A Comparative Study of Bernoulli Gaussian-max Filter and Bernoulli Gaussian-sum Filter

As a class of exact Bayesian filtering algorithms for non-linear/non-Gaussian recursive estimation of dynamic stochastic systems which can randomly switch on and off, the Bernoulli filter has been extensively studied and applied in target tracking and other dynamic phenomena. In general, there is no analytic solution for the Bernoulli filter, and it is implemented in two ways: Monte Carlo approximation and Gaussian-sum filter (GSF) based on Gaussian-sum models. GSF can be given in the analytic form and has the computational advantage. The possibility Bernoulli filter, which is based on Uncertain Finite Set (UFS) instead of Random Finite Sets (RFS) and implemented as an analogue of standard Bernoulli filter, has been introduced to address the epistemic uncertainties arising from imprecise or partial knowledge of models and/or filtering parameters. Similarly, the Bernoulli Gaussian-max filter (GMF) is formulated as an analogue of the Bernoulli GSF in the framework of possibility theory, rather than the framework of probability theory, with an objective to achieve enhanced ro-bustness. The performance of the Bernoulli GMF and Bernoulli GSF is evaluated and compared through simulation tests in a single target tracking application.