Track-Before-Detect for Single-Photon LiDAR Histograms via Rao–Blackwellised Sequential Bayesian Inference

Single-photon LiDAR imaging is challenging in sparse-photon and low signal-to-background ratio (SBR) regimes, where per-scan \emph{detect-then-track} pipelines often yield unstable detections and noisy depth estimates. This paper proposes a Track-Before-Detect framework that operates directly on full Time-of-Flight histograms and performs long-time integration across scans to jointly infer target existence and depth under a single-surface-per-pixel assumption. The core contribution is a Rao--Blackwellised Bayesian recursion that analytically integrates out the background level and marginalises the SBR via fast one-dimensional quadrature, enabling online filtering while preserving interpretability. Likelihood evaluation reduces to a matched-filter term that can be computed efficiently over depths using FFT-based correlation. The method outputs, at each scan, a posterior target-existence probability map together with depth estimates and uncertainty measures. Experiments on a dynamic scene quantify gains over scan-independent baselines in depth RMSE, probability of detection and false alarm, and per-scan runtime, especially in background-dominated and photon-starved conditions.