A kernel density-based particle filter for state and time-varying parameter estimation in nonlinear state-space models

In linear/nonlinear dynamical systems, there are many situations where model parameters cannot be obtained a priori or vary with time. As a consequence, the estimation algorithms that are based on the exact knowledge of these model parameters cannot be accurate in this context. In this work, a kernel density-based particle filter is investigated to jointly estimate the states and unknown time-varying parameters of a dynamical system described by nonlinear state and measurement equations. The approach combines an auxiliary particle filter with the kernel smoothing method so as to obtain a stationary kernel density for the unknown parameters. The performance of the proposed approach is investigated for positioning using measurements from a global navigation satellite system that are possibly contaminated by multipath interferences.