Hybrid quantum-inspired robot localization in indoor environments

Accurate and robust robot localization remains a fundamental challenge in complex and uncertain environments. This paper introduces a hybrid quantum-inspired robot localization (HQIRL) framework that replaces particle filters with a grid-based probabilistic approach enhanced by quantum amplification principles. The method estimates robot pose on a 2D occupancy grid with unknown initialization. Unlike classical approaches limited by particle deprivation, HQIRL employs continuous likelihood fields to model sensor noise and partial observations through Bayesian fusion. The key innovation integrates Grover-inspired reflection operators to amplify consistent pose hypotheses while suppressing incorrect ones. Experimental validation across medium- and large-scale environments demonstrates strong performance. HQIRL achieves over 85% success with sub-2 cm precision and significantly outperforms AMCL and scan context (p < 0.05), while remaining comparable to neural particle filter. It reduces mean error by up to 85% and improves robustness under noise and uncertainty. These results are achieved without requiring quantum hardware, establishing HQIRL as a scalable and reliable solution for real-world robotic localization.