Event-triggered remote state estimation over a collision channel with incomplete information

This paper investigates the stochastic event-triggered remote state estimation problem over a collision channel. The remote estimator does not have the knowledge of the measurement in the case of collision and the origin of the data packet in the case of successful transmission, resulting in the non-Gaussianity of the estimation process in the two cases. By using a commonly used Gaussian approximation method, the posterior distribution of the system state is proved to be a mixture of two Gaussians and a mixture of three Gaussians in the cases of collision and successful transmission, respectively. Then an approximate minimum mean squared error estimator with adaptive weights is proposed, and the weights convexly combine the estimates for the possible transmission situations. Moreover, the proposed estimator is also shown to be conventional forms under three extreme situations. Finally, numerical results illustrate the effectiveness of the proposed estimator based on the incomplete information.