Stability Analysis for Multirate Interlaced Kalman Filter

Distributed systems are often chosen since centralized solutions are often impractical when dealing with state estimation of complex systems due to computational complexity. The Interlaced Extended Kalman Filter is a distributed state observer that enables each subsystem to predict a subset of the state space and communicate with other subsystems. How-ever, the Interlaced Extended Kalman Filter requires precise synchronization between subsystems, which may be unfeasible when, for instance, the sampling rates of the subsystems vary. To address this issue, this paper suggests an Interlaced Extended Kalman Filter extension that enables each subsystem to use the most recent estimate when up-to-date information is unavailable. Adjusting the covariance matrix, which can be done using Age of Information metrics, increases the uncertainty in the approximation. Each subsystem's stability is investigated, showing that changes in the covariance matrix do not affect the analysis. The suggested algorithm is validated in a scenario with four water tanks fed by two pumps, where the operating rates of the subsystems are different but fixed. The findings demonstrate that the proposed algorithm successfully handles the multirate problem while striking a reasonable balance between convergence rate and efficiency.