Distributed maximum likelihood for self-localization in sensor networks

We show that the sensor localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we develop fully decentralized versions of the Recursive Maximum Likelihood and the Expectation-Maximization algorithms to localize the network. For linear Gaussian models, our algorithms can be implemented exactly using a distributed version of the Kalman filter and a message passing algorithm to propagate the derivatives of the likelihood. In the non-linear case, a solution based on local linearization in the spirit of the Extended Kalman Filter is proposed. In numerical examples we show that the developed algorithms are able to learn the localization parameters well.

Distributed maximum likelihood for simultaneous self-localization and tracking in sensor networks

We show that the sensor self-localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we implement fully decentralized versions of the Recursive Maximum Likelihood and on-line Expectation-Maximization algorithms to localize the sensor network simultaneously with target tracking. For linear Gaussian models, our algorithms can be implemented exactly using a distributed version of the Kalman filter and a novel message passing algorithm. The latter allows each node to compute the local derivatives of the likelihood or the sufficient statistics needed for Expectation-Maximization. In the non-linear case, a solution based on local linearization in the spirit of the Extended Kalman Filter is proposed. In numerical examples we demonstrate that the developed algorithms are able to learn the localization parameters. © 2012 IEEE.