Distributed Kalman Filters with State Equality Constraints: Time-based and Event-triggered Communications

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SECs). We propose a distributed Kalman filter design based on a covariance intersection approach by combining a filtering structure and a fusion-projection scheme for time-varying dynamics, in order to overcome the strong correlation between the estimates of agents and timely provide an upper bound of the error covariance matrix of each agent.It is shown that all SECs will be satisfied as the fusion-projection number goes to infinity. Further, given a finite fusion-projection number, the SECs will be satisfied as time goes to infinity. Based on the extended collective observability, we prove the Gaussianity, consistency, upper boundedness of the covariance matrix and convergence of the proposed distributed time-based filter, and show how the SEC improves the estimation performance and relaxes the observability condition. Moreover, to reduce the communication cost, we propose a distributed event-triggered filter with SECs for time-invariant dynamics, and provide the Gaussianity, consistency and upper boundedness of the covariance matrix for the proposed filter under the extended collective observability. We also show that a smaller triggering threshold leads to a smaller upper bound of the covariance matrix. Finally, we study the distributed tracking on a land-based vehicle for illustration. The simulation results demonstrate the effectiveness of the proposed algorithms.