基于约束相位解卷绕的正弦信号高精度相位估计

High-accuracy phase estimation of single-tone based on restricted phase unwrapping

在Tretter相位估计算法基础上,提出了一种基于约束相位解卷绕的相位估计方法。通过对观测相位进行适当的线性组合,将相位约束在较小的模糊相位集合之中,最后基于相位误差最小原则实现约束相位解卷绕。理论分析与Monte Carlo模拟结果显示,约束相位解卷绕的信噪比阈值低于常规解卷绕方法,且在高信噪比条件下相位估计均方根误差接近克拉美罗下限(CRLB),相位估计性能优于分段DFT相位差法以及全相位FFT测相法。在信噪比为5 dB、数据长度为1023的情况下,相位估计均方根误差约为0.9°。当信噪比为0 dB时,约束相位解卷绕的错误概率仅为10-3量级。

Abstract： In order to estimate the original phase of a sinusoidal signal under noisy circumstances precisely, this paper pro- posed a novel phase estimation method which based on restricted phase unwrapping and Tretter＇ s phase estimation algorithm. Firstly it acquired the coarse estimation of initial phase by using modified segmented D^F estimator. Then an appropriate linear combination of observed phase, by which the ambiguity number of whole cycle restricted in a smaller integer set, was simply unwrapped on the basis of the principle of minimum phase error. Formulas for evaluating the error probability of restricted phase unwrapping and the RMS error of the initial phase estimation with different SNRs and lengths of signal are also presen- ted. Simulation results show that the SNR threshold of restricted phase unwrapping method is much lower than that of common unwrapping methods, and the estimator derived attains the Cramer-Rao lower bound （CRLB） at high SNR, which has better performance than the segmented DFT estimator developed and the all-phase FFF estimator . For SNR = 5 dB and N = 1023, the RMS error of the initial phase estimation is about 0.9 degrees, and the error probability of restricted phase unwrapping is only about 10-3 orders of magnitude when SNR = 0 dB.