Multi-target angle tracking method combining exponential weight and Kalman filtering

Abstract

The invention discloses a multi-target angle tracking method in combination with an exponential weight and Kalman filtering. According to the method, an FAPI algorithm is adopted as an initial framework for improved design, firstly, a novel exponential weight factor self-adaptive soft threshold amplitude limiting method is superimposed on a signal subspace tracking cost function, and soft threshold amplitude limiting is carried out on abnormal measured values based on signal energy residual errors at adjacent moments; useful information of the signal is effectively and reliably reserved while alpha stable distribution noise is suppressed, so that a relatively steady signal subspace tracking result is obtained; secondly, a TLS-ESPRIT algorithm is combined to obtain a real-time estimation result of a multi-radiation source target angle; and finally, taking the real-time estimation result of the multi-radiation source target angle as a measurement value of Kalman filtering, and further smoothing the real-time estimation result by using the Kalman filtering characteristics to improve the accuracy of the angle estimation result in the scene of rapid angle change. And finally, accurate tracking of the maneuvering multi-radiation source target angle under the complex electromagnetic environment noise is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of electronic countermeasures, and in particular relates to a multi-target angle tracking method combining exponential weighting and Kalman filtering. Background Art

[0002] Passive tracking and positioning technology for multi-radiator targets is widely used in many military and national economic application fields such as radar, wireless communication, sonar, seismology, radio astronomy and biomedical engineering. On the battlefield, the angle tracking of multi-radiator targets faces the constraints of complex electromagnetic environment.

[0003] The complex electromagnetic environment is mainly reflected in two aspects. On the one hand, there is the technological development of the radio signal system itself. For example, spread spectrum communication technology will reduce the signal-to-noise ratio when the signal reaches the antenna array receiving system, and the use of frequency hopping communication technology will reduce the number of sampling snapshots of the antenna array receiving system. On the other hand, there is the influence of non-Gaussian distributed electromagnetic environmental noise. These electromagnetic environmental noises are often composed of irregular pulses or noise spikes with short duration and large amplitude, such as α-stable distributed noise, which has obvious thick tail characteristics.

[0004] Traditionally, for the maneuvering of radiation source targets, it is always assumed that the target is a slow-changing process when maneuvering, so the conventional angle tracking algorithm is not very effective for fast maneuvering scenes. In addition, when the conventional Gaussian white noise model signal subspace tracking algorithm is present in the presence of α-stable distribution noise, the obtained signal subspace diffuses mutually, and the algorithm performance is significantly reduced, resulting in the deterioration of the accuracy of angle tracking of multi-radiator targets, which is difficult to meet engineering implementation requirements. Summary of the invention

[0005] In view of the above problems, the present invention proposes a robust maneuvering multi-target angle tracking method combining exponential weight and Kalman filtering. Firstly, the exponential weight factor is used to perform adaptive soft threshold limiting on the α stable distribution noise, so as to improve the environmental adaptability of the signal subspace tracking technology in low signal-to-noise ratio scenarios; secondly, the characteristic that the current state of the multi-radiation source target angle in the Kalman filter is only related to the state at the previous moment is used to further smooth the signal subspace tracking result, so as to finally realize robust maneuvering multi-target angle tracking in complex electromagnetic environment noise, which can meet the application requirements of many scenarios in engineering.

[0006] The technical solution adopted by the present invention is:

[0007] The present invention adopts the Fast Approximate Power Iteration (FAPI) algorithm as the initial framework for improved design. Firstly, a new exponential weight factor adaptive soft threshold clipping is superimposed on the signal subspace tracking cost function therein, which performs soft threshold clipping on abnormal measurement values ​​based on the signal energy residuals at adjacent moments, effectively and reliably retains the useful information of the observed signal while suppressing the α-stable distribution noise, thereby obtaining a relatively robust signal subspace tracking result; secondly, the real-time estimation result of the angle of the multi-radiator target is obtained by combining the rotational invariance technology based on the total least squares method (TLS-ESPRIT); finally, the real-time estimation result of the angle of the multi-radiator target is used as the measurement value of the Kalman filter, and the real-time estimation result is smoothed by using the Kalman filter characteristics to improve the accuracy of the angle estimation result in the scene of rapid angle change, and finally realizes the accurate tracking of the angle of the mobile multi-radiator target in the complex electromagnetic environment noise.

