Bayesian multilateration for localization and regression

Abstract

In this work, we present an innovative approach called Bayesian Multilateration (BMLAT), which addresses challenges in localization and regression systems. The conventional Multilateration (MLAT) technique, commonly used for locating points of interest (POIs), often produces unreliable estimates due to sensor noise and provides only point estimates of the POI. BMLAT employs Bayesian modeling to handle uncertainties in MLAT by utilizing likelihood functions and prior distributions. This Bayesian framework is easy to implement and uses available Markov Chain Monte Carlo (MCMC) software for inference. Moreover, BMLAT can accommodate sensors with incomplete location information and multiple measurements per reference point. Extensive experiments with synthetic and real-world data demonstrate that BMLAT provides better position estimation and uncertainty quantification compared to alternative methods. In another domain, the Minimal Learning Machine (MLM) has gained attention for its efficiency in handling complex classification and regression tasks. However, the traditional MLAT approach, when combined with MLM, does not account for the inherent uncertainties in real-world datasets and only produces a point estimate. To address this challenge, Bayesian principles are integrated into MLM to create the Bayesian MLM (BMLM). BMLM offers a probabilistic perspective, providing not only point estimates but also a comprehensive output distribution, capturing uncertainties in the estimation process. The study aims to elucidate the theoretical and practical implications of BMLM, demonstrating its consistency with Gaussian processes through empirical analyses. The incorporation of Bayesian principles enhances the output estimate quality of MLM and provides a deeper understanding of uncertainties. Additionally, we propose the combined application of BMLAT and BMLM for localization and regression tasks, exploring the synergistic potential of these approaches.