Performance analysis for remote state estimation via measurement combination*

We consider the discrete linear state estimation problem over a packet-dropping network. Before transmitting the data, the linear measurement combination is designed at the local sensor side. In order to improve the remote estimation performance, whether transmitting the current data or the combination depends on whether the previous packet is successfully received or not. A linear minimum mean square error estimation algorithm is proposed for the novel scheme. Moreover, the recursive expression between estimate and smooth error covariance of the last step, as well as the current estimation error covariance is explicitly established via properly constructing a state observer. The equivalency of the two methods is shown via some basic transformations in algebraic Riccati equation theory. The optimal weight for minimizing the estimation error covariance is derived for scalar systems.