February Fourier Talks 2009

Anna Gilbert


Near-optimal 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 sparse approximation framework for the localization problem and demonstrate that the optimal solution can be computed using fast 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.

Joint work with Volkan Cevher (Rice Univ.), Petros Boufounos (Rice Univ.), Richard Baraniuk (Rice Univ.), and Martin Strauss (Univ. of Michigan).