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

Ruangrawee Kitichotkul, Joshua Rapp, Vivek K Goyal

Abstract:

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 Cram ́erRao 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.