Unambiguous range extension for Doppler single-photon lidar

Single-photon lidar (SPL) measures the time delay between a laser pulse emission and a single photon detection. SPL typically uses a periodic sequence of illumination pulses to improve the accuracy of distance estimates, and the radial velocity of a moving target can also be determined from the Doppler shift in the pulse repetition frequency. Although increasing the repetition frequency increases the photon detection rate, it also decreases the unambiguous range. Several alternative pulsing modes have been proposed to break this tradeoff for SPL measurements of static scenes, e.g., using multiple repetition rates or random pulse trains to yield both high count rates and a long unambiguous range. In this work, we show that velocity can still be estimated despite the use of non-periodic range extension pulse patterns. We derive a general model for the photon acquisition process with a moving target and propose maximum likelihood estimators (MLEs) to recover the distance, velocity, and photon flux levels. Each range extension mode requires a tailored initialization scheme in order for our MLE solver to converge to the global optimum. We demonstrate through simulations and experiments that non-periodic SPL can simultaneously achieve long-range, high-accuracy distance and velocity estimates.