Adaptive Multi-Stage Hybrid Localization for RIS-Aided 6G Indoor Positioning Systems: Combining Fingerprinting and...

Reconfigurable intelligent surfaces (RISs) represent a paradigm shift in wireless communications, offering unprecedented control over electromagnetic wave propagation for next-generation 6G networks. This paper presents a comprehensive framework for high-precision indoor localization exploiting cooperative multi-RIS deployments. We introduce the adaptive multi-stage hybrid localization (AMSHL) algorithm, a novel approach that strategically combines fingerprinting-based and geometric time-difference-of-arrival (TDoA) methods through condition-aware adaptive fusion. The proposed framework employs a 4-RIS cooperative architecture with strategically positioned panels on room walls, enabling comprehensive spatial coverage and favorable geometric diversity. AMSHL incorporates five key innovations: (1) a hybrid fingerprint database combining received signal strength indicator (RSSI) and TDoA features for enhanced location distinctiveness; (2) a multi-stage cascaded refinement process progressing from coarse fingerprinting initialization through to iterative geometric optimization; (3) an adaptive fusion mechanism that dynamically adjusts algorithm weights based on real-time channel quality assessment including signal-to-noise ratio (SNR) and geometric dilution of precision (GDOP); (4) a robust iteratively reweighted least squares (IRLS) solver with Huber M-estimation for outlier mitigation; and (5) Bayesian regularization incorporating fingerprinting estimates as informative priors. Comprehensive Monte Carlo simulations at 3.5 GHz carrier frequency with 400 MHz bandwidth demonstrate that AMSHL achieves a median localization error of 0.661 m, root-mean-squared error (RMSE) of 1.54 m, and mean-squared error (MSE) of 2.38 m², with 87.5% probability of sub-2m accuracy, representing a 4.9× improvement over conventional hybrid fingerprinting in median error and a 7.1× reduction in MSE (from 16.83 m² to 2.38 m²). An optional sigmoid-based fusion variant (AMSHL-S) further improves sub-2m accuracy to 89.4% by eliminating discrete switching artifacts. Furthermore, we provide theoretical analysis including Cramér-Rao lower bound (CRLB) derivation with an empirical MSE comparison to quantify the gap between practical algorithm performance and theoretical bounds (MSE-to-CRLB ratio of approximately 4.0×104), as well as a computational complexity assessment. All reported metrics have been cross-validated for internal consistency across formulas, tables, and textual descriptions; improvement factors and error statistics are verified against primary simulation outputs to ensure reproducibility. The complete simulation framework is made publicly available to facilitate reproducible research in RIS-aided positioning systems.