一种基于频移补偿的apFFT相位估计改进方法及应用

全相位快速傅里叶变换（all phase Fast Fourier Transform，apFFT)相位一致性特点使正弦信号相位估计不受频率估计影响，但由于频谱泄露和栅栏效应，apFFT相位估计性能受信号频率位置影响。针对该问题，提出了一种基于高精度频率估计和补偿的apFFT相位估计方法。首先，对信号进行高精度频率估计，并以此对信号进行频移补偿，然后对补偿信号进行apFFT，最后求解信号相位。蒙特卡洛仿真结果表明：所提算法的相位估计性能不受信号频率位置影响，相位估计误差性能与理论值一致，受两参数克拉美罗界（CRLB₂）约束，约为1.158 2倍的CRLB₂；相位估计性能和抗噪声能力明显优于经典apFFT算法和其他对比算法。更进一步，利用我国首次火星探测器TW-1（天问一号）近火捕获段干涉测量数据进行算法验证，结果表明：相位估计精度约4 mrad，干涉测量时延估计精度约50 ps。

An improved apFFT phase estimation method based on frequency compensation and its application in deep space exploration

The all-phase FFT (apFFT) has the advantage of phase consistency, which makes the phase estimation unaffected by frequency estimation performance. While the phase estimation performance of apFFT may be degraded by frequency offset because of spectrum leakage and fence effect. In refer to the problem, this paper proposed an improved apFFT method based on frequency compensation. Firstly, the frequency was accurately estimated to compensate the signal, and then calculate the apFFT of the compensated signal, and finally the phase was estimated. The Monte Carlo simulation results showed that the phase estimation performance of the novel method was almost immune to the frequency offset, and also was coincide with the theoretical analysis. Moreover, its performance which was restrained by Two-parameter Cramer Lower Band (CRLB₂), was about 1.158 2 times CRLB2 under the Monte Carlo situation. The anti-noise capacity and phase estimation performance of the proposed method were significantly better than that of the traditional apFFT method and other two compared algorithms. Moreover, the raw data of TW-1 satellite was utilized to verify the proposed method, obtaining an accuracy of about 4 mrad of phase estimation, and an accuracy of about 50 ps of interferometry delay estimation.