Event-based state estimation with variance-based triggering

An event-based state estimation scenario is considered where a sensor sporadically transmits observations of a scalar linear process to a remote estimator. The remote estimator is a time-varying Kalman filter. The triggering decision is based on the estimation variance: the sensor runs a copy of the remote estimator and transmits a measurement if the associated measurement prediction variance exceeds a tolerable threshold. The resulting variance iteration is a new type of Riccati equation with switching that corresponds to the availability or unavailability of a measurement and depends on the variance at the previous step. We study asymptotic properties of the variance iteration and, in particular, asymptotic convergence to a periodic solution.