To address the performance degradation of the conventional linear frequency modulation signal ranging method in the presence of impulse noise, this paper proposes a novel technique that integrates a sliding-window tracking differentiator (TD) with the fractional Fourier transform (FrFT) ranging method. First, the sliding-window TD filtering algorithm is used to suppress the noise in the echo. Subsequently, the filtered signal is subjected to FrFT to calculate the time delay based on the difference in the peak point positions in the fractional domain for realizing target ranging. The simulation results show that the proposed method can effectively suppress impulse noise of different intensities and achieve an accurate and robust ranging of the target.

To address the challenge of low accuracy of the range image recovery of Geiger-mode avalanche photodiode (GM-APD) LiDAR in low signal-to-background ratios (SBRs), this paper proposes a non-local regularization-based fractional-order total variational compressive sensing (CS) algorithm for recovering GM-APD LiDAR images. First, the kurtosis factor peak method was utilized to obtain the target range image at low SBRs. Subsequently, a non-local regularization-based fractional-order total variational CS model for GM-APD LiDAR image recovery is proposed, leveraging the sparse and constrained isometric properties of CS as well as the memorability of fractional-order calculus. This model aims to compress and sample high-dimensional range images while performing a sparse representation. Finally, an augmented Lagrange algorithm was employed to precisely recover the target range image. The results of the experiments demonstrate that the proposed method can enhance the degree of target recovery by a minimum of 4.29% and increase the peak signal-to-noise ratio by at least 9.29% under conditions of a 60% sampling rate, identical SBR, and statistical frame number.

The target is often obstructed by obstacles with the dynamic tracking scene, leading to a loss of target information and a decrease in tracking accuracy or even complete failure. To address these challenges, we leverage the capabilities of Geiger-mode Avalanche Photodiode (GM-APD) LiDAR to acquire both intensity images and point cloud data for researching a target tracking method that combines the fusion of intensity images and point cloud data. Building upon Kernelized correlation filtering (KCF), we introduce Fourier descriptors based on intensity images to enhance the representational capacity of target features, thereby achieving precise target tracking using intensity images. Additionally, an adaptive factor is designed based on peak sidelobe ratio and intrinsic shape signature to accurately detect occlusions. Finally, by fusing the tracking results from Kalman filter and KCF with adaptive factors following occlusion detection, we obtain location information for the central point of the target. The proposed method is validated through simulations using the KITTI tracking dataset, yielding an average position error of 0.1182m for the central point of the target. Moreover, our approach achieves an average tracking accuracy that is 21.67% higher than that obtained by Kalman filtering algorithm and 7.94% higher than extended Kalman filtering algorithm on average.

The fractional Fourier transform (FRFT) serves as an effective tool for linear frequency modulated (LFM) signal parameter estimation, whose performance depends on the search efficiency for the optimal transform order. To address the issues of fixed inertia weight in the standard particle swarm optimization (PSO) algorithm, which tends to fall into local optima and suffers from insufficient convergence accuracy, this paper introduces a proportional-integral-derivative (PID) control strategy and proposes a PID-PSO-FRFT-based LFM signal parameter estimation method. This approach introduces a PID controller, which takes the deviation between the particle’s current position and the global best position as input and dynamically adjusts the inertia weight through proportional, integral, and derivative regulation, thereby achieving an adaptive balance between global exploration and local exploitation capabilities of the particles. Simulation results demonstrate that, compared with the basic PSO-FRFT algorithm, the proposed method significantly improves the estimation accuracy of the center frequency and chirp rate of LFM signals under SNR conditions ranging from −9 dB to −7 dB, while considerably reducing computation time, exhibiting superior noise resistance, and exhibiting superior robustness.