In this paper, we consider a general class of optimal sensor scheduling problems in discrete time. There are N-1 sensors available for acquiring data so as to estimate the needed but unknown signal. Only N-2 out of the N-1 sensors can be turned on at any moment, while different weights can be assigned to different sensors. This problem is formulated as a discrete time deterministic optimal control problem involving both discrete and continuous valued controls. A computational method is developed for solving this discrete time deterministic optimal control problem based on a branch and bound method in conjunction with a gradient-based method. The branch and bound method is used to determine the optimal schedule of sensors, where a sequence of lower bound dynamic systems is introduced so as to provide effective lower bounds for the construction of the branching rules. Each of the branches is an optimal weight vector assignment problem and a gradient-based method is developed for solving this optimal control problem. For illustration, two numerical examples are solved. (c) 2008 Elsevier Ltd. All rights reserved.