Pass-stop band response weighted constrained adaptive spatial domain filter design method

Abstract

The present invention provides a method for designing a pass-stopband response weighted constrained adaptive spatial filter, which belongs to the field of array signal processing technology. The present invention performs weighted constraints on the passband response error and constrains the stopband response at the same time, so that the overall output response is minimized. By designing a spatial filter through an optimization problem and converting it into a solution to the optimization problem, the optimal solution of the filter is obtained mathematically. The filter design described in the present invention is highly efficient and has a wide range of applications. It can suppress interference signals of various spatial incident models and can achieve a balance in the response errors in all directions of the passband.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing and relates to an adaptive spatial domain filter design method with passband response error weighting and stopband response constraint. Background Art

[0002] Target detection based on sensor arrays is an important means of improving target orientation and positioning accuracy. However, the data received by sensor arrays often contains strong far-field or near-field interference. This interference reduces the accuracy of sensor array-based target orientation and positioning, and reduces target detection and identification capabilities.

[0003] Spatial matrix filtering technology achieves the desired spatial filter response for the passband and stopband by designing the detection space and employing appropriate filter design methods. Spatial filtering is achieved by multiplying the filter matrix with the array data received by the sensor. Spatial filtering suppresses stopband interference while retaining the useful signal in the passband.

[0004] Conventional spatial filter design techniques primarily utilize fixed passband and stopband divisions to produce filter responses specific to the passband and stopband. When the intensity of interference in the spatial domain varies, conventional spatial filters are unable to adaptively adjust their suppression capabilities based on the energy level of the interference. Prior art document 1, "Spatial Matrix Filtering and Its Applications" (Han Dong, Zhang Haiyong, Science Press, April 2016), details the design of discrete, weighted discrete, and continuous filters, all employing conventional spatial filter design methods.

[0005] Prior art document 2, “Adaptive Spatial Matrix Filter Design and Target Direction Estimation”, Feng Jie, Yang Yixin, Sun Chao, Journal of System Simulation, 2007, 19(20): 4798-4802; and prior art document 3, “Convex Optimization Based Beam-Space Preprocessing With Improved Robustness Against Out-of-Sector Sources”, Hassanien A, Elkader SA, Gershman AB et al., IEEE Trans. Signal Processing, 2006, 54(5): 1587-1595, designed an adaptive spatial filter design method to constrain the response error at each direction of the passband and the response at a specific direction of the stopband. The passband and stopband settings are both based on a model of a far-field plane wave signal incident on the array. That is, the target signal to be detected is located in the spatial passband of the far-field plane wave model, and the interference signal is located in the stopband of the far-field plane wave model. This method has two main drawbacks: First, the interference signal incident model is limited to plane wave incidence, making it not widely applicable. It fails to account for the complexity of signal propagation. When the noise is a near-field interference incident model or a model after multipath incidence, the stopband design should adapt to the spatial incident response vector of the interference, rather than the plane wave direction vector. Second, the solution is inefficient, computationally intensive, and time-sensitive. The design method requires conversion to a second-order cone programming solution, which cannot provide a concise optimal solution expression, thus limiting the practicality of this technology. Summary of the Invention

[0006] The purpose of the present invention is to provide an adaptive spatial filter design method with weighted passband response errors and stopband response constraints. By solving the optimization problem, the optimal filter solution is mathematically obtained. The present invention solves three technical problems: first, the filter design is efficient, and the optimal solution of the adaptive filter driven by the received data can be directly obtained; second, it has a wide range of applications, and can achieve specific response constraints for interference signals from various spatial incidence models such as planar models, multipath models, and near-field models; third, it can achieve an equalization effect on the response errors in all directions of the passband through an iterative algorithm.

[0007] The technical solution of the present invention is:

[0008] Assume that the received array data x(t) contains passband signal, stopband interference and additive ambient noise.

