Maximum likelihood parameter estimation with iterative and stochastic measurement schedule

This paper considers the parameter estimation problem of linear system by constructing the iterative and stochastic measurement schedule (ISMS) rule for efficiently implementing the maximum likelihood (ML). When the unknown parameter varies or even mutates with the time proceeding, in the existing measurement schedule rule, estimator can not keep both accuracy and speed of parameter estimation due to the fact that the rule is established before communication. That is, the convergency of the parameter estimation is not fast and accurate enough, especially for the mutational parameter. So we propose a novel ISMS rule to solve this problem. Our ISMS rule can smartly choose these important measurements which are close to the current sampling time and correspondingly drop those useless and unimportant measurements far away from the current time. The accuracy of estimator is improved obviously, because these chosen measurements are able to well reflect the parameter variation. Correspondingly, those dropped measurements further contribute to increase the computation complexity and decrease the speed of tracking the mutational parameter. Based on the constructed ISMS rule, we derive the analytical maximum likelihood parameter estimation (MLPE) and prove its unbiasedness. Moreover, a new concept of average windows length (AWL) is defined as the evaluation index of estimator, and its computation expression is derived. Finally, a numerical example is given to demonstrate the superiority of the new ISMS rule and MLPE in quickly and efficiently estimating the constant or time-varying parameter compared with the existing methods.