Bayesian estimation in observation systems with Markov jump processes: game-theoretic approach

The paper is devoted to the mutual estimation/identification problem for the finite-state Markov jump processes given both the diffusion and counting observations. The dynamic and observation equations depend on the random parameter with uncertain distribution having a known support set. An objective is a conditional expectation of some quadratic function of estimation error. The paper contains an assertion concerning saddle-point existence in the stated minimax problem. The least favorable distribution and the minimax estimate are characterized in terms of the dual optimization problem. Practical applicability of the obtained results is demonstrated by the illustrating example of TCP link status monitoring under uncertain channel characteristics.