State Estimation by Continuous-Time Observations in Multiplicative Noise * * The research is partially supported by the Russian Foundation for Basic Research (grants Nos. 15-37-20611 and 16-07-00677).

摘要

The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is a function of the estimated vector, hence the traditional optimal filtering framework fails in this case. The estimate is obtained both in the explicit integral form and as the solution to a stochastic Differential system with some jump processes in the right hand side. The presence of the multiplicative noise gives a possibility to raise the estimation quality up to the exact value restoration. The numerical procedure for the estimate calculation is accompanied with the accuracy analysis. An example illustrating the performance of the proposed estimate is also presented.