State-Space Refinement Kalman Filter Model for Roadway Roof Deformation Detection in Underground LiDAR Scanning

Abstract

In repeated underground laser scanning, road-roof deformation can be reliably determined through irregular sampling, support occlusion, registration drift, oblique incidence, and dust backscattering. In this paper, a state-space refined Kalman filter is developed, which integrates the following components: normal displacement, deformation rate, acceleration trend, registration bias, and local shape persistence. Without affecting field deployability, innovative statistics refined the delay estimation, fixed-lag backward smoothing refined the delay estimation, and robust patch correspondences generated roof-aligned observations. The experiment was conducted 18 times on a 2.4-kilometer-long road, including natural deformations and controlled roof offsets. Among the 36,720 roof patches evaluated, the proposed model reduced the root mean square error of the direct point-to-plane differential displacement from 8.7 mm to 3.4 mm, while the root mean square error of the traditional Kalman filter was reduced from 6.1 mm to Under a 10mm alarm threshold, the accuracy is 94.1%, the recall rate is 92.6%, and the false alarm rate is 2.8%. The processing time for each 20-meter segment at the standard workstation is 0.43 seconds, and the 95% uncertainty interval covers 94.7% of the reference observations. The ablation results indicate that innovative conditional covariance adaptation and bias state separation are the main contributors under dusty and low-overlap scanning conditions. Therefore, this model provides an interpretable and computationally feasible basis for the deformation screening of underground road operations.