Haitao Fang

Xingkang He, Chen Hu, Yiguang Hong et al.

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the covariance intersection fusion method, we propose a distributed Kalman filter with guaranteed consistency and satisfied SEC. Furthermore, we establish the relationship between consensus step, SEC and estimation error covariance in dynamic and steady processes, respectively. Employing a space decomposition method, we show the error covariance in the constraint set can be arbitrarily small by setting a sufficiently large consensus 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 asymptotic unbiasedness of state estimate, respectively. Moreover, under the ECO condition for linear time-invariant systems with SEC, we provide a novel event-triggered communication protocol by employing the consistency, and give an offline design principle of triggering thresholds with guaranteed boundedness of error covariance. More importantly, we quantify and analyze the communication rate for the proposed event-triggered distributed Kalman filter, and provide optimization based methods to obtain the minimal (maximal) successive non-triggering (triggering) times. Two simulations are provided to demonstrate the developed theoretical results and the effectiveness of the filters.

Xingkang He, Wenchao Xue, Haitao Fang

This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter, since it requires each sensor to have global information which is usually forbidden in large networks. Then, a sub-optimal distributed Kalman filter (DKF) is proposed by employing the covariance intersection (CI) fusion strategy. It is proven that the proposed DKF is of consistency, that is, the upper bound of error covariance matrix can be provided by the filter in real time. The consistency also enables the design of adaptive CI weights for better filter precision. Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor's measurements to be unobservable. Meanwhile, to keep the covariance of the estimation error bounded, the proposed DKF does not require the system matrix to be nonsingular at each moment, which seems to be a necessary condition in the main DKF designs under global observability. Finally, simulation results of two examples show the effectiveness of the algorithm in the considered scenarios.

Yu Xing, Xingkang He, Haitao Fang et al.

This paper studies the estimation of network weights for a class of systems with binary-valued observations. In these systems only quantized observations are available for the network estimation. Furthermore, system states are coupled with observations, and the quantization parts are unknown inherent components, which hinder the design of inputs and quantizers. To fulfill the estimation, we propose a recursive algorithm based on stochastic approximation techniques. More precisely, to deal with the temporal dependency of observations and achieve the recursive estimation of network weights, a deterministic objective function is constructed based on the likelihood function by extending the dimension of observations and applying ergodic properties of Markov chains. It is shown that this function is strictly concave and has unique maximum identical to the true parameter vector. Finally, the strong consistency of the algorithm is established. Our recursive algorithm can be applied to online tasks like real-time decision-making and surveillance for networked systems. This work also provides a new scheme for the identification of systems with quantized observations.

Xingkang He, Xiaocheng Zhang, Wenchao Xue et al.

This paper studies the distributed state estimation problem for a class of discrete-time stochastic systems with nonlinear uncertain dynamics over time-varying topologies of sensor networks. An extended state vector consisting of the original state and the nonlinear dynamics is constructed. By analyzing the extended system, we provide a design method for the filtering gain and fusion matrices, leading to the extended state distributed Kalman filter. It is shown that the proposed filter can provide the upper bound of estimation covariance in real time, which means the estimation accuracy can be evaluated online.It is proven that the estimation covariance of the filter is bounded under rather mild assumptions, i.e., collective observability of the system and jointly strong connectedness of network topologies. Numerical simulation shows the effectiveness of the proposed filter.