Steering Vector Matrix Reconstruction for Closely Spaced DoA Estimation
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Solution Overview
Problem
Existing gridless DoA estimation methods perform poorly under low signal-to-noise ratio (SNR) conditions or when the angular separation of incident signals is small, leading to reduced accuracy and inability to distinguish similar targets.
Innovation Solution
A direction of arrival estimation method based on steering vector matrix reconstruction, utilizing a Hankel matrix transformation operator and column extraction operator to constrain a target variable, and solving a multivariable optimization model with alternating direction method of multipliers to obtain an optimal result.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If gridless DoA estimation methods are used, then the basis mismatch problem caused by grid discretization is solved, but the performance deteriorates when signal-to-noise ratio is low or angular resolution is low
Solution Approach 1:
The patent transforms the DoA estimation problem into a parameter estimation problem by exploiting the Vandermonde structure of the steering matrix. It changes the approach from direct spectral estimation to estimating the parameters (angles) of incident signals through optimization, which improves performance under low SNR and small angular separation conditions while avoiding grid discretization issues
Solution Approach 2:
The patent introduces an auxiliary variable representing the steering matrix with Vandermonde structure as an intermediary. This auxiliary variable connects the observed covariance matrix to the unknown DoA parameters, enabling the use of optimization methods to achieve both gridless operation and high estimation accuracy
2Ease of operation
If spatial spectrum estimation methods are used, then DoA estimation can be performed using array covariance matrix, but the method fails to provide satisfactory performance when angular separation of incident signals is small
Solution Approach 1:
The patent replaces the mechanical spectral search approach of traditional spatial spectrum methods with an optimization-based parameter estimation system. By substituting the spectral peak search mechanism with an optimization algorithm that directly estimates signal parameters, the method achieves superior angular resolution for closely spaced sources
3Adaptability or versatility
If discrete grids are used in sparsity-based methods, then the nonlinear parameter estimation problem is transformed into sparse signal recovery, but adjacent atoms become strongly correlated which reduces estimation performance
Solution Approach 1:
Instead of discretizing the continuous angular space into grids (which causes atom correlation), the patent inverts the approach by directly estimating continuous DoA parameters through optimization. It replaces the grid-based sparse recovery paradigm with a gridless parameter estimation paradigm, thereby eliminating the atom correlation problem while maintaining the benefits of sparsity exploitation
Data Source
AI summary
A DoA estimation method and device based on steering vector matrix reconstruction, related to the field of array signal processing. The method includes: obtaining an array sampling covariance matrix according to an array received signal; setting a target variable, and limiting a feasible domain of the target variable by using two operators to determine a first constraint condition; characterizing an estimation error based on the target variable and the array sampling covariance matrix, and using the characterized estimation error as a second constraint condition; establishing an initial optimization model according to a preset norm based on partial sum of singular values and constraint conditions of the target variable; determining a multivariable optimization model according to the initial optimization model; and solving the multivariable optimization model to obtain an optimal result; analyzing the optimal result to obtain a DoA of the target incident signal.