State Estimation of Linear Systems With Sparse Inputs and Markov-Modulated Missing Outputs

In this paper, we consider the problem of estimating the states of a linear dynamical system whose inputs are jointly sparse and outputs at a few unknown time instants are missing. We model the missing data mechanism using a Markov chain with two states representing the missing and non-missing data. This mechanism with memory governed by the Markov chain models intermittent outages due to communication channels and occlusions corresponding to moving objects. We rely on the sparse Bayesian learning framework to derive an estimation algorithm that uses Kalman smoothing to handle temporal correlation and the Viterbi algorithm to handle missing data. Further, we demonstrate the utility of our algorithm by applying it to the frequency division duplexed multiple input multiple output downlink channel estimation problem.