Fig. 1. Principle of Hough transform. (a) Simulated echo signal points to be detected; (b) echo signal points are converted to sine curves in polar coordinate by the Hough transform; (c) detection of a straight line connecting the echo signal points

Fig. 2. Schematic diagram of the definition for the parameters of Hough transform

Fig. 3. Flowchart of proposed algorithm

Fig. 4. Sine curves of different resolutions. (a) Resolution of 0.1; (b) resolution of 0.5; (c) resolution of 1.5; (d) resolution of 5.0

Fig. 5. Simulated point cloud under extreme motion condition. (a) Point cloud; (b) localization image of point cloud

Fig. 6. Processed results of simulated data by proposed algorithm. (a) Overall result; (b) result of large error area (region ①); (c) result of low signal-to-noise ratio area (region ②)

Fig. 7. Schematic diagram of experimental facilities

Fig. 8. Schematic diagram of experimental process

Fig. 9. Processed results of measured echo point cloud. (a) Overall map of measured echo point cloud; (b) point cloud of local high signal-to-noise ratio area (region ①); (c) point cloud of local sparse area (region ②)

Fig. 10. Comparison between traditional Hough transform and the proposed algorithm. (a) Traditional Hough transform; (b) proposed algorithm

Fig. 11. Processed results of measured data by proposed algorithm. (a) Measured echo point cloud; (b) part of the point cloud that needs to be processed; (c) extracted effective echo point cloud; (d) overall data processed result; (e) processed result of high signal-to-noise ratio area (region ①); (f) processed result of partial echo missing area (region ②)

Fig. 12. Processed results of measured data by proposed algorithm. (a) Measured echo point cloud; (b) part of the point cloud that needs to be processed; (c) extracted effective echo point cloud; (d) overall data processed result; (e) predicted trajectory corrected result after the effective echo is extracted (region ①); (f) Kalman filter prediction result when the echo is missing (region ②)

Table 1. Main parameters of single-photon LiDAR tracking and ranging system