A Unified Analytical Framework for RSS-based Localization Systems

Positioning based on received signal strength (RSS) is regarded as a promising candidate for localization purposes in wireless networks due to its feasibility and deployability. In general, multilateration and fingerprinting algorithms are the primary localization methods in RSS-based localization systems, which are assessed by the Cramér-Rao lower bound (CRLB), given fixed node locations, including the target and participating anchors. However, this methodology produces only definite values for the CRLB specific to the scenario of interest while does not provide insights into the fundamental limits of localization performance. Thus, we are motivated to analyze the RSS-based localization performance using stochastic geometry to allow for randomly distributed nodes and investigate how the nodes’ locations influence this performance. To characterize the localization performance of the multilateration method, a tractable expression of localizability is first provided to indicate the probability that a target is localizable. Then, conditioned on the number of participating anchors, 𝐿, we provide an accurate approximation of the CRLB using the 𝐿/4-th value of ordered distances to quantify the localization accuracy on a random network setting and examine how its performance is influenced under different propagation channels by utilizing 𝜅-𝜇 shadowed fading. Next, a fingerprinting localization problem is regarded as a hypothesis testing problem, and thus, its performance can be evaluated based on the similarity analysis of the observed RSS fingerprints. A comprehensive analysis of these two methods is performed, and the numerical results are compared with the experimental results to demonstrate that our unified framework can precisely reflect localization performance in real-world scenarios. Based on the analysis, we can develop an insight to optimally design an RSS-based localization system that achieves the specified localization requirements.