The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These to data fusion problems are solved is a distributed way using low-pass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. The stability properties of consensus filters is discussed in a companion CDC ’05 paper [24]. We show that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable to provide an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter given that all nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums and that gives an approximate distributed Kalman filtering algorithm. A detailed account of the computational and communication architecture of the algorithm is provided. Simulation results are presented for a sensor network with 200 nodes and more than 1000 links.

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Distributed Kalman Filter with Embedded Consensus Filters

This paper deals with data (or information) fusion for the purpose of estimation. Three estimation fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and a general framework for these three architectures are established. Optimal fusion rules based on the best linear unbiased estimation (BLUE), the weighted least squares (WLS), and their generalized versions are presented for cases with complete, incomplete, or no prior information. These rules are more general and flexible, and have wider applicability than previous results. For example, they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time. They are also in explicit forms convenient for implementation. The optimal fusion rules presented are not limited to linear data models. Illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete, incomplete, or no prior information.

Optimal linear estimation fusion .I. Unified fusion rules

New approach to information fusion steady-state Kalman filtering

This paper is concerned with distributed Kalman filtering for linear time-varying systems over multiagent sensor networks. We propose a diffusion Kalman filtering algorithm based on the covariance intersection method, where local estimates are fused by incorporating the covariance information of local Kalman filters. Our algorithm leads to a stable estimate for each agent regardless of whether the system is uniformly observable locally by the measurements of its neighbors which include the measurements of itself as long as the system is uniformly observable by the measurements of all the agents and the communication is sufficiently fast compared to the sampling. Simulation results validate the effectiveness of the proposed distributed Kalman filtering algorithm.

https://researchbank.swinburne.edu.au/file/8b04fbbb-f168-4790-aa58-2cf8a1acea63/1/PDF (Accepted manuscript).pdf

Diffusion Kalman Filtering Based on Covariance Intersection

Multi-sensor distributed fusion estimation with applications in networked systems

Technical Communique: The optimality for the distributed Kalman filtering fusion with feedback

For pt.IV see proc. 2001 International Conf on Information Fusion. .In this paper, we continue our study of optimal linear estimation fusion in. a unified, general, and systematic setting. We clarify relationships among various BLUE and WLS fusion rules with complete, incomplete, and no prior information presented in Part I before; and we quantify the effect of prior information and data on fusion performance, including conditions under which prior information or data are redundant.

/pdf/optimal-linear-estimation-fusion-part-v-relationships-4tlgr9othd.pdf

Optimal linear estimation fusion. Part V. Relationships

A rigorous performance analysis is dedicated to track fusion with feedback for distributed recursive state estimators of dynamic systems. It is shown that the track fusion formula with feedback is, same as the track fusion without feedback, exactly equivalent to the corresponding centralized track fusion formula. Moreover, the so called P matrices in the feedback Kalman filtering at both local trackers and fusion center are still the covariance matrices of tracking errors. Although the feedback here cannot improve the performance at the fusion center, the feedback does reduce the covariance of each local tracking error. The above results can be extended to a hybrid track fusion with feedback received by partial local trackers.

Juan Zhao

Papers

Technical Communique: The optimality for the distributed Kalman filtering fusion with feedback

Optimal linear estimation fusion. Part V. Relationships

Performance analysis for distributed track fusion with feedback