ToF-Wheel Odometry: Navigating Degeneration of Localization With Limited Sensing Capabilities

Wheel odometry provides an efficient motion prior for ground robots but is prone to transient violations such as wheel slip or terrain-induced tilt. In filtering-based odometry, these violations frequently trigger divergence when they coincide with constrained geometric observability (e.g., featureless corridors). We address this challenge by proposing ToF-Wheel Odometry (TWO), a tightly-coupled filtering framework that integrates wheel kinematics with geometric constraints from Time-of-Flight (ToF) cameras. The primary contribution of this work is a degeneracy-aware, directional covariance-shaping strategy that replaces heuristic online covariance tuning with geometry-conditioned inflation. The core idea is to infer process noise from geometric corrections with a strict reliability check. We decompose the posterior-to-prior correction into a wheel-explainable subspace and an orthogonal remainder. The process covariance is anisotropically adjusted according to the observability of the ToF update: if the geometry is degenerate in non-kinematic directions, the remainder is suppressed as sensor noise; if the geometry is distinct, it is admitted as a valid kinematic violation. Additionally, we introduce an intra-frame feedback loop that retrospectively repairs the process covariance within the current frame to reduce structural lag during bursty disturbances. Extensive experiments on challenging scenarios demonstrate that TWO improves trajectory accuracy and robustness compared to static and adaptive Gaussian filtering, robustly navigating the trade-off between kinematic reliability and limited sensing capabilities.