Array Self-Calibration With Polynomial Root Finding

Direction of Arrival(DOA)estimation is important in array signal processing.It is widely used in radar,unmanned aerial vehicle exploration,and autonomous driving.Most of the existing DOA estimation methods require the array flow pattern matrix to be accurately known.However,in practical applications,the array flow pattern error inevitably exists,resulting in a sharp deterioration in the performance of the algorithm.So,calibration is very significant.Aiming at the problem of array error calibration,scholars at home and abroad have proposed a large number of error self-calibration algorithms.The RARE algorithm,as one of the classic self-calibration algorithms,can calibrate the array flow pattern error without losing the array aperture,but it still has the following defects: 1)When array mutual coupling error exists,the spectral peak search is required in RARE algorithm,and the calculation complexity is high;2)When RARE algorithm handles the problem of situation when gain-phase and mutual coupling errors exist simultaneous,every time the gain-phase and the mutual coupling parameters are updated iteratively,the spectral peak search is inevitable,and resulting in a high calculation complexity.In response to the above problems,the research content of this article is as follows:First of all,when mutual coupling error exists in the array,the existing RARE algorithm needs to perform spectral peak search,and the calculation complexity is relatively high.A new self-calibration method for mutual coupling error based on polynomial root finding is proposed.The algorithm uses the polynomial root finding to perform a determinant calculation of the cost function matrix,and jointly calibrate DOA and mutual coupling errors.This method effectively avoids the processing of spectral peak search and reduces the computational complexity.The comparison experiment with the existing method shows that the method can achieve accurate estimation of DOA,especially when the signal-to-noise is relatively low,it still has good estimation performance.Secondly,when gain-phase and mutual coupling errors coexist,the existing RARE algorithm needs to use cumbersome iterations: 1)fix the gain-phase and mutual coupling error matrix to update the DOA;2)fix the DOA and mutual coupling error matrix to update gain-phase;3)Fix DOA and gain-phase error matrix to update mutual coupling.In addition,every time the gain-phase and the mutual coupling parameters are updated iteratively,the spectral peak search is inevitable,and resulting in a high calculation complexity.To solve this problem,a joint calibration method for mutual coupling and gain-phase errors based on polynomial rooting is proposed.This method reduces the tedious iteration to two steps: 1)Fix the mutual coupling matrix,and update the DOA and gain-phase jointly;2)Fix DOA and gain-phase matrix to update mutual coupling.In addition,this method extends the idea of polynomial root finding to update iterations of flow pattern error parameters,avoiding the spectral peak search,and further reducing the complexity of the algorithm.The comparison experiment with the existing method shows that this method can effectively improve the DOA estimation performance.