Objective   The ranging accuracy is one of the important indicators that characterize the performance of phase-based laser ranging systems. The improvement of ranging accuracy is mainly achieved by improving modulation frequency and phase discrimination accuracy. If the modulation frequency is too high, meeting the high sampling frequency required for Nyquist sampling will result in high requirements for ADC hardware and increase system design costs. The traditional differential frequency phase detection method has complex circuit design, which can easily lead to the loss of signal frequency, phase and other information during the mixing process. Due to direct sampling of high-frequency signals, undersampling technology can maximize the retention of the original phase information of the signal, with simple circuit design and low hardware costs. In digital phase detection, spectrum leakage is a prominent drawback of traditional spectrum analysis, and the degree of spectrum leakage directly affects the accuracy of phase detection. All-phase FFT (apFFT) has "phase invariance", which can effectively suppress spectrum leakage and improve phase detection accuracy. In the actual measurement process, it is unavoidable to produce Gaussian white noise that affects the stability of the measurement results. Kalman filtering algorithm is a recursive time-domain filtering algorithm that meets the minimum mean square error estimation, and can effectively remove the Gaussian white noise generated in the measurement process. In order to improve the ranging accuracy, this paper proposes an undersampling all-phase FFT phase detection method based on Kalman filtering.

  Methods   This paper first introduces the principle of phase laser ranging (Fig.1) and the principle of undersampling apFFT phase detection based on Kalman filter (Fig.3), and analyzes the phase detection performance under different sampling frequencies and signal frequencies (Fig.5) through simulation, as well as the phase detection performance under the influence of Gaussian white noise, frequency shift, stray frequency, harmonics and other factors (Fig.6). On the basis of simulation analysis, an undersampling phase detection circuit (Fig.9) was developed based on the FPGA chip of XC7K325T-1FFG676C model and the AD9250-170 chip. Phase detection performance verification experiments and laser ranging verification experiments were conducted, respectively (Fig.12).

  Results and Discussions   The simulation results show that undersampling does not affect the phase detection accuracy (Fig.4). The ability of noise resistance and overcoming frequency offset of the undersampling apFFT method are significantly better than those of the undersampling FFT method (Fig.7). The phase detection accuracy of the undersampling apFFT method is ± 0.012°, and the phase detection accuracy of the undersampling apFFT method is better than that of the FFT method (Fig.8). The experimental results of phase discrimination performance show that the undersampling apFFT method has better noise resistance and anti-interference ability than the FFT method (Fig.10), and the phase discrimination accuracy of the undersampling apFFT method is better than 0.04° (Fig.11). The experimental data of the laser ranging system shows that the phase discrimination accuracy of apFFT is 0.134° without Kalman filtering, and 0.023° after filtering. The phase discrimination accuracy has been improved by 82.84% (Tab.1), and Kalman filtering can significantly improve the phase discrimination stability of apFFT (Fig.13). When the modulation frequency is 201 MHz, the ranging accuracy can reach 0.20 mm, achieving submillimeter precision ranging.

  Conclusions   In order to improve the ranging accuracy, a phase detection circuit was designed using undersampling method and all-phase FFT algorithm, and Kalman filtering was used to improve the stability of the measurement data. According to the principle of phase detection, the phase detection accuracy under different sampling frequencies and signal frequencies is simulated and analyzed, and the phase detection performance of FFT phase detection method based on undersampling and apFFT phase detection method under the influence of Gaussian white noise, frequency offset and other factors is compared. The simulation results show that undersampling does not affect the phase detection accuracy, and the phase detection accuracy of the undersampling apFFT method is better than that of the undersampling FFT method. Experimental verification of phase discrimination performance was conducted, and the experimental data showed that when the sampling frequency was 100 MHz and the signal modulation frequency was 201 MHz, the phase discrimination accuracy of apFFT was 0.134°. After Kalman filtering, the phase discrimination accuracy was better than 0.023°, and the ranging accuracy could reach 0.20 mm. Therefore, the undersampling apFFT phase detection method based on Kalman filtering has the advantages of high accuracy and strong anti-interference ability, and has important application value in phase laser ranging systems.