications. Traditionally, many methods for DOA estimation, such as Maximum Likelihood, Subspace Fitting, Multiple Signal Classification, and Estimation of Signal Parameters via Rotational Invariance Technology, are all based on the assumption of a Gaussian white noise background. Similarly, many methods for tracking the signal subspace, such as PAST, PASTd, YAST, and FAPI, are also based on the assumption of a Gaussian white noise background.

[0003] This severely restricts the transition of such methods from theory to practical engineering applications. This is because signals widely present in the electromagnetic environments of numerous systems such as radar, sonar, and wireless communications—including atmospheric noise, sea clutter, ground clutter, radar backscatter echoes, and electromagnetic noise in urban mobile radio channels—all exhibit short-time pulse characteristics in the time domain and thick tails in their probability density functions. These electromagnetic noises, significantly different from Gaussian white noise—that is, non-Gaussian noise—are ubiquitous. When non-Gaussian noise appears, the tracking error in the signal subspace immediately increases, leading to the failure of real-time DOA estimation performance. Traditional methods cannot be applied to real-time DOA tracking and estimation of multi-source targets. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a robust DOA tracking method based on zero-memory nonlinear transformation. This method significantly reduces the performance degradation caused by non-Gaussian noise in real-time DOA tracking estimation for multi-radiation source targets. The method exhibits good adaptability to electromagnetic noise environments in signal subspace tracking estimation, strong robustness, and low computational complexity, thus meeting the application requirements of many systems in complex electromagnetic environments in practical engineering.

[0005] The technical solution adopted in this invention is:

[0006] This invention employs a zero-memory nonlinear transformation based on the residual vector composed of the signal energy residuals of adjacent time steps in the received data from the antenna array. According to the characteristics of this transformation function, when the signal energy residual vector is small, the zero-memory nonlinear transformation is in the linear region, effectively preserving the current useful signal information; when the signal energy residual vector is large, the zero-memory nonlinear transformation is in the nonlinear region, adaptively applying soft thresholding to non-Gaussian noise, significantly reducing the adverse effects of non-Gaussian noise. This method uses the Fast Data Projection (FDPM) algorithm as a framework. When the incoming signal is interfered with by non-Gaussian noise, the data projection method loses its ability to track the signal subspace. By changing the step size of the signal subspace during iterative updates through the zero-memory nonlinear transformation of the signal energy residual vector, the weight coefficient of the step size is significantly reduced when non-Gaussian noise is present, which can reduce the adverse effects of non-Gaussian noise on the tracking accuracy of the signal subspace. Furthermore, the adjustment of the step size weight coefficient is based on an adaptive soft thresholding mode, offering high flexibility.

[0007] Assuming the antenna array has M elements, the number of spatial radiation signal sources is L, and the number of sampling points is T, then the mathematical model for the observed data at time t is as follows:

[0008]

[0009] in, It is a time-varying array manifold. It is a radiated signal. The following Gaussian mixture model is used, and its probability density function is:

[0010]

[0011] The first term on the right-hand side of the above equation is a standard Gaussian distribution, i.e., it follows x ~ N(0,1), and the second term follows x ~ N(μ,σ). 2 The expression follows 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 of (1-ε):ε forms a typical Gaussian mixture model.

[0012] In the signal subspace tracking method based on the Fast Data Projection (FDPM) algorithm, the first step is to initialize the signal subspace D0 = eye(M,L) and set the update iteration step size s. The core of the zero-memory nonlinear transform proposed in this invention is to adaptively apply a soft threshold to this fixed update iteration step size. The actual signal subspace tracking iteration step size s(t) for each iteration is determined by the following formula (s0 is the initial update iteration step size):

[0013]

[0014] The denominator ω(t) in the above formula is the weighting 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 the robustness of the control algorithm, and the signal energy residual is...

[0017] The robust DOA tracking method for multi-radiation source targets described in this invention includes the following steps:

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

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

[0020]

[0021] Where y n It is the projection of the observed data x(n), m n It is the signal energy residual, and then an adaptive soft thresholding is applied to the update iteration step size using a zero-memory nonlinear transformation. Specifically, the weighting 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, the tracking signal subspace D at time n is obtained. n for:

[0029]

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

[0031] The beneficial effects of this invention are as follows: This invention can effectively suppress sudden non-Gaussian noise in complex electromagnetic environments where multiple radiation source signals are located, in the absence of prior knowledge. Moreover, this suppression is based on zero-memory nonlinear adaptive soft thresholding, avoiding the defects of hard thresholding. It can effectively preserve the useful information of radiation source signals and realize accurate real-time tracking of the target angle of multiple radiation sources. This method has low computational cost, good flexibility, and strong robustness, making it suitable for application needs in complex electromagnetic environment scenarios. Attached Figure Description

[0032] Figure 1 This is a diagram showing the actual angular trajectory of the radiation source target.

