A Set-Theoretic Approach to Collaborative Position Location for Wireless Networks

In this work, we propose a set-theoretic approach to collaborative position location for wireless networks. The proposed method borrows the concept from the parallel projection method (PPM), originally developed for signal recovery with inconsistent convex feasibility sets, modifies and extends the technique to an iterative and distributed numerical algorithm to estimate node locations, based on incomplete and noisy internode distance estimates. We demonstrate that in the case of noncollaborative position location, the proposed method is analytically equivalent to the parallel implementation of Kaczmarz Algorithm that is guaranteed to converge to a local minimizer and thus a stationary point. For collaborative position location, the proposed iterative PPM is computationally much more efficient than existing methods such as SDP and MDS-MAP, while achieving comparable or better localization accuracy and robustness to non-line-of-sight (NLOS) bias. Finally, our proposed method can be implemented in a parallel and distributed fashion, and is scalable for large network deployment.