Distributed Estimation of Dynamic Fields over Multi-agent Networks

This work presents distributed algorithms for estimation of time-varying random fields over multi-agent/sensor networks. A network of sensors makes sparse and noisy local measurements of the dynamic field. Each sensor aims to obtain unbiased distributed estimates of the entire field with bounded mean-squared error (MSE) based on its own local observations and its neighbors' estimates. This work develops three novel distributed estimators: Pseudo-Innovations Kalman Filter (PIKF), Distributed Information Kalman Filter (DIKF) and Consensus+Innovations Kalman Filter (CIKF). We design the gain matrices such that the estimators achieve unbiased estimates with bounded MSE under minimal assumptions on the local observation and network communication models. This work establishes trade-offs between these three distributed estimators and demonstrates how they outperform existing solutions. We validate our results through extensive numerical evaluations.

[1]  José M. F. Moura,et al.  Distributed Kalman filtering and Network Tracking Capacity , 2013, 2013 Asilomar Conference on Signals, Systems and Computers.

[2]  H. Vincent Poor,et al.  Distributed Kalman Filtering Over Massive Data Sets: Analysis Through Large Deviations of Random Riccati Equations , 2014, IEEE Transactions on Information Theory.

[3]  José M. F. Moura,et al.  Distributed Kalman filtering , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[4]  José M. F. Moura,et al.  Distributed Kalman Filtering With Dynamic Observations Consensus , 2015, IEEE Transactions on Signal Processing.

[5]  Magdi S. Mahmoud,et al.  Distributed Kalman filtering: a bibliographic review , 2013 .

[6]  Soummya Kar,et al.  On connectivity, observability, and stability in distributed estimation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[8]  Reza Olfati-Saber,et al.  Kalman-Consensus Filter : Optimality, stability, and performance , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[9]  José M. F. Moura,et al.  Distributed linear estimation of dynamic random fields , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[10]  Subhro Das.  Distributed Linear Filtering and Prediction of Time-varying Random Fields , 2016 .

[11]  José M. F. Moura,et al.  Consensus+Innovations Distributed Kalman Filter With Optimized Gains , 2016, IEEE Transactions on Signal Processing.

[12]  José M. F. Moura,et al.  Distributed state estimation in multi-agent networks , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.