Multi-sensor Optimal Linear Estimation With Unobservable Measurement Losses

For a multiple-channel system with sensor measurement losses, if the loss of sensor measurements can be observed by the estimator, the system is called a system with observable measurement losses; otherwise, it is called a system with unobservable measurement losses (a UML system). We first obtain the optimal linear estimator (OLE) for multiple-channel UML systems and then establish a necessary and sufficient condition for the stability and convergence of the OLE. We give a tight bound of the estimation performance loss caused by the unobservability of measurement losses. We show that the estimation performance is a monotonically increasing function of the measurement-loss rate and then analytically characterize the relation between the OLE-performance-loss rate and the measurement-loss rate. Finally, numerical examples are provided to show the effectiveness of the proposed OLE, when the measurement-loss status, that is, the private information of measurement losses, cannot be observed.