Photon counting LiDAR is widely used in target ranging, three-dimensional imaging, and other fields, owing to the advantage of high sensitivity. The return echo data are obtained in the photon counting LiDAR by recording the presence or absence of photon events at the corresponding time, resulting in the inability to acquire the target echo waveform in one detection. The cumulative histogram of the photon count is obtained by the accumulation of multiple detections. The probability histogram of the photon count is regarded as the photon return detection probability waveform, which is closely related to the true return waveform of the target. In traditional LiDAR, the distance of a target can be determined by calculating the centroid of the return signal. However, in photon counting radar, the detection probability waveform of the photon echo is significantly distorted relative to the target waveform owing to the long response dead time of the detector, which significantly affects the accuracy of the photon ranging and the effective acquisition of the target information. Most researchers recover photon echo information based on the detection probability function with a large data error under low signal-to-noise ratio (SNR), making it difficult to obtain the target echo waveform information. Therefore, we discuss the photon echo correction method for the photon counting signal with a low SNR in this paper.
A photon detection echo model is discussed based on the LiDAR detection equation and probability response of photon detection. Combined with the simulated annealing algorithm, the particle swarm optimization algorithm is modified to estimate the photon echo parameters, including the echo signal strength, signal pulse width, peak position of the signal, and average photon noise intensity. The simulated annealing algorithm makes the swarm particles jump out of the local optimal position and effectively improves the global solution search ability. However, to avoid losing the possible dominant particle population, only a few particles are randomly selected for simulated annealing. The consistency between the recovery signal and target true return signal is evaluated by defining the evaluation function. The algorithm’s accuracy is evaluated by calculating the difference between the real target location and location information determined by peak method for the recovered target echo signal.
The algorithm proposed in this study can achieve fine signal recovery results at a low SNR, whereas the iterative solution based on the photon detection probability has a severe signal recovery distortion (Fig. 2). When the total number of noise photons increases from 0.5 to 5.0, the difference between the recovered signal recovered by the iterative method and true signal increases from 0.007 to 0.061, and the ranging error oscillates from 5.5 cm to 13.7 cm. The difference between the recovered signal acquired by our algorithm and the real signal is always below 0.005, and the ranging error is below 3.4 cm (Fig. 3). The signal recovered by our algorithm, which still maintains good performance in the case of high noise, is closer to the real target echo signal. The photon detection experiments are conducted on a deep plane target with a distance of 120 cm from the front to the back. Using our method, the recovered distance of the two target signals is 123.45 cm and the error is 3.45 cm. The corresponding distance of the two target signal peaks obtained by the iterative recovery algorithm is 130.32 cm and the error is 10.32 cm (Fig. 6). The method proposed in this study can better extract the target information with the depth structure.
The simulation and experimental results show that the target signal recovery algorithm based on partial annealing particle swarm optimization can obtain stable target echo signal recovery results under the condition of a low SNR. Compared with the existing iterative method, it improves the effectiveness of signal recovery under the condition of a low SNR and avoids the increase of the error caused by iterative accumulation. Furthermore, the algorithm proposed in this paper has better performance in recovering the depth information of the target.
