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摘要:
全球导航卫星系统反射测量(GNSS-R)海面测高作为GNSS技术应用领域之一,其凭借全天时、低成本、高时空分辨率等特点在海洋遥感领域占据极大的优势。但受GNSS码片宽度的限制,岸基GNSS-R码延迟海面测高的最优精度仅为分米级,难以满足大地测量学领域对海面高的精度要求。提出利用傅里叶级数拟合法对码延迟测高结果进行优化,并于山东省威海市开展GNSS-R码测高实验进行验证,分别对QZSS L2C信号、QZSS L5信号及GPS L5信号的码延迟测高结果进行拟合处理并计算反演精度,对比原始测高结果发现:3段不同时长的原始测高结果经过傅里叶级数拟合优化后,其均方根误差(RMSE)从70~90 cm提升至9~15 cm。在此基础上,利用拟合所得傅里叶级数曲线对未来24 h内的海面高进行预测,与验潮站数据相比,预测结果仍保持较高精度,RMSE为13~18 cm,相关系数大于0.97。结果表明所提出的方法不仅能对码延迟测高结果进行优化,能对存在数据缺失的情况进行补充,还能对未来海面高度进行高精度的预测。
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关键词:
- 岸基 /
- 全球导航卫星系统反射测量 /
- 码延迟 /
- 海平面高度 /
- 傅里叶级数拟合
Abstract:With the continuous innovation of GNSS technology, its application fields continue to expand. Because of its all-weather capabilities, low cost, and high spatiotemporal resolution, Global Navigation Satellite System-Reflectometry (GNSS-R) sea surface altimetry has many benefits in the field of ocean remote sensing. However, due to the limitation of GNSS chip width, the optimal accuracy of shore-based GNSS-R code-delay sea level measurements is only decimeter level, which makes it difficult to meet the accuracy requirements of Geodesy for sea surface height. In order to maximize the GNSS-R code-delay altimetry results, this research suggested using the Fourier series fitting method. To validate the suggested approach, GNSS-R code altimetry experiments were conducted in Weihai City, Shandong Province. The code-delay altimetry results of QZSS L2C signal, QZSS L5 signal and GPS L5 signal are respectively fitted and processed, and the inversion accuracy is calculated. When compared to the original altimetry findings, it is discovered that the RMSEs of the three original altimetry values with varying lengths have improved from 70-90 cm to 9-15 cm following Fourier series fitting. On this basis, the sea surface heights in the next 24 hours are predicted using the fitted Fourier series curve. Compared with the tide gauge data, the prediction results still maintain high accuracy, with RMSE of 13-18 cm and correlation a coefficient greater than 0.97. The above results indicate that the method proposed in this article can not only optimize the code-delay height measurement results and supplement the missing data, but also make high-precision predictions for future sea levels.
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Key words:
- shore-based /
- GNSS-R /
- code delay /
- sea surface height /
- Fourier series fitting
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表 1 3次实验期间实验地点潮汐变化表
Table 1. Table of tidal change at experimental site during the three experiments
潮汐 潮时 潮高(峰值)/cm 第1段 第2段 第3段 第1段 第2段 第3段 干潮 05:35 04:29 00:40 37 45 84 满潮 11:27 10:17 07:26 222 209 239 干潮 17:53 16:06 14:26 42 55 65 满潮 23:48 22:25 20:15 221 242 196 表 2 3段实验数据的GNSS-R码测高精度统计
Table 2. Statistical analysis of the three experimental data for GNSS-R code-delay altimetry
数据类型 均值/m RMSE/m QZSS L2C − 0.0467 0.7618 GPS L5 0.2877 0.8083 QZSS L5 − 0.0438 0.8606 表 3 3段实验数据的傅里叶级数拟合结果与比对数据对比精度统计
Table 3. Statistical analysis of the Fourier series fitting results comparing with in-situ data
数据类型 均值/m RMSE/m R2/% QZSS L2C(m=1) − 0.0451 0.1481 99.33 QZSS L2C(m=2) − 0.0429 0.1961 98.14 GPS L5(m=1) 0.0256 0.1011 98.07 GPS L5(m=2) 0.0138 0.1077 97.36 QZSS L5(m=1) 0.0610 0.1861 91.60 QZSS L5(m=2) 0.0392 0.0961 97.99 QZSS L5(m=3) 0.0417 0.1016 97.76 表 4 QZSS L5模型预测海面高与验潮站结果比较
Table 4. Statistical analysis of the sea levels from Fourier series fitting model comparing with in-situ data
时间 均值/m RMSE/m R2/% 未来1 h − 0.1307 0.1321 99.64 未来12 h − 0.1512 0.1856 97.15 未来24 h − 0.0476 0.1419 95.16 -
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