State Estimation with Event Sensors: Observability Analysis and Multi-sensor Fusion

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 167-190, February 2024.
Abstract. This work investigates a state estimation problem for linear time-invariant systems based on polarized measurement information from event sensors. To enable estimator design, a new notion of observability, namely, [math]-observability is defined with the precision parameter [math] which relates to the worst-case performance of inferring the initial state, based on which a criterion is developed to test the [math]-observability of discrete-time linear systems. Utilizing multisensor polarity data from event sensors and the implicit information hidden in event-triggering conditions at no-event instants, an iterative event-triggered state estimator is designed to evaluate a set containing all possible values of the state. The proposed estimator is built by outer approximation of intersecting ellipsoids that are predicted from previous state estimates and the ellipsoids inferred from received polarity information of event sensors as well as the event-triggering protocol; the estimated regions of the state derived from multisensor event measurements are fused together, the sizes of which are proved to be asymptotically bounded. Distributed implementation of the estimation algorithm utilizing a two-layer processor network of hierarchy architecture is discussed, and the temporal computational complexity of the algorithm implemented in centralized and distributed ways is analyzed. The efficiency of the proposed event-triggered state estimator is verified by numerical experiments.