Optimal Scheduling of Scalar Gauss-Markov Systems With a Terminal Cost Function

In this technical note, we consider the problem of optimal measurement scheduling for a particular class of Gauss-Markov systems. These type of scheduling problems arise in applications such as multi-target tracking and sensor management. General solutions to such problems in the Gauss-Markov framework are still the subject of ongoing research. Here, for the first time, we present a set of results for scalar systems, where we consider optimality in the context of minimizing a terminal cost. Complete proofs are given in each case. In some cases, proof outlines have been previously available; other cases are presented here for the first time. For the class of problems considered we demonstrate that simple index policies are optimal. We further examine practical problems in which suboptimal solutions may suffice. Numerical examples are presented for each case.