小波与BP神经网络联合反演GNSS IR高精度水库水位变化

GNSS-IR技术作为一种近地表遥感的新兴手段，在水库水位监测方面凭借其成本低、精度高等优势成为了研究热点。为了提高GNSS-IR技术反演水库水位变化的精度，提出了利用GPS、BDS双系统观测量基于小波分解与BP神经网络联合的方法反演水库水位变化。选取位于南水北调山东境内双王城水库GNSS变形观测站2017年10月1日—12月26日共87天的信噪比(SNR）数据为研究对象，分别利用小波分解和二阶多项式拟合两种方法消除其趋势项并生成SNR残差序列，然后进行Lomb-Scargle谱分析得到水库水位高度变化值，并与实测水位结果相比较。结果表明：各频段SNR利用小波分解和二阶多项式反演水位变化的平均均方根误差分别为0.1062m和 0.2245m，说明小波分解去趋势项的方法更优。最后，在小波分解去趋势项的基础上，利用阈值筛选出融合所用的频段(S1C、S2L、S5Q和S7I），分别采用均值算法、中值算法、随机森林算法和BP神经网络算法对GPS、BDS多频多模信号进行水库水位的融合反演。结果表明，对于水面较为平静的环境，以上算法均能实现厘米级的反演精度，其中BP神经网络算法用于水位反演的效果更优。

Inversion of High Accuracy Reservoir Water Level Changes with Wavelet Analysis and BP Neural Network Based on GNSS-IR

As a new method of near surface remote sensing, GNSS-IR technology has become a research hotspot in reservoir water level monitoring due to its low cost and high accuracy. In order to improve the accuracy of GNSS-IR technology in inversion of reservoir water level changes, an inversion method of reservoir water level based on wavelet decomposition and BP neural network is proposed by using GPS and BDS dual system observations. The signal-to-noise ratio (SNR) data of 87 days from October 1 to December 26, 2017 at the GNSS deformation observation station of Shuangwangcheng reservoir in Shandong Province of the South-to-North Water Diversion Project is selected as the observation data. Firstly, wavelet decomposition and second-order polynomial fitting are respectively used to eliminate the trend term of the original SNR observation data. Secondly, the Lomb-Scargle spectrum analysis method is employed to obtain the corresponding inversion water level changes. Comparing with the in situ water level measurements, results show that the mean root mean square errors of all the frequency ranges are 0.1062m and 0.2245m, respectively, indicating that the result of wavelet decomposition is better than that of second-order polynomial fitting for SNR detrending. Finally, based on wavelet decomposition without the trend term, the available SNR signals of S1C, S2L, S5Q and S7I are selected through threshold method, while different data fusion algorithms including the average algorithm, the median algorithm, the random forest algorithm and the BP neural network algorithm are employed to carry out the fusion inversion for the reservoir water level from the GPS and BDS multi-frequency and multi-mode signals. Results show that all these algorithms can achieve the inversion water level at centimeter precision, while the result of BP neural network algorithm is the best of the four algorithms.