[0008] Assuming that the number of antenna array elements is M, the number of spatial signal sources is L, and the number of sampling points is N, the mathematical modeling of the angle tracking problem of multiple radiation source targets at time t is:

[0009]

[0010] in, is the time-varying array flow pattern, is the radiation source signal in the airspace, is Gaussian white noise, is α-stable distribution noise. The characteristic function of α-stable distribution noise is expressed as follows:

[0011]

[0012] Among them, μ is the position parameter, γ is the dispersion coefficient, β is the symmetry parameter, α is the characteristic index, and the smaller α is, the more serious the pulse characteristics of the noise are. The energy relationship between the radiation source signal and the α stable distribution noise is described by GSNR and satisfies:

[0013] is the radiation source signal variance

[0014] In order to reduce the computational cost, the present invention adopts the fast approximate power iteration (FAPI) algorithm based on data projection as the initial framework, and estimates the observation covariance matrix R according to the adaptive estimation. x (t) = E[x(t)x H (t)], and its underlying signal subspace basis is W(t), the recursive relationship of the observation covariance matrix can be obtained:

[0015] R x (t) = λR x (t-1)+ω(t)x(t)xH (t)

[0016] In the above formula, λ is the forgetting factor, and ω(t) is the exponential weight factor in the present invention.

[0017] Solving the underlying signal subspace basis W(t) can be converted into minimizing the following cost function:

[0018]

[0019] y(i) is projected from the observed data x(i):

[0020] y(i)=W H (i-1)x(i)

[0021] The exponential weight factor in the present invention is in the form of:

[0022]

[0023] σ and z are adaptive parameters for controlling robustness. When soft thresholding is performed on the spatial radiation source target, the residual of the signal energy at adjacent moments is used as a reference to best measure the abnormality of the observed data. Therefore, we have:

[0024] υ(t)=‖x(t)‖ 2 -‖y(t)‖ 2

[0025] Based on the robust tracking estimation of the signal subspace W(t), the angle of the multi-radiator target can be extracted using the total least squares-based rotational invariance technique (TLS-ESPRIT).

[0026] Finally, in order to adapt to the fast-changing angle of the radiation source target, the Kalman filter is used to smooth the angle extraction results to improve the tracking and estimation quality of the angle.

[0027] Set the Kalman filter to capture the state every T time interval, and first establish the following state equation:

[0028]

[0029] are the angle, velocity and acceleration of the i-th target at the k-th moment, respectively. k|k-1 indicates the prior estimate at the k-th moment obtained from the posterior estimate at the k-1-th moment. k|k indicates the posterior estimate at the k-th moment. The state process noise covariance matrix is ​​recorded as Q(k), and the state transfer matrix F is:

[0030]

[0031] Secondly, the prior covariance of the state estimation error of the i-th target at the k-th time is obtained:

[0032] P i (k|k-1)=FP i (k-1|k-1)F T +Q i (k-1)

[0033] Establish the measurement equation:

[0034]

[0035] The measurement equation matrix H = [1 0 0], and the measurement noise variance during the measurement process is denoted by R(k).

