On stochastic and deterministic event-based state estimation

This paper investigates the problem of remote event-based state estimation for a linear discrete-time plant. Both stochastic and deterministic event-based transmission policies are considered for the systems implemented with smart sensors, where local Kalman filters are embedded. Based on the concept of generalized closed skew normal distributions, the exact probability density functions of the remote event-based state estimation processes are provided. With the properties of smart sensors, the explicit form of the remote event-based state estimators can be derived, without involving numerical integration. In addition, in the case of scalar plants, the estimation and transmission performances under different kinds of event-based scheduling policies are compared theoretically. An important inequality on a truncated covariance of some particular multivariate Gaussian distribution is proved, which builds a bridge between performances of the two event-based policies. Based on this inequality, it is proved that for any considered stochastic event-based transmission policy, there always exists a deterministic counterpart that leads to better estimation performance using the same communication and computational resources. Numerical simulations are provided to illustrate the theoretical results.