On an Optimization Problem in Sensor Selection*

We address the following sensor selection problem. We assume that a dynamic system possesses a certain property, call it Property D, when a set G of sensors is used. There is a cost c A associated with each set A of sensors that is a subset of G. Given any set of sensors that is a subset of G, it is possible to determine, via a test, whether the resulting system-sensor combination possesses Property D. Each test required to check whether or not Property D holds incurs a ®xed cost. For each set of sensors A that is a subset of G there is an a priori probability p A that the test will be positive, i.e., the system-sensor combination possesses Property D. The objective is to determine a test strategy, i.e., a sequence of tests, to minimize the expected cost, associated with the tests, that is incurred until a least expensive combination of sensors that results in a system-sensor combination possessing Property D is identi®ed. We determine conditions on the sensor costs c A and the a priori probabilities p A under which the strategy that tests combinations of sensors in increasing order of cost is optimal with respect to the aforementioned objective.