On the use and misuse of Bayesian filters

Since the groundbreaking work of the Kalman filter in the 1960s, considerable effort has been devoted to discrete time filters for dynamic state estimation, especially including a variety of suboptimal implementations of the Bayesian filter. The essence of the Bayesian filter is to make the (sub)optimum fusion of the observation information in time sequence based on the hidden Markov model of the state process. While admitting the success of filters in many cases, this study investigates the cases when they in fact loose to the deterministic observation-only (O₂) inference that infers the estimate by using the observation information only without modeling the state dynamics. Special attention has been paid to quantitatively analyzing when and why the Bayesian filter will underperform the O₂ inference from the information fusion perspective. Classic state space models have shown that the O₂ inference can perform better (in terms of both accuracy and computing speed) than filters in certain cases. Therefore attention is desired for the use of a filter when the model is not guaranteed to be accurate and much approximation is used.