Continuous wavelet transform and iterative decrement algorithm for the Lidar full-waveform echo decomposition

In this paper, we propose a continuous wavelet transform and iterative decrement algorithm to decompose the light detection and ranging (LiDAR) full-waveform echoes into a series of components, each of which can be assumed as Gaussian essentially. We calculate the scale of continuous wavelet transform in real time according to the relationship between the center frequency of the mother wavelet and the approximate frequency of the transmitted laser pulse. The approximated frequency is calculated according to the half-width of the effective part of transmitted laser pulse. The positions of the Gaussian model components in the echoes can be precisely predicted according to the positions of the maxima of the continuous wavelet transform coefficient. And the boundary points which locate at the left and right sides of the position of the detected components can be detected. Then, the effective sections can be clipped according to the positions of the boundary points. In order to detect the hidden components which are obscured by the high responses from their adjacent components and estimate the initial parameters, the iterative decrement algorithm is carried out. The initial parameters are fitted by the Levenberg-Marquardt algorithm. In order to verify the proposed method, the simulations and experiments whose data is recorded by our coding LiDAR have been done. The simulations and experiments results indicate that the proposed method exhibits excellent performances, and it is valid for the complex full-waveform echo, which includes serious overlapping components.