Using Fisher Information Criteria for Chemical Sensor Selection via Convex Optimization Methods
Abstract This report presents methodology for the near optimal selection of chemical sensors in a chemical sensing array. While the sensing criteria are task specific, generally one may consider a criterion which maximizes the signal strength or conversely minimizes global error to be best. The quantification of this criteria proceeds from the determinant of the inverse Fisher information matrix which is proportional to the global error volume. If a practitioner has a suitable probabilistic noise model for his or her chemical sensing array and pool of available sensors, the Fisher information matrix may be parametrized to select the best sensors after an optimization procedure. Due to the positive definite nature of the Fisher information matrix, convex optimization may be used to accomplish this task. This report presents the derivation of the supporting set up, expressions, and constraints for this procedure.