Matrix computations (3rd ed.)
Approximate distributed Kalman filtering in sensor networks with quantifiable performance
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Distributed Estimation from Relative Measurements in Sensor Networks
ICISIP '05 Proceedings of the 2005 3rd International Conference on Intelligent Sensing and Information Processing
Estimation and control with relative measurements: algorithms and scaling laws
Estimation and control with relative measurements: algorithms and scaling laws
LOCALE: Collaborative Localization Estimation for Sparse Mobile Sensor Networks
IPSN '08 Proceedings of the 7th international conference on Information processing in sensor networks
Distributed optimal estimation from relative measurements for localization and time synchronization
DCOSS'06 Proceedings of the Second IEEE international conference on Distributed Computing in Sensor Systems
Performance analysis of multirobot Cooperative localization
IEEE Transactions on Robotics
Performance of collaborative GPS localization in pedestrian ad hoc networks
Proceedings of the third ACM international workshop on Mobile Opportunistic Networks
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We consider the problem of estimating the locations of mobile agents by fusing the measurements of displacements of the agents as well as relative position measurements between pairs of agents. We propose an algorithm that computes an approximation of the centralized optimal (Kalman filter) estimates. The algorithm is distributed in the sense each agent can estimate its own position by communication only with nearby agents. The problem of distributed Kalman filtering for this application is reformulated as a parameter estimation problem. The graph structure underlying the reformulated problem makes it computable in a distributed manner using iterative methods of solving linear equations. With finite memory and limited number of iterations before new measurements are obtained, the algorithm produces an approximation of the Kalman filter estimates. As the memory of each agent and the number of iterations between each time step are increased, the approximation improves. Simulations are presented that show that even with small memory size and few iterations, the estimates are quite close to the centralized optimal. The error covariances of the location estimates produced by the proposed algorithm are significantly lower than what is possible if inter-agent relative position measurements are not available.