Accuracy analysis of GNSS-IR snow depth inversion algorithms

In recent years, with the continuous development of Global Navigation Satellite System (GNSS), it has been applied not only to navigation and positioning, but also to Earth surface environment monitoring. At present, when performing GNSS-IR (GNSS Interferometric Reflectometry) snow depth inversion, Lomb-Scargle Periodogram (LSP) spectrum analysis is mainly used to calculate the vertical height from the antenna phase center to the reflection surface. However, it has the problem of low identification of power spectrum analysis, which may lead to frequency leakage. Therefore, Fast Fourier Transform (FFT) spectrum analysis and Nonlinear Least Square Fitting (NLSF) are introduced to calculate the vertical height in this paper. The GNSS-IR snow depth inversion experiment is carried out by using the observation data of P351 station in PBO (Plate Boundary Observatory) network of the United States from 2013 to 2016. Three algorithms are used to invert the snow depth and compared with the actual snow depth provided by the station 490 in the SNOTEL network. The observations data of L1 and L2 bands are respectively used to find the optimal combination between different algorithms further to improve the accuracy of GNSS-IR snow depth inversion. For L1 band, different snow depths correspond to different optimal algorithms. When the snow depth is less than 0.8 m, the inversion accuracy of NLSF algorithm is the highest. When the snow depth is greater than 0.8 m, the inversion accuracy of FFT algorithm is higher. Therefore, according to the different snow depth, a combined algorithm of NLSF + FFT is proposed for GNSS-IR snow depth inversion. Compared with the traditional LSP algorithm, the inversion accuracy of the combined algorithm is improved by 10%. For L2 band data, the results show that the accuracy of snow depth inversion of various algorithms do not change with the variations of snow depth. Among the three single algorithms, the inversion accuracy of FFT algorithm is better than that of LSP and NLSF algorithms.     

Fast approximate maximum likelihood period estimation from incomplete timing data

 To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate (MLE) with a computational complexity of O(n²). Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.     

基于周期图法的残留载波BPSK信号检测

讨论高斯白噪声背景下基于周期图法的残留载波BPSK(RC-BPSK)信号的检测问题。标准周期图法在正弦信号检测中的性能最优,但是在RC-BPSK信号检测中的性能却不佳;能量检测法只在信噪比很低的情况下性能较好;在信噪比较高时,虽然Bartlett法有较好的性能,但需要分段多次计算周期图,不利于与其他检测方法配合使用。文中在频谱匹配法的基础上发展了一种频谱相关检测方法,仿真结果表明该方法可以获得和Bartlett法相似的性能,同时只需要计算一次周期图。