A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes

In this paper, approximations of an optimal level-crossing predictor for a zero-mean stationary linear dynamical system driven by Gaussian noise in state-space form are investigated. The study of this problem is motivated by the practical implications for design of an optimal alarm system, which will elicit the fewest false alarms for a fixed detection probability in this context. This work introduces the use of Kalman filtering in tandem with the optimal level-crossing prediction problem. It is shown that there is a negligible loss in overall accuracy when using approximations to the theoretically optimal predictor, at the advantage of greatly reduced computational complexity.