An event-based state estimation scenario is considered where multiple distributed sensors sporadically transmit observations of a linear process to a time-varying Kalman filter via a common bus. The triggering decision is based on the estimation variance: each sensor runs a copy of the Kalman filter and transmits its measurement only if the associated measurement prediction variance exceeds a tolerable threshold. The resulting variance iteration is a new type of Riccati equation, with switching between modes that correspond to the available measurements and depend on the variance at the previous step. Convergence of the switching Riccati equation to periodic solutions is observed in simulations, and proven for the case of an unstable scalar system (under certain assumptions). The proposed method can be implemented in two different ways: as an event-based scheme where transmit decisions are made online, or as a time-based periodic transmit schedule if a periodic solution to the switching Riccati equation is found.