Random-Set-Based Estimation in Networked Environments and a Relationship to Kalman Filtering with Intermittent Observations

Firstly, an exposition of random-set-based estimation in general networked control systems is examined. This provides a background for the work introduced in this paper. This exposition is also aimed at highlighting the advantages of the random-set-based estimator formulation. Then, the case of state estimation across packet-dropping networks (but with instantaneous transmission times) is shown to be a special case of the standard random-set-based system/measurement model. A well-known result in the control literature concerning the convergence of the Kalman filter's covariance estimate is related to a simplified random-set-based algorithm for this packet-dropping scenario. Finally, a novel algorithm for random-set-based estimation across general networks with irregular measurement sequences (delayed and out-of-sequence measurements) is developed. This is the first attempt to extend random-set-based estimation to accommodate realistic, networked, scenarios.