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In this paper, we investigate a distributed estimation problem formulti-agent systems with state equality constraints (SEC). First, under atime-based consensus communication protocol, applying a modified projectionoperator and the covariance intersection fusion method, we propose adistributed Kalman filter with guaranteed consistency and satisfied SEC.Furthermore, we establish the relationship between consensus step, SEC andestimation error covariance in dynamic and steady processes, respectively.Employing a space decomposition method, we show the error covariance in theconstraint set can be arbitrarily small by setting a sufficiently largeconsensus step. Besides, we propose an extended collective observability (ECO)condition based on SEC, which is milder than existing observability conditions.Under the ECO condition, through utilizing a technique of matrix approximation,we prove the boundedness of error covariance and the exponentially asymptoticunbiasedness of state estimate, respectively. Moreover, under the ECO conditionfor linear time-invariant systems with SEC, we provide a novel event-triggeredcommunication protocol by employing the consistency, and give an offline designprinciple of triggering thresholds with guaranteed boundedness of errorcovariance. More importantly, we quantify and analyze the communication ratefor the proposed event-triggered distributed Kalman filter, and provideoptimization based methods to obtain the minimal (maximal) successivenon-triggering (triggering) times. Two simulations are provided to demonstratethe developed theoretical results and the effectiveness of the filters.

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