# Adaptive Multi-Stage Hybrid Localization for RIS-Aided 6G Indoor Positioning Systems: Combining Fingerprinting and Geometric Methods with Condition-Aware Fusion

## TL;DR

This paper introduces a new indoor positioning system for 6G networks using reconfigurable intelligent surfaces, achieving high accuracy through a combination of fingerprinting and geometric methods.

## Contribution

The novel AMSHL algorithm combines fingerprinting and TDoA methods with adaptive fusion, achieving significant improvements in localization accuracy.

## Key findings

- AMSHL achieves a median localization error of 0.661 m and sub-2m accuracy with 87.5% probability.
- The algorithm reduces mean-squared error by 7.1× compared to conventional hybrid fingerprinting.
- A sigmoid-based variant (AMSHL-S) improves sub-2m accuracy to 89.4%.

## Abstract

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.