Delay-State Dynamics to Filtering Gaussian Systems with Markovian Delayed Measurements

In this paper we propose a solution to the problems of detecting a stochastic output delay sequence characterized by a Markov chain and estimating the state of a linear system driven by Gaussian noise through an augmented delaystate dynamics. This is the model for uncertain observations resulting from losses in the propagation channel due to fading phenomena or packet dropouts that is common in wireless sensor networks, networked control systems, or remote sensing applications. The solution we propose consists of two parallel stages: a nonlinear detector, which identifies at each time instant the delay and a filtering stage. Numerical simulations show the performance of the proposed method.