[0036] Then the Kalman gain in the Kalman filtering algorithm is obtained as:

[0037] Gain = P i (k|k-1)H T (R i (k)+HP i (k|k-1)H T ) -1

[0038] Finally, the posterior angle estimate of the i-th target at the k-th moment and the posterior covariance of the state estimation error at the k-th moment are obtained:

[0039]

[0040] P i (k|k)=(I3-Gain·H)P i (k|k-1)

[0041] The beneficial effects of the present invention are

[0042] 1) This paper proposes a new exponential weighted cost function for signal subspace tracking when there is α-stable distributed noise corrupting the observation data for multi-radiation source target angle tracking. By selecting appropriate robustness parameters, adaptive soft threshold limiting of the corrupted observation data can be achieved. This method enhances the robustness of signal subspace tracking and is suitable for application scenarios with low signal-to-noise ratio.

[0043] 2) The present invention aims at the application of multi-radiation source target angle tracking in fast-changing applications, combines the advantages of Kalman filtering algorithm, improves the traditional method of requiring the signal subspace to change slowly, and the radiation source target angle tracking and estimation is limited to observation data, and improves the estimation by using Kalman filtering for smoothing. This method can provide better flexibility in high dynamic environments and has good effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is the real time-varying DOA of the radiation source target;

[0045] Figure 2 It is the deviation of the signal subspace of the unimproved algorithm in the presence of α-stable distribution noise;

[0046] Figure 3 To estimate DOA without improving the algorithm in the presence of α-stable distribution noise;

[0047] Figure 4 To improve the algorithm signal subspace deviation in the presence of α-stable distributed noise;

[0048] Figure 5 Improved algorithm + Kalman filtering to track and estimate DOA in the presence of α stable distribution noise. DETAILED DESCRIPTION

[0049] The present invention is described in detail below with reference to the embodiments.

[0050] Example

[0051] In this example, Matlab is used to improve the design of the above-mentioned fast approximate power iteration (FAPI) algorithm as the initial framework. The robust maneuvering multi-target angle tracking method combining exponential weight factors and Kalman filtering is mainly verified. For the sake of simplicity, the following assumptions are made for the observation data model: the antenna array adopts a uniform linear array.

[0052] The effectiveness of the present invention is explained below with reference to the accompanying drawings and simulation examples.

[0053] Simulation conditions and parameters

[0054] Simulation environment:

[0055] The number of antenna elements is set to 9, the antenna array is half wavelength, the number of radiation sources in the target space is 3, and the sampling period is 1000 seconds. Among them, the angle of target 1 changes slowly from 50° to 47° in the sampling period [0,300], changes rapidly from 47° to 22° in [301,400], and changes slowly from 22° to 17.5° in [401,1000]. The angle of target 2 changes slowly from 20.5° to 27.5° in the sampling period [0,500], changes rapidly from 27.5° to 57.5° in [501,600], and changes slowly from 57.5° to 59.5° in [601,1000]. The angle of target 3 does not change during the sampling period and is constant at 35°. α-stable distributed noise is added at the sampling period [400,499], with μ1 set to 0, γ1 set to 1, β1 set to 0, and α1 set to 0.9. α-stable distributed noise is added at the sampling period [600,699], with μ2 set to 0, γ2 set to 1, β2 set to 0, α2 set to 1.1, and GSNR set to 0 dB.

[0056] In the fast approximate power iteration (FAPI) algorithm, the forgetting factor λ is set to 0.98, the robustness control parameter σ in the exponential weight factor is set to 1, and z is set to 2.

[0057] Set the Kalman filter to track once every 1 second, and set the state process noise size to Then the state process noise covariance matrix is:

[0058]

[0059] The measurement noise size setting is divided according to the period of time when the α stable distribution noise appears:

[0060]

[0061] The state estimation error covariance matrix is ​​initialized as:

[0062]

