Wavelet denoising and cycle slip detection and repair of BDS triple-frequency signal
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摘要: 传统的三频伪距相位组合方法易受到伪距观测噪声的影响，难以检测不敏感的小周跳. 三个频率的载波相位观测数据组成的无几何距离组合(GF)方法具有检测敏感小周跳的能力，但存在病态方程组的问题. 鉴于此，提出了一种利用小波去噪的无几何伪距相位组合与GF组合建立组合模型的方法，即利用小波变换对伪距观测值进行去噪，通过选择最优组合系数，构建优化的组合模型. 该方法通过小波去噪保证了源数据的质量，采用无几何伪距相位组合与GF组合模型提高了周跳检测和修复的准确性，同时病态方程组问题得到解决. 最后利用最小二乘方法结合正交三角(QR)分解算法，以及用空间搜索和L1范数最小原理固定周跳的最优整数并修复周跳，采集北斗卫星导航系统(BDS)三频测量数据用于实验验证. 实验结果表明：小波变换去噪的优化组合模型可以检测和修复各种周跳，尤其是对不敏感的小周跳.
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关键词:
- 周跳探测 /
- 伪距相位组合 /
- 无几何距离组合 (GF) /
- 小波去噪 /
- 北斗卫星导航系统(BDS)
Abstract: The traditional triple-frequency code-phase combination method is easily affected by the pseudorange observation noise, and it is difficult to detect the insensitive small cycle slip. The triple-frequency geometry-free (GF) phasemethod has the ability to detect sensitive small cycle slip, but it has the problem of ill-conditioned equations. In view of this, this paper proposes a method of combining code-phase combination and GF model using wavelet denoising. Firstly, the pseudorange observations were denoised by wavelet transform. Then, the optimal combination model is constructed by selecting the optimal combination coefficient. Therefore, the quality of source data is ensured by wavelet denoising, and the accuracy of cycle-slip detection and repair is improved by code-phase combination and GF combination. At the same time, the problem of ill-conditioned equations is solved. Finally, the least square method combined with QR decomposition algorithm is used to fix the optimal integer of the cycle slip and repair the cycle slip by using spatial search and 1-norm minimum principle, and the triple-frequency measurement data of the BeiDou Navigation Satellite System (BDS) is collected for experimental verification. The experimental results show that the optimal combination model of wavelet transform denoising can detect and repair all kinds of cycle slips, especially for insensitive small cycle slips. -
表 2 各组合的周跳探测量与GFPMP-GF组合在去噪前后周跳修复结果
发生历元 加入的周跳值 周跳探测量 修复周跳浮点解 修复周跳浮点解 周跳整数解 伪距相位
(0,−1,1)伪距相位
(1,4,−5)GF
(−1,1,0)去噪后
(0,−1,1)去噪后
(1,4,−5)去噪前 去噪后 50 (1,0,0) - –1.049 5 0.191 52 - –1.051 2 1.085 9
0.068 5
0.061 81.032 5
0.027 2
0.018 41
0
099 (0,1,0) 1.002 60 –4.040 4 −0.247 91 1.001 30 –4.041 4 0.146 3
1.111 3
0.110 10.112 3
1.085 0
0.082 40
1
0149 (0,0,1) –1.013 40 5.112 6 –1.019 80 5.107 7 0.220 8
0.175 4
0.838 00.058 6
0.050 0
0.969 90
0
1199 (1,1,1) - - –0.055 40 - - 1.145 0
1.108 4
1.141 91.127 8
1.095 1
1.127 91
1
1299 (5,4,4) - −1.003 3 −0.032 60 - −1.007 8 4.663 2
3.737 0
3.721 64.812 5
3.852 5
3.842 95
4
4399 (2,2,2) - - −0.111 85 - - 2.195 4
2.148 0
2.153 02.070 6
2.051 5
2.051 62
2
2499 (14,14,15) –0.994 93 4.969 7 –0.790 74 –0.993 79 4.970 5 14.064 7
14.059 7
15.054 614.035 5
14.037 1
15.030 914
14
15
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