Effectiveness of Bayesian filters

A fundamental issue concerned the effectiveness of the Bayesian filter is raised.The observation-only (O2) inference is presented for dynamic state estimation.The "probability of filter benefit" is defined and quantitatively analyzed.Convincing simulations demonstrate that many filters can be easily ineffective. The general solution for dynamic state estimation is to model the system as a hidden Markov process and then employ a recursive estimator of the prediction-correction format (of which the best known is the Bayesian filter) to statistically fuse the time-series observations via models. The performance of the estimator greatly depends on the quality of the statistical mode assumed. In contrast, this paper presents a modeling-free solution, referred to as the observation-only (O2) inference, which infers the state directly from the observations. A Monte Carlo sampling approach is correspondingly proposed for unbiased nonlinear O2 inference. With faster computational speed, the performance of the O2 inference has identified a benchmark to assess the effectiveness of conventional recursive estimators where an estimator is defined as effective only when it outperforms on average the O2 inference (if applicable). It has been quantitatively demonstrated, from the perspective of information fusion, that a prior "biased" information (which inevitably accompanies inaccurate modelling) can be counterproductive for a filter, resulting in an ineffective estimator. Classic state space models have shown that a variety of Kalman filters and particle filters can easily be ineffective (inferior to the O2 inference) in certain situations, although this has been omitted somewhat in the literature.