[0009] x(t)=V P s1(t)+V S s0(t)+n(t)

[0010] In the formula, the array manifold matrices composed of the passband and stopband direction vectors are and V P =[a(θ1),…,a(θ p ),…,a(θ P )],1≤p≤P,θ p ∈Θ P ; V S =[v1,…,v s ,…,v S ], 1≤s≤S. ​​Θ P Indicates the passband region where the direction vector is located, a(θ p ) is the pth direction vector after discretization of the passband region, v s is the array response vector of the interference signal with known bearing; P is the number of direction vectors after discretization of the passband region, and S is the number of stopband interferences. s1(t) is the passband target signal, s0(t) is the stopband interference signal, and n(t) is the additive ambient noise.

[0011] Design an N×N dimensional adaptive spatial filter H, use it to filter the received array data, and obtain the output filtered signal:

[0012] y(t)=Hx(t)=HV P s1(t)+HV S s0(t)+Hn(t)

[0013] Let w(θ p ) is the passband direction vector response error weighting coefficient, W 12 is a diagonal matrix consisting of the square roots of the passband direction vector weights, that is,

[0014]

[0015] Establish an optimization problem, design an adaptive spatial filter H, and find the adaptive spatial filter with the minimum output signal norm for the passband response error weighted constraint and the stopband overall response constraint. The adaptive spatial filter corresponds to the optimization problem:

[0016]

[0017]

[0018]

[0019] Where ε ≥ 0 is the passband response error weighting constraint value, and δ ≥ 0 is the stopband response constraint value.

[0020] The optimal solution of the adaptive spatial filter H is:

[0021]

[0022] Where, C x =x(t)x H (t) is the covariance matrix of the received array data, W = diag[w(θ1),w(θ2),…,w(θ P )] is a diagonal matrix composed of the weighted values ​​of the passband direction vector; is the optimal Lagrange multiplier, which is determined by the following formula:

[0023]

[0024]

[0025] By setting an appropriate weighting coefficient w(θ p ),p=1,…,P, the response error equalization effect of the passband signal can be achieved. The key to the design of the adaptive spatial filter H lies in the iteration of the weighting coefficients.

[0026] Initial value:

[0027] w1(θ p )=1,p=1,…,P,θ p ∈Θ P

[0028] Iteration:

[0029] W k =diag[w k (θ1),w k (θ2),…,w k (θ P )]

[0030]

[0031]

[0032]

[0033]

[0034] w k+1 (θ p )=β k (θ p )w k (θ p )+ο,p=1,…,P

[0035] Among them, in the iterative step, and is the optimal Lagrange multiplier for the kth iteration, determined by the following formula:

[0036]

[0037]

[0038] w k (θ p ) is the weighted coefficient of the filter's response error to the passband direction vector during the kth iteration. In the iteration step, o is a relatively small value set. is the adaptive spatial filter obtained in the kth iteration, F k (θ p ) is the filter Response error to passband signal, β k (θ p ) is the kth iteration of w k (θ p ) product vector of weighted values, W k is the weighting coefficient matrix used for the kth iteration.

[0039] Termination condition: k = K. At this point, after K iterations, the algorithm terminates.

[0040] The beneficial effects of the present invention are as follows: the present invention can directly provide the optimal solution of the filter by designing an adaptive spatial domain filter with weighted constraints on the passband and stopband responses, and at the same time, utilize the iteration of the passband response error weighting coefficient to obtain the equalization effect of the response errors in all directions of the passband. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 shows the effect of the adaptive spatial filter H, with the passband response error weight constraint set to 10 -5 , the overall response constraint value of the stop band is 10 -6 The passband range is [-15°, 15°], and the stopband interference is set to the plane wave incident model, with a range of [-90°, -18°] ∪ [18°, 90°]. Figure 1(a) shows the filter response, and Figure 1(b) shows the filter response error.

[0042] Figure 2 shows the effect of the adaptive spatial filter H, with the passband response error weight constraint set to 10 -5 The overall stopband response constraint value is 0, the passband range is [-15°, 15°], and the stopband interference is set to a plane wave incident model with a range of [-90°, -18°] ∪ [18°, 90°]. Figure 2(a) shows the filter response, and Figure 2(b) shows the filter response error. DETAILED DESCRIPTION

[0043] The specific embodiments of the present invention are described in detail below in conjunction with the invention content and the accompanying drawings.

