Efficient False Alarm Probability Identification for Linear System with Uncertain Measurement

This paper focuses on quickly and analytically identifying the unknown or time-varying false alarm probability (FAP) of the measurements uncertainty or missing in the linear networked multi-sensor system by resorting to the efficient implementation of maximization likelihood (ML) estimation. Firstly, the full-probability likelihood computation is equivalently transformed into a log-likelihood function summation form parameterized by FAP through Bayes' rule. Secondly, the computation of the log-likelihood function is further transferred by skillfully introducing Jessen's inequality for facilitating the rapid and analytical maximization. Thirdly, the analytical identification result of FAP is obtained by constructing Lagrange operator to maximize the transferred log-likelihood with the parameter constraint. Naturally, such analytical result is so simple that it can be efficiently carried out, and has no precision loss for meeting the high performance. Finally, an example motivated by the target tracking application is presented to demonstrate the superiority of the new method.