A State Estimation Method for Markov Jump Processes Using a Neural Network

A neural network designed to minimize an energy function is shown to be effective in nonlinear estimation. The problem treated in this paper is to estimate states of Markov jump processes from noisy observations. The estimation is accomplished by minimizing an energy function, which bears both information about the measured data and a priori information about the process. The energy function takes the minimum at the point corresponding to a sub-optimal state estimate, which is the optimal estimate under the hypothesis about jumps with maximum a posteriori probability. Though the energy function is not differentiable and has extremely many local minima, it is shown that the network attains the minimum by a continuous modification of the energy function. It is also shown that the network is applicable not only to batch processing, but also to recursive processing using a sliding window. Finally, the method is extended to the estimation of processes which have jumps in velocity.