Asynchronous Multi-Sensor State Estimation for Systems Subject to Multiplicative and Cross-Correlated Noises With Measurement Packet Dropping

This paper is concerned with the optimal state estimation problem for linear discrete-time systems with both multiplicative and cross-correlated noises. The measurement outputs for state estimation are collected from multiple sensors whose sampling rates are different that provide asynchronous data. In addition, the noises that affect the measurement information are correlated among different sensors and also coupled with the process noises as well. The aim of the addressed problem is to propose an optimal state estimation algorithm such that the estimation error is minimized in the mean-square sense with the existence of asynchronous data, possible sensor faults and correlated noises. In order to mitigate the impact of measurement missing, this paper utilizes neural networks to compensate the state estimation when measurement packets are dropping. Then, a fault detection mechanism that utilizes normalized innovation test is adopted to ensure that the abnormal data would be detected and removed. By resorting to the projection theorem and mathematical induction approach, sufficient conditions are derived for the existence of the desired optimal state estimator where the optimized estimation gains are formulated and can be computed iteratively at each time step. The proposed theoretical results are demonstrated via an illustrative numerical example.