Importance Resampling Approach for Sensor Mutual Coupling Correction

To achieve accurate direction parameter estimation of sensor array, mutual coupling between sensor elements should be properly handled. This problem becomes more challenging when the sources are coherent. In this paper, we derive an importance resampling approach (IRA) for joint mutual coupling and DOA estimation. Aiming to DOA estimation of coherent sources using the spatial smoothing technique and MUSIC algorithm, error analysis is first provided for the estimate of the corresponding mutual coupling coefficient matrix in a uniform linear array setting. An optimization formulation based on MUSIC is then established for joint estimation of mutual coupling coefficients and DOAs. The proposed IRA framework, which solves this optimization problem, has the advantages of few parameters and low computational complexity. Four different importance resampling algorithms which are the position resampling algorithm, the number resampling algorithm, the number and position resampling algorithm and the zero forcing resampling algorithm are proposed for the implement of the IRA framework with different arrangement and combination according to the characteristic of the real coupling coefficients vector. The proposed approach is effective not only to the case of coherent sources, but also for independent sources, and it can work in both single- and multiple-snapshot scenarios. The excellent performance of our methods for mutual coupling correction and DOA estimation is demonstrated via extensive simulation results, which can also be applied to other sensor parameter estimation scenarios.