Bayesian Kalman filtering, regularization and compressed sampling

Bayesian Kalman filter (BKF) is an important tool in signal processing, communications, control and statistics. This paper briefly reviews the principle of BKF for Gaussian mixture and proposes a new and efficient method for real-time implementation. Moreover, the close relationship between conventional KF and regularization theory in estimation is reviewed. Using this framework, the problem of sampling, smoothing and interpolation can be treated in a unified framework. New results on under-sampling using non-uniform samples will be presented.