Variational Bayesian Learning Based Joint Localization and Channel Parameter Estimation in Wireless Sensor Networks With Distance-Dependent Noise

This paper focuses on the challenge of jointly optimizing location and path loss exponent (PLE) in distance-dependent noise. Departing from the conventional independent noise model used in localization and path loss exponent estimation problems, we consider a more realistic model incorporating distance-dependent noise variance, as revealed in recent theoretical analyses and experimental results. The distance-dependent noise introduces a complex noise model with unknown noise power and PLE, resulting in an exceptionally challenging non-convex and nonlinear optimization problem. In this study, we address a joint localization and path loss exponent estimation problem encompassing distance-dependent noise, unknown parameters, and uncertainties in sensor node locations. To surmount the intractable nonlinear and non-convex objective function inherent in the problem, we introduce a variational Bayesian learning-based framework that enables the joint optimization of localization, path loss exponent, and reference noise parameters by leveraging an effective approximation to the true posterior distribution. Furthermore, the proposed joint learning algorithm provides an iterative closed-form solution and exhibits superior performance in terms of computational complexity compared to existing algorithms. Computer simulation results demonstrate that the proposed algorithm approaches the performance of the Bayesian Cramer-Rao bound (BCRB), achieves localization performance comparable to the (maximum likelihood-Gaussian message passing) ML-GMP algorithm in some cases, and outperforms the other comparison algorithm in all cases.