Robust Adaptive Beamforming Based on the Kalman Filter

In this paper, we present a novel approach to implement the robust minimum variance distortionless response (MVDR) beamformer. This beamformer is based on worst-case performance optimization and has been shown to provide an excellent robustness against arbitrary but norm-bounded mismatches in the desired signal steering vector. However, the existing algorithms to solve this problem do not have direct computationally efficient online implementations. In this paper, we develop a new algorithm for the robust MVDR beamformer, which is based on the constrained Kalman filter and can be implemented online with a low computational cost. Our algorithm is shown to have a similar performance to that of the original second-order cone programming (SOCP)-based implementation of the robust MVDR beamformer. We also present two improved modifications of the proposed algorithm to additionally account for nonstationary environments. These modifications are based on model switching and hypothesis merging techniques that further improve the robustness of the beamformer against rapid (abrupt) environmental changes.