Laser radar echo signals are easily contaminated by noise, such as background light and electronic noise, and this noise is an obstacle for the subsequent signal detection. However, the conventional denoising methods cannot achieve satisfactory effects when the signal-to-noise-ratio (SNR) is ultralow. In this paper, a novel denoising method for laser radar echo signals based on the parameter-optimal variational mode decomposition (VMD) combined with the Hausdorff distance (HD) and wavelet transform (WT) is proposed. Compared with conventional VMD-based methods, the proposed method utilizes a newly developed grasshopper optimization algorithm (GOA) to obtain the optimal combination of parameters for the VMD. Then, the HD is applied to select the relevant modes and then uses the basis function to reconstruct the signal. In addition, the relevant modes are further processed by the WT denoising method, which allows the reconstructed signal to obtain a higher SNR. The simulation and experimental results show the feasibility, effectiveness and robustness of the proposed method compared to three other available denoising techniques. The proposed method could promote the distance measurement performance of laser radars in harsh environments.INDEX TERMS Laser radar echo signal denoising, variational mode decomposition, Hausdorff distance, wavelet transform, grasshopper optimization algorithm.

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When an aircraft loaded with pulsed laser radar flies at supersonic speed, the laser beam will be distorted by the uneven outflow field, resulting in a significant reduction in ranging accuracy. In this study, the influence mechanism of the shock wave on the performance of forward pulsed laser radar is investigated. First, a novel semi-analytical method is proposed to model the pulsed laser echo wave affected by shock waves, which combines the laser radar equation with optical distortion parameters. Second, an improved ray tracing method based on inverse distance-weighted interpolation with a quadrilateral mesh is proposed to trace the trajectory of the laser beam passing through the flow field, and the effectiveness and superiority of the algorithm are verified. Thereafter, an evaluation method based on the optimal confidence interval is proposed to evaluate the ranging error of pulsed laser radar; which can effectively evaluate the ranging accuracy of pulsed laser radar under the influence of the shock wave. The simulation results show that the ranging performance of pulsed laser radar below Mach 3 is slightly affected, and the detection system error and random error reach the minimum and maximum at Mach 4, respectively. This study provides a theoretical basis for the suppression of the aero-optical effect of forward pulsed laser radar at supersonic speed.