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

[0034] Figure 3 The results of DOA tracking using the original algorithm under non-Gaussian noise conditions;

[0035] Figure 4 The accuracy of robust algorithm for signal subspace estimation under non-Gaussian noise conditions;

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

[0037] The present invention will now be described in detail with reference to the embodiments.

[0038] Example

[0039] This example uses MATLAB to verify the robust DOA multi-source target tracking estimation method based on zero-memory nonlinear transformation, which uses the Fast Data Projection (FDPM) algorithm as the original framework. For simplicity, the following assumptions are made about the observation data model: the antenna array is a uniform linear array.

[0040] The effectiveness of the present invention will be illustrated below with reference to the accompanying drawings and simulation examples.

[0041] Simulation conditions and parameters

[0042] Simulation environment:

[0043] The antenna array is configured with 9 elements, equal spacing of half a wavelength, and 3 radiation sources in the target space. The sampling period is 1000 seconds. During the sampling period, the angle of target 1 changes from 60° to 80°, the angle of target 2 changes from 50° to 30°, and the angle of target 3 remains constant at 15°. Simultaneously, electromagnetic environmental noise based on a Gaussian mixture model probability density function is added to the sampling period [300, 399], with μ1 set to 10. Set to 100; add electromagnetic environmental noise based on the probability density function of a Gaussian mixture model during the sampling period [500, 599], with its μ2 set to 20. Set to 200, electromagnetic environmental noise based on the probability density function of a Gaussian mixture model is added during the sampling period [700, 799], with its μ3 set to 40. The value was set to 400, and the probability density function ε of the three Gaussian mixture models was set to 0.2.

[0044] Simulation content and result analysis

[0045] Figure 1 The actual time-varying DOA trajectories of three radiation source targets are displayed. From Figure 2 The accuracy of the signal subspace estimation shows that, within the sampling period where non-Gaussian noise exists, the original algorithm's signal subspace estimation accuracy has deviated significantly from the true signal subspace, resulting in severe distortion of the DOA tracking results for each radiation source target within the sampling period where non-Gaussian noise exists. Figure 3 As shown. From Figure 4 The accuracy of the signal subspace estimation shows that, through robust modifications to the original algorithm—specifically, applying adaptive soft thresholding based on zero-memory nonlinear transformation to the signal energy residual—non-Gaussian noise is suppressed, significantly reducing its negative impact. Even within sampling periods containing non-Gaussian noise, the robust algorithm's signal subspace estimation accuracy closely approximates the true signal subspace, thus achieving effective real-time DOA tracking of various radiation source targets. Figure 5 As shown in the figure. As can be seen from the above description, the method proposed in this 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 elements as M, the number of spatial radiation signal sources as L, and the number of sampling points as T, the mathematical modeling of observation data at the tth moment is as follows: wherein is a time-varying array flow pattern, is a radiation signal, A Gaussian mixture model is adopted, and its probability density function is as follows: In the above equation, the first term on the right side is a standard Gaussian distribution, i.e., x ~ N(0, 1), and the second term is a Gaussian distribution, i.e., x ~ N(μ, σ 2 ), with a mean μ >> 0 and a variance σ 2 >> 1, and ε is a value slightly greater than 0. characterized in that The improved fast data projection algorithm is used for DOA tracking, including: S1, initializing the signal subspace D0=eye(M, L), the iteration step s0, the robustness adaptive parameter λ0, and β0; S2, calculating the following parameters in the n th iteration process: where y n is the projection of the observation data x(n), m n is the signal energy residual, then an adaptive soft thresholding of the update iteration step is performed using a zero-memory nonlinear transform, which is specifically to first calculate the weight factor ω n : Then the iteration step s is calculated n : The intermediate variable z is calculated n , g n and q n : z n = D n-1 y n S3, the tracking signal subspace D at time n is finally obtained n is: S4, based on the data obtained in S3, finally estimating each radiation source signal based on the rotation invariance technology of the total least squares method to obtain the n th DOA parameter.

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