A robust distributed signal-level fusion positioning method

Abstract

The present invention belongs to the technical field of spatial signal source positioning, and in particular, relates to a robust distributed signal-level fusion positioning method. The method of the present invention is based on a traditional norm model, and uses the robust equivalence transformation in the distributed robust optimization theory to transform the sparse signal recovery problem under disturbance into a solvable convex problem, and obtains a credible solution when there is a receiving phase error. The method is theoretically applicable to receiving arrays of arbitrary structures, such as non-uniform linear arrays, etc., and therefore has strong practicality; compared with the ideal signal reception model, the error model established by the method of the present invention is more general in form, and does not require a complete knowledge of the entire model of the array amplitude and phase errors, making the positioning process of the signal source more robust.

Claims

1. A robust distributed signal-level fusion positioning method, characterized in that: The following steps are involved: S1. Collect signal source signals through multiple antennas and build a near-field signal reception model: y(t)=A(θ)s(t)+n(t) Where A(θ) is the array manifold matrix, s(t) and n(t) are the signal and noise vectors at time t, respectively; S2, reconstruct the received signal matrix, complete the SVD decomposition of the matrix, construct a sparse dictionary matrix, and establish a phase error model, specifically including: Reconstruct y(t) as: in, M is the number of receiving array elements, T is the number of sampling snapshots, and N θ is the size of the overcomplete set. The overcomplete set is a set of directional grids divided in the spatial domain. The corresponding sparse signal matrix is: X=[x1 … x T ] in Represents a sparse signal, converting the positioning problem into the x in the restored signal vector t The indices of the non-zero elements; Perform SVD decomposition on matrix Y: Y=WOLF H Among them, U and V are standard orthogonal matrices, and the columns of U and V are respectively composed of matrices YY T and the matrix Y T Y is composed of the normalized eigenvectors; L is the singular value matrix, and the diagonal elements of L are composed of Y T The singular values ​​of Y are arranged from large to small; retain the signal subspace, set the number of sources to K, and obtain the retained matrix: Y SV =ULD K =YVD K Where the matrix D is selected K =[I K 0] T , I K is the identity matrix of order K, and 0 is the zero matrix of K×(TK); With the goal of minimizing the number of non-zero items in x to ensure the sparsity of the signal, the phase error model is established as: stvec(I K ) H thing(Δ)≤η Among them, X SV =XVD K , is a sparse direction matrix, Γ is a diagonal matrix whose diagonal elements are the phase errors of the corresponding array elements, ||X SV || 2,1 is to calculate X SV l 2,1 norm, η is the threshold of the constraint inequality; S3. Using the distributed robust optimization algorithm, the phase error model is transformed into a convex problem and solved to obtain the position information of the target signal, specifically: Using the distributed robust optimization algorithm, the phase error model is transformed into the following convex problem: Among them, β is an intermediate variable, which is a constant, and p is the probability that the constraint condition is satisfied. is the set of all possible probability distributions that δ obeys, δ = d(Γ), d(Γ) is the column vector consisting of the diagonal elements of the matrix Γ, The first-order moment of all probability distribution statistics in is μ, and the second-order moment is Σ. η is the threshold of the constraint inequality, which is related to the noise power; By solving the convex problem, the location information of the target signal is obtained.

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