Remote Sensing of Unstructured Urban Environments: Spatial Divergence and Heavy-Tail Error Modeling of FMCW Radar vs. LiDAR

Characterizing sensor reliability in unconstrained driving environments is vital for the safety-critical verification of autonomous navigation stacks. This study provides a large-scale empirical analysis of spatial divergence between raw, unfiltered Frequency-Modulated Continuous-Wave (FMCW) radar returns and dense 128-channel Light Detection and Ranging (LiDAR) point clouds within the unstructured urban traffic landscape of Hyderabad, India. Utilizing approximately 410,000 synchronized detection points from the open-source TiAND dataset, we model the absolute geometric disagreement across high-clutter operational scenes using a nearest-neighbor Euclidean distance metric framework.

Our empirical findings identify a highly right-skewed, non-Gaussian heavy-tail error distribution that presents unique challenges for classical tracking filters. While the well-behaved bulk of the data registers a median baseline error (P50) of 1.157 m due to predictable radar cross-section (RCS) material penetration offsets, the absolute root mean square error (RMSE) expands dramatically to 10.083 m with an overall spatial variance of 93.250 m². Crucially, the survival function demonstrates a slow-decaying profile where the 99th-percentile (P99) spatial deviation reaches 43.008 m, with maximum multi-path anomalies tracking up to 217.216 m. We document a total of 4,113 catastrophic anomalies exceeding a conservative 15 m threshold. Spatial mapping confirms that these extreme errors exhibit acute temporal clustering across consecutive sweeps near stationary urban infrastructure. This structural persistence indicates that fixed reflective surfaces generate highly stable multi-path geometries that standard tracking filters risk reinforcing rather than suppressing. These results establish empirical error bounds for remote sensing in complex urban domains and underscore the immediate necessity for robust cross-modal geometric verification mechanisms in autonomous perception frameworks.