Bayesian Surprise in Linear Gaussian Dynamic Systems: Revisiting State Estimation

Yeganeh Zamiri-Jafarian, Konstantinos N. Plataniotis

Abstract: This article proposes a Bayesian surprise minimization scheme to perform adaptive estimation for a family of linear Gaussian dynamic models. It is shown that the redefined Bayesian surprise in linear Gaussian dynamic systems is a function of the Kalman filter parameters and plays a key role in the state-estimation process. The proposed representation of the Kalman filter illustrates that the information from the Bayesian surprise and the innovation process contributes to the estimation of the state vector and its covariance matrix. This unique approach yields a new set of linear estimation algorithms, where filtering is purely performed with respect to the Bayesian surprise. Simulation results confirm that the information in Bayesian surprise can be sufficient to achieve optimal estimation. In addition, an alternative approach is proposed to test filter consistency based on Bayesian surprise.