Lagrange插值定理辅助小波变换法在周跳探测中的应用  

Application of Lagrange interpolation theorem-assisted wavelettransform method in cycle slip detection

作　　者：刘春[1] 刘滔 李维华[1] 卫吉祥 汪志宁 Liu Chun;Liu Tao;Li Weihua;Wei Jixiang;Wang Zhining(School of Electrical and Automation Engineering,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学电气与自动化工程学院,合肥230009

出　　处：《电子测量与仪器学报》2020年第8期195-202,共8页Journal of Electronic Measurement and Instrumentation

基　　金：合肥市北斗卫星导航重大应用示范资助项目。

摘　　要：在北斗导航定位领域,为获得准确的载波相位观测数据,必须对载波相位观测中出现的周跳现象进行有效探测和修复。首先构造了单差、双差检测量,利用小波变换对单差、双差检测序列进行三尺度分解,同时提取高频系数和低频系数,从高频系数奇异值可以观察出明显的周跳,然后通过Lagrange线性插值法对高频系数奇异值进行替换,将替换后的高频系数和低频系数进行重构。最后将重构信号与原始信号相减,可以获得周跳差值,利用该值对周跳进行一层一层的修复。实验选择了200个无周跳历元,在100历元处加入不同周跳,仿真结果发现该方法可以对0.5周以上的周跳进行有效地探测和修复。In the field of Beidou navigation and positioning, in order to obtain accurate carrier phase observation data, the cycle slip phenomenon in carrier phase observation must be effectively detected and repaired. This paper first constructs single-difference and double-difference detection quantities, then using wavelet transform to three-scale decomposition of single-difference and double-difference detection sequences,and extracting high-frequency coefficients and low-frequency coefficients at the same time. Obvious cycle slips can be observed from singular values of high-frequency coefficients. Then, the singular values of high frequency coefficients are replaced by Lagrange linear interpolation, and the high frequency coefficients and the low frequency coefficients are reconstructed. Finally, the reconstructed signal is subtracted from the original signal to obtain the cycle slip difference value, which is used to repair the cycle slip layer by layer.In the experiment, 200 cycle-free epochs were selected, and different cycle slips were added at 100 epochs. Simulation results show that the method can effectively detect and repair cycle slips of more than 0.5 weeks.

关 键 词：北斗导航定位 载波相位 周跳 小波变换 Lagrange线性插值 

分 类 号：P228.1[天文地球—大地测量学与测量工程]