Odhad stavu skrytého markovovského řetězce pomocí sekvenčních Monte Carlo metod

Abstract

Physical and other processes affected by random influences can be modelled using Markov chains. These processes often cannot be observed directly. Various approaches are used to estimate these processes, such as the extended Kalman filter, which can be used to estimate the state of a nonlinear model using a linear approximation. Furthermore, sequential Monte Carlo methods that generate samples from a sequence of target probability densities. In this paper, we describe and demonstrate the extended Kalman filter, introduce the principle of sequential Monte Carlo algorithms that we implement on the nonlinear model, and finally compare the estimates from the two methods.