Nonlinear Bayesian mode filtering

This work proposes a non-parametric nonlinear Bayesian mode filtering technique for estimating the state of discrete time dynamical systems. The mathematical model of the system can be evaluated for any input of interest, and the corresponding output can be obtained without any knowledge of the model internal functioning. In the proposed method, a set of weighted samples are updated by evaluating the system state transition function, and then the kernel function based non-parametric approximation of the weighted samples is used to estimate the prior probability. The natural evolution gradient of the posterior conditional probability is derived, and hence a Monte Carlo method is applied to recursively locate the mode of the posterior conditional probability. The two dimensional Van der Pol oscillator system is considered as a numerical example. The simulation results show superior performance compared to the standard Particle filter, especially in the cases with small number of particles.