Estimation with lossy measurements: jump estimators for jump systems

The problem of discrete time state estimation with lossy measurements is considered. This problem arises, for example, when measurement data is communicated over wireless channels subject to random interference. We describe the loss probabilities with Markov chains and model the joint plant / measurement loss process as a Markovian Jump Linear System. The time-varying Kalman estimator (TVKE) is known to solve a standard optimal estimation problem for Jump Linear Systems. Though the TVKE is optimal, a simpler estimator design, which we term a Jump Linear Estimator (JLE), is introduced to cope with losses. A JLE has predictor/corrector form, but at each time instant selects a corrector gain from a finite set of precalculated gains. The motivation for the JLE is twofold. First, the real-time computational cost of the JLE is less than the TVKE. Second, the JLE provides an upper bound on TVKE performance. In this paper, a special class of JLE, termed Finite Loss History Estimators (FLHE), which uses a canonical gain selection logic is considered. A notion of optimality for the FLHE is defined and an optimal synthesis method is given. In a simulation study for a double integrator system, performances are compared to both TVKE and theoretical predictions.