Abstract: Waveform threshold method is one of the important approaches to obtain the ranging values of linear system spaceborne lidar, and its ranging accuracy is determined by multiple factors such as noise level, pulse broadening and threshold of returned signal waveform. According to the waveform distribution model and noise characteristics of the returned signals of linear system spaceborne lidar, a laser ranging error model based on the waveform threshold method is established by deriving the variance distribution of the rising edge time over the waveform threshold. Furthermore, taking the Mercury lidar developed by the European Space Agency as an example, the distributions of laser ranging error under different normalized waveform thresholds are simulated using numerical simulation. The results demonstrate that when the normalized waveform threshold is close to 0 and 1, the ranging error is most affected by noise and reaches the maximum. However, when the normalized waveform threshold is optimal, the ranging error presents a sharp decrease trend. In addition, it is found that the optimal normalized waveform threshold is proportional to surface slope. The fitting model of the optimal normalized waveform threshold is derived using a linear fractional function, and the root mean square error of the fitted curve residuals is only 0.005 with a correlation coefficient of 0.99. By comparing the laser ranging errors obtained from the optimal normalized waveform threshold with those from the traditional 50% threshold, it is found that the optimal normalized waveform threshold can significantly reduce the laser ranging error for the targets with steep slope, which indicates that the proposed method can provide methodological support for optimizing the ranging threshold of spaceborne lidar.

Key words: laser techniques, spaceborne lidar, waveform threshold, returned signal waveform, laser ranging error