Filtering of a class of Markov jump processes by heterogeneous observations with additive noises

The paper is devoted to the optimal filtering problem of a class of Markov jump processes. The estimated system state is a Markov jump process with a finite set of possible states representing the probabilistic distributions. The available measurement information includes continuous and counting observations. The continuous observation is a function of the system state corrupted by an independent Wiener process. The counting observation intensity also depends on the state. The filtering problem is to find the conditional mathematical expectation of a scalar function of the state (a signal process) given the available observations. The required estimate represents the solution to a system of the stochastic differential system. The paper also introduces an analog of the Kushner–Stratonovich equation describing the temporal evolution of the state conditional distribution. A numerical example illustrates the performance of the proposed filtering estimate. It presents the monitoring of the quality state and numerical parameters of a communication channel given the oscillating observations of round-trip time and the flow of the packet losses.