The Role of Detection Times in Reflectivity Estimation With Single-Photon Lidar

In direct time-of-flight single-photon lidar, the photon detection times are typically used to estimate the depth, while the number of detections is used to estimate the reflectivity. This paper examines the use of detection times in reflectivity estimation with a free-running SPAD by proposing new estimators and unifying previous results with new analysis. In the low-flux regime where dead times are negligible, we examine the Cramér--Rao bound of reflectivity estimation. When depth is unknown, we show that an estimator based on censoring can perform almost as well as a maximum likelihood estimator, and, surprisingly, incorrect depth estimation can reduce the mean-squared errors of reflectivity estimation. We also examined joint estimation of signal and background fluxes, for which our proposed censoring-based estimator performs as well as the maximum likelihood estimator. In the high-flux regime where dead times are not negligible, we model the detection times as a Markov chain and examine some reflectivity estimators that exploit the detection times.