Particle Filter without a Prior Information for Probability Distribution

Abstract

Kalman filter is one of the most famous state estimation methods. Many state estimations based on Kalman filter have been proposed for various conditions of systems and noise. These estimation methods need to know probability density functions of dynamical systems. However, the probability density functions and a prior information of noise in particular are rarely known in practice. On the other hand, in the field of machine learning, probability density estimations have been studied extensively, and conditional probability density estimations were proposed as extensions of the probability density estimations. In this paper, we propose a direct design method of probability density functions for dynamical systems from data by using conditional probability density estimations because the systems are represented as conditional probability density functions. In addition, we apply the method to particle filter, which is one of nonlinear Kalman filters, and propose a new state estimation method without a prior knowledge for the dynamical systems. Numerical simulations demonstrate the effectiveness of the proposed method.