A Unified Framework for Robust and Fair Localization Using Hybrid Learning-Optimization Methods

Accurate localization is essential for wireless and Internet of Things (IoT) systems, particularly indoors where signals are weak and noisy. Traditional optimization-based methods are reliable and interpretable, but they often produce large errors when noise levels are high or the initialization is poor. Learning-based approaches can capture complex signal relationships, yet they tend to overfit and struggle to generalize to new devices or environments. This work introduces a hybrid approach called Robust Fair Localization (RFL). RFL first generates a coarse position estimate using a learning-based prior, refines it through a damped Gauss-Newton optimization, and then applies a confidence-weighted consensus step to smooth local errors. This combination enables RFL to take advantage of both data-driven inference and model-based structure. Simulations were conducted over noise levels ranging from σ = 1.0 to 3.0 dB. At medium noise (σ = 2.0 dB), RFL achieves about 5 % lower RMSE than k-nearest neighbor (kNN) and Consensus (12.2 m vs. 12.9 m) and about 36 % lower than the optimization-only baseline (19.0 m). The fairness score (φ) for RFL remains near 0.61, compared with 0.64 for kNN and Consensus and 0.43 for Optimization, showing balanced error distribution across the area. The robustness index (ρ) of RFL is about 8 % higher than kNN and over 25 % higher than optimization, indicating that RFL maintains stable performance as noise increases.