Near-optimal Bayesian localization via incoherence and sparsity

Source localization using a network of sensors is a classical problem with applications in tracking, habitat monitoring, etc. A solution to this estimation problem must satisfy a number of competing resource constraints, such as estimation accuracy, communication and energy costs, signal sampling requirements and computational complexity. This paper exploits recent developments in sparse approximation and compressive sensing to efficiently perform localization in a sensor network. We introduce a Bayesian framework for the localization problem and provide sparse approximations to its optimal solution. By exploiting the spatial sparsity of the posterior density, we demonstrate that the optimal solution can be computed using fast sparse approximation algorithms. We show that exploiting the signal sparsity can reduce the sensing and computational cost on the sensors, as well as the communication bandwidth. We further illustrate that the sparsity of the source locations can be exploited to decentralize the computation of the source locations and reduce the sensor communications even further. We also discuss how recent results in 1-bit compressive sensing can impact the sensor communications by transmitting only the timing information relevant to the problem. Finally, we develop a computationally efficient algorithm for bearing estimation using a network of sensors with provable guarantees.