[0063] Simulation content and result analysis

[0064] from Figure 1 It can be seen that the DOA of target 1 and target 2 has slow change and fast change process. Figure 2 It can be seen from the signal subspace estimation deviation that in the sampling period with α stable distribution noise, the signal subspace estimation of the unimproved 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 α stable distribution noise, such as Figure 3 As shown. Figure 4It can be seen from the signal subspace estimation deviation that after the robustness modification of the original algorithm, that is, the adaptive soft threshold limiter with exponential weight is applied to the signal energy residual, the purpose of suppressing the α-stable distribution noise is achieved, and the negative impact of the α-stable distribution noise is significantly reduced. Even in the sampling period where the α-stable distribution noise exists, the signal subspace estimation accuracy is very close to the real signal subspace, so that the DOA of each radiation source target can be effectively tracked in real time. At the same time, combined with the Kalman filtering algorithm, the DOA of the radiation source target can be accurately tracked in the sampling period where the DOA of target 1 and target 2 changes rapidly, such as Figure 5 As shown in the above description, it can be seen that the method proposed in the present invention has strong robustness and flexibility, and can adapt to the scene requirements of low signal-to-noise ratio and rapid change of target angle.

Claims

1. A multi-target angle tracking method combining exponential weight and Kalman filtering, defining the number of antenna array elements as M, the number of spatial signal sources as L, and the number of sampling points as N. The mathematical modeling of the multi-radiation source target angle tracking problem at time t is: in, is the time-varying array flow pattern, is the radiation source signal in the airspace, is Gaussian white noise, is α-stable distribution noise, and the characteristic function of α-stable distribution noise is expressed as follows: Among them, μ is the position parameter, γ is the dispersion coefficient, β is the symmetry parameter, α is the characteristic index, and the smaller α is, the more serious the pulse characteristics of the noise are. The energy relationship between the radiation source signal and the α stable distribution noise is described by GSNR and satisfies: in is the signal variance of the radiation source; Characterized in that, the tracking method is: The fast approximation power iteration algorithm based on data projection is used as the initial framework, and the observation covariance matrix R is estimated according to the adaptive x (t) = E[x(t)x H (t)], after introducing the exponential weight factor ω(t), we can get the recursive relationship of the observation covariance matrix: R x (t)=λR x (t-1)+ω(t)x(t)x H (t) Where λ is the forgetting factor; The solution of the underlying signal subspace basis W(t) is converted into the minimization of the following cost function: y(i) is projected from the observed data x(i): y(i)=W H (i-1)x(i) The functional form of the exponential weight factor is: Among them, σ and z are adaptive parameters for controlling robustness. When soft thresholding is performed on the spatial radiation source target, the residual of the signal energy at adjacent moments is used as a reference to best measure the abnormality of the observed data: v(t)=‖x(t)‖ 2 -‖y(t)‖ 2 The signal subspace W(t) is obtained by solving the cost function, and then the angle of the multi-radiator target is extracted based on the rotation invariance technology of the total least squares method. Finally, the angle extraction result is smoothed by Kalman filtering.

2. The multi-target angle tracking method combining exponential weighting and Kalman filtering according to claim 1, characterized in that: The specific method of smoothing the angle extraction result through Kalman filtering is: Set the Kalman filter to capture the state every T time interval and establish the state equation: in are the angle, velocity and acceleration of the i-th target at the k-th moment, respectively. k|k-1 indicates the prior estimate at the k-th moment obtained from the k-1-th posterior estimate. k|k indicates the posterior estimate at the k-th moment. The state estimation noise covariance is recorded as Q(k). The state transfer matrix F is: Get the prior covariance of the state estimation error at the kth moment: P i (k|k-1)=FP i (k-1|k-1)F T +Q i (k-1) Establish the measurement equation: Wherein the measurement equation matrix H = [1 00], R (k) is the measurement noise variance in the measurement process; The Kalman gain in the Kalman filtering algorithm is obtained as: Gain=P i (k|k-1)H T (R i (k)+HP i (k|k-1)H T ) -1 Finally, the posterior angle estimate of the i-th target at the k-th moment and the posterior covariance of the state estimation error at the k-th moment are obtained: P i (k|k)=(I3-Gain·H)P i (k|k-1)。

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