Adaptive beamforming using the constrained Kalman filter

From the viewpoint of achieving rapid convergence, application of a Kalman filter to an adaptive array is considered. Compared with the Frost´s (1972) constrained least-mean-square algorithm, the constrained Kalman algorithm for adaptive beamforming is proposed to overcome the problem of signal distortion along the look direction which occurs in the unconstrained Kalman beamformer of Baird (1974). A constraint on the array response along the look direction is added to the measurement equation of the Kalman filter. The weight vector of the constrained Kalman beamformer is derived and shown to converge to that of the minimum-variance distortionless-response beamformer. The convergence rate of the proposed algorithm is also analyzed. Compared to Baird´s algorithm and the sidelobe canceller with one-step Kalman predictor, simulation results show the effectiveness of the proposed algorithm