Estimation of Continuous-Discrete Valued Markov Processes

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  • 連続-離散空間で値をとる Markov 過程の推定
  • レンゾク リサン クウカン デ アタイ オ トル Markov カテイ ノ ス

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Abstract

An algorithm is presented for a general class of nonlinear filtering problems. The process to be estimated is a Markov process with a piecewise-constant component taking values in a finite set of integers. A nonlinear stochastic differential equation modulated by the piecewise-constant component generates another component in a multi-dimensional Euclidean space. The observation is also nonlinear and is corrupted by an additive noise of a Brownian motion process.<br>The a posteriori probability and the conditional filtered estimate of another component evolve with time as shown by calculation for each possible value of the piecewise-constant component. The stochastic linearization technique is used to obtain a feasible algorithm. A numerical example is shown to illustrate the applicability of the proposed algorithm.

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