Optimal multiple-sensor scheduling for general scalar Gauss-Markov systems with the terminal error

In this work, we study finite-horizon multiple-sensor scheduling for general scalar Gauss-Markov systems, extending previous results where only a class of systems are considered. The scheduling objective is to minimize the terminal estimation error covariance. At each time instant, only one sensor can transmit its measurement and each sensor has limited energy. Through building a comparison function and solving its monotone intervals, an efficient algorithm is designed to construct the optimal schedule. In addition, we also provide the result for selecting multiple sensors per time instant under an assumption. Examples are provided to illustrate the proposed results.