Error Correction Method in Measurement of High-Speed Targets with Frequency-Modulated Continuous-Wave Lidar

Objective Frequency -modulated continuous -wave (FMCW) lidar has the ability to measure ranges and velocities of moving targets simultaneously with high precision, and thus it has great potential in numerous applications such as space debris detection and space situational awareness. The conventional measuring method is to perform fast Fourier transform (FFT) to the intermediate frequency signal, and then the peak -value frequency is used as the intermediate frequency to calculate the target range and velocity. However, this method cannot achieve high -precision measurement of high-speed targets. The high-speed movements of targets could cause spectral broadening of the intermediate frequency signal, resulting in a multi -peak spectral structure. Therefore, it is difficult to accurately find the intermediate frequency, especially in noisy environments, which has a serious impact on the measurement precision. To deal with this problem, a new spectrum analysis method is desired. In this paper, we propose a novel algorithm for calculating intermediate frequency based on self -convolution of the spectrum. By conducting numerical simulations, we verify the ability of the proposed algorithm in correcting measurement error induced by spectral broadening and realizing high -precision measurements of the target range and velocity. Meanwhile, it has small computation, strong anti -noise ability and broad application prospect. Therefore, it is of great significance for promoting the applications of FMCW lidar in space technologies.Methods A novel algorithm (Fig. 3) is proposed to correct the measurement error caused by high -speed -movement -induced spectral broadening of the intermediate frequency signal, and its validity is verified by numerical simulation. With a theoretical analysis, we find that the intermediate frequency spectrum of FMCW lidar when measuring high-speed targets has the symmetry characteristics, and its center frequency has a certain relationship with target range and velocity. Therefore, as long as the center frequency is known, the target range and velocity can be calculated. We utilize the following algorithm to calculate the center frequency. First, we calculate the self -convolution of the amplitude of the intermediate frequency spectrum, Fn(f). Then we search the peak value of the self -convolution function O(f) and its position. O(f) is calculated by integrating the product of Fn(f) and its shifted mirror image, and O(f) takes its peak value only when Fn(f) overlaps its mirror image completely, since Fn(f) is symmetric. Hence, with the position of the peak value of O(f), we can obtain the center frequency of Fn(f). Utilizing this algorithm, we simulate single -target measurement and multi -target measurement with a model of double-sideband FMCW lidar.Results and Discussions We first conduct numerical simulations of single -target measurement, where the target velocity is 5 km/s and the signal - to-noise ratio (SNR) is set to be 10, 5 and 1, respectively. The results show that the proposed method can realize accurate measurement of the target range and velocity, and the measurement precision decreases with the decrease of the SNR (Fig. 7). With the SNR of 1, the random errors of the target range and velocity are 421.48 p.m (1 & sigma;) and 65.19 p.m/s (1 & sigma;), respectively. As a contrast, we also conduct a simulation with the traditional method, where the peak -value frequency of the intermediate frequency spectrum is used to calculate the target range, and the SNR is set to be 10. Compared with the traditional method, our method can improve the measurement precision by more than three orders of magnitude under the same SNR (Fig. 5). This shows that our method can effectively correct the measurement error caused by the high-speed movement of the target. Moreover, we also conduct a numerical simulation of multi -target measurement (Table 2). The results show that the proposed method can realize accurate range and velocity measurements of multiple targets (Fig. 8).Conclusions In this paper, the measurement of high-speed targets with FMCW lidar is studied. A novel algorithm for analyzing the intermediate frequency spectrum is proposed to correct the measurement error caused by high -speed -movement -induced spectral broadening of the intermediate frequency signal. Firstly, with theoretical analysis, we derive the theoretical expression of the intermediate frequency spectrum, and we study the variation of the intermediate frequency spectral structure with the increase of target velocity. Based on the symmetry characteristics of the intermediate frequency spectrum, the center frequency of the spectrum can be found by searching the peak value of the self -convolution function of the spectrum amplitude. With this algorithm applied to the double-sideband FMCW lidar, the target distance and velocity can be calculated. Then, the validity of the theoretical analysis and the effectiveness of the algorithm in correcting the measurement error of high-speed targets are verified by numerical simulation. Compared with the traditional method, the proposed method can improve the measurement precision by more than three orders of magnitude under the same SNR. The advantages of the proposed method also include the small computation burden and strong anti -noise ability. The research work in this paper provides a feasible approach for high -precision range and velocity measurement of high- speed targets, and we believe it will promote the application of FMCW lidar in space technologies.