Bayesian NLoS detection and accommodation for ultrasonic localization in cluttered environments through probabilistic obstacle modeling

This paper introduces a novel Bayesian framework designed explicitly for detecting and accommodating Non-Line-of-Sight (NLoS) conditions in ultrasonic time-of-flight (ToF) positioning systems, particularly suited for cluttered industrial environments. Unlike conventional methods, the proposed approach does not require detailed signal characteristics or large pre-classified datasets, and operates effectively with asynchronous measurements. The method integrates an Extended Kalman Filter (EKF) for continuous estimation of the receiver’s kinematic state (augmented with a speed-of-sound state), with individual, per-anchor (transmitter) Hidden Markov Models (HMM) tracking LoS/NLoS probabilities used for weighting EKF innovations. The HMM transition rates are derived from a probabilistic obstacle-coverage model via an M/M/ ∞ queueing model reduction, requiring only minimal environment statistics. Evaluation on extensive real-world data, collected in a 14 m × 40 m, densely populated industrial laboratory environment with 14 ultrasonic anchors transmitting totally at approximately 5 Hz and survey-grade (Leica) ground-truth, demonstrates that the proposed Bayesian filter significantly reduces localization errors, nearly halving RMS errors: from 0 . 61 m to 0 . 28 m (East–West) and from 0 . 47 m to 0 . 28 m (North–South), while the 95% error quantile decreases by approximately 20% relative to an EKF baseline employing simple factory setting measurement rejection. Additionally, estimating the speed of sound within the EKF yields consistent accuracy gains under nominal conditions and pronounced gains under biased initialization (0.95 scale). The framework delivers robust, low complexity, hall-scale localization for mobile robotic platforms using only ToF measurements. It requires no geometric map other than the position of ultrasonic anchors and only minimal environmental statistics, facilitating sufficiently precise navigation relative to workstations and hand-off to high-precision local positioning systems.