Indoor Positioning with Probabilistic Graphical Models in RIS-Enhanced mmWave MIMO Systems

We apply a Bayesian-based framework to address indoor positioning in a reconfigurable intelligent surface (RIS) assisted MIMO communications system. By employing a two-stage estimation approach, we first estimate the channel parameters using atomic norm minimization (ANM) via downlink training. In the second stage, we model the system as a probabilistic graphical model (PGM) and utilize the No-U-Turn Sampler (NUTS) algorithm to approximate the posterior distribution of the coordinates based on the estimated channel parameters. Unlike existing algorithms, our framework does not require additional pilot acquisition in the second stage. The numerical results are presented using kernel density estimation, cumulative distribution function (CDF), and root mean square error (RMSE). Our findings are compared with the non-linear least squares (NLS) estimator and the Cramér-Rao lower bound to evaluate its performance. In particular, when the signal-to-noise ratio (SNR) exceeds −15 dB, our proposed method significantly outperforms the NLS estimator, bringing an accuracy percentage improvement of over 50% in the considered set-up.