Effectiveness of Bayesian filters: An information fusion perspective

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.