Event-Triggered Continuous-Discrete Kalman Filter With Controllable Estimation Error

In this paper, we first study the event-triggered continuous-discrete Kalman filtering problem to control the MSE under a given triggering threshold, where if the mean squared error (MSE) is smaller than this threshold, then an event is triggered to let the system take a new measurement to reduce the MSE. Previously, since the accurate relationship between the sampling period and the MSE is unknown, it is difficult to control the MSE under a certain system requirement by tuning the sampling period. With our proposed event-triggered continuous-discrete Kalman filter, we are able to upper bound the MSE as expected. Specifically, we strictly prove that whenever a measurement is taken, and the decrease in MSE is lower bounded by a constant determined by the system parameters as well as the triggering threshold if the output matrix has no zero columns. Based on this important property, we provide a rigorous proof that the MSE is finally upper bounded by the triggering threshold, as time goes to infinity. Also, we prove that the event-triggered continuous-discrete Kalman filter can be implemented in a self-triggered manner. Finally, our simulation results corroborate the effectiveness and accuracy of the theoretical results.