Finite cell weight variation bayesian filtering: an efficient posterior-transformation approach for strongly nonlinear, non-gaussian problems

This paper develops the finite-cell weight-variation (FCWV) method for recursive Bayesian filtering and evaluates it on both one-dimensional nonlinear benchmark problems and a multivariate robot localization problem with three state variables. FCWV is based on the transformation law of probability density and represents the posterior as a discretized probability density function composed of local cells, each characterized by its own mean and variance. This deterministic local-cell representation allows FCWV to capture arbitrary posterior shapes, including strongly nonlinear, non-Gaussian and multimodal distributions, without kernel smoothing or special mode-handling procedures. Because it represents posteriors deterministically via local cell statistics rather than importance-weighted samples, FCWV avoids particle degeneracy, sample impoverishment, and resampling-induced instability, which are common issues in particle filtering. In both the one-dimensional and multivariate cases, FCWV is compared with bootstrap particle filtering, and the results show comparable accuracy with substantially lower computational cost, typically by at least an order of magnitude in the examples studied. In the multivariate robot localization problem, the smooth posterior representation also enables efficient mode estimation through standard optimization methods, which is particularly useful when localization is the primary objective. A key limitation of the present formulation is the growth in discretization complexity with state dimension, motivating adaptive cell allocation and related strategies for future high-dimensional extensions.