Bayesian Cooperative Localization Using Received Signal Strength With Unknown Path Loss Exponent: Message Passing Approaches
Di Jin, Feng Yin, Carsten Fritsche, Fredrik Gustafsson, Abdelhak M. Zoubir
Abstract
We propose a Bayesian framework for the received-signal-strength-based cooperative localization problem with unknown path loss exponent. Our purpose is to infer the marginal posterior of each unknown parameter: the position or the path loss exponent. This probabilistic inference problem is solved using message passing algorithms that update messages and beliefs iteratively. For numerical tractability, we combine the variable discretization and Monte-Carlo-based numerical approximation schemes. To further improve computational efficiency, we develop an auxiliary importance sampler that updates the beliefs with the help of an auxiliary variable. An important ingredient of the proposed auxiliary importance sampler is the ability to sample from a normalized likelihood function. To this end, we develop a stochastic sampling strategy that mathematically interprets and corrects an existing heuristic strategy. The proposed message passing algorithms are analyzed systematically in terms of computational complexity, demonstrating the computational efficiency of the proposed auxiliary importance sampler. Various simulations are conducted to validate the overall good performance of the proposed algorithms.