CALCULATION OF WEIGHT COEFFICIENTS IN CONTINUOUS PARTICLE FILTER

Abstract

This article shows the relationship between filters based on modeling of the random process paths with terminating and branching and a continuous particle filter that are related to sequential Monte Carlo methods. Different variants for calculation of weight coefficients in the particle filter for stochastic continuous systems (stochastic diffusion systems) are given. Along with the representation by a continuous function, it is shown that the path of the weight function can be presented by a piecewise constant function with nonnegative real values and also by a piecewise constant function with nonnegative integer values. This representation is based on paths modeling of the general Poisson process. The relation with the differential equation for the weight function is indicated. All the given variants for weight coefficients calculation in the particle filter do not require a complex software development, they are suitable for the particle filter software using various parallel programming technologies for high-performance computing systems. The continuous particle filter considered in this paper can be used in various applied estimation tasks, for example, tracking applications, restoring the motion trajectory from observations, restoring a signal from the noise, identifying the dynamic system parameters, and many others. In the future, it is planned to expand the use of the particle filter for stochastic jump-diffusion systems. In addition, it is planned to develop algorithms for predicting the states of stochastic diffusion and jump-diffusion systems based on the calculation of weight coefficients in the particle filter considered in this article.

Keywords

• weight coefficient
• branching process
• monte carlo method
• statistical modeling
• optimal filtering problem
• random process
• stochastic system
• particle filter