[0044] A method for designing a pass-stopband response weighted constraint adaptive spatial domain filter comprises the following steps:

[0045] Step 1: Select the passband detection area Θ to be retained P , the passband detection area Θ P Discretize into P directions and obtain the corresponding plane wave incident azimuth angle θ p ,p=1,…,P. Use the signal incident model to find the corresponding direction vector a(θ p ) and the array manifold matrix V P =[a(θ1),…,a(θ p ),…,a(θ P )],1≤p≤P.

[0046] Select the interference signal to be suppressed, determine the number of stopband interferences S and the array response vector v of the interference signal s ; Generate the array manifold matrix V consisting of the stopband array response vector S =[v1,…,v s ,…,v S ], 1≤s≤S, and find C S =V S V S H .

[0047] Calculate the covariance matrix C using the received array data x(t) x =x(t)x H (t). Set the value ο, the passband response error weight constraint value ε, and the stopband response constraint value δ.

[0048] Step 2: Set the initial iteration count k = 1. Set the initial weighting coefficient matrix W1 = (diag[1,1,…,1]) P×P , W1 is a unit diagonal matrix of dimension P×P.

[0049] Step 3: For the kth iteration, calculate the following formulas:

[0050] W k =diag[w k (θ1),w k (θ2),…,w k (θ P )]

[0051]

[0052]

[0053]

[0054]

[0055] Among them, in the iterative step, and is the optimal Lagrange multiplier for the kth iteration, determined by the following formula:

[0056]

[0057]

[0058] Step 4: Calculate iterative weighting coefficients

[0059] w k+1 (θ p )=β k (θ p )w k (θ p )+ο,p=1,…,P

[0060] Step 5: Termination condition judgment

[0061] If k = K, the algorithm terminates; This is the final adaptive spatial filter. Otherwise, set k = k + 1 and repeat steps 3 to 5.

[0062] The filter design of the present invention has high efficiency and a wide range of applications, can suppress interference signals of various spatial incident models, and can achieve balanced response errors in all directions of the passband.

Claims

1. A pass-stopband response weighted constraint adaptive spatial domain filter design method, characterized in that: The method comprises the following steps: Step 1: Select the passband detection area Θ to be retained P , the passband detection area Θ P Discretize into P directions and obtain the corresponding plane wave incident azimuth angle θ p ,p=1,…,P;Use the signal incident model to find the corresponding direction vector a(θ p ) and the array manifold matrix V P =[a(θ1),…,a(θ p ),…,a(θ P )]; Select the interference signal to be suppressed, determine the number of stopband interferences S and the array response vector v of the interference signal s ; Generate the array manifold matrix V consisting of the stopband array response vector S =[v1,…,v s ,…,v S ], 1≤s≤S, and find Calculate the covariance matrix C using the received array data x(t) x =x(t)x H (t); Set the value ο, the passband response error weight constraint value ε, and the stopband response constraint value δ; Step 2: Set the initial iteration count k = 1; set the initial weight coefficient matrix W1 = (diag[1,1,…,1]) P×P , W1 is a unit diagonal matrix of dimension P×P; Step 3: For the kth iteration, calculate the following formulas: W k =diag[w k (θ1),w k (θ2),…,w k (i P )] Among them, w k (θ p ) is the weighted coefficient of the filter’s response error to the passband direction vector during the k-th iteration; W k is the weighting coefficient matrix used for the kth iteration; is the adaptive spatial filter obtained in the kth iteration; F k (θ p ) is the filter Response error to passband signal; β k (θ p ) is the kth iteration of w k (θ p ) product vector of weighted values; In the iterative step, and is the optimal Lagrange multiplier for the kth iteration, determined by the following formula: Step 4: Calculate iterative weighting coefficients w k+1 (i p )=β k (i p )w k (i p )+o,p=1,…,P Step 5: Termination condition judgment If k=K, the algorithm terminates. This is the final adaptive spatial filter; otherwise, let k = k + 1 and repeat steps 3 to 5.

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