Application of combination model of quadric surfaces and least squares collocation in GPS height anomaly fitting

doi:10.13474/j.cnki.11-2246.2020.0160

Abstract

Abstract: In engineering practice, in order to make the best of GPS elevation data and reduce the dependence on traditional leveling, it is very important to improve the fitting accuracy of GPS height anomaly. Therefore, based on the analysis of the basic principle of quadric surfaces fitting and least squares collocation fitting and the derivation of algorithm process, a new height anomaly fitting method is proposed. According to quadric surfaces fitting, the residual value sequence between the original observation data and the fitting data is calculated, and then the comprehensive error including the quadric surfaces fitting model error is optimized and weakened by using the least squares collocation model. Finally, a new height anomaly is obtained. Through an example, the quadric surfaces fitting method and the least squares collocation method are compared with the new method separetely proposed in this paper. The results show that the fitting prediction accuracy of the new combination method is obviously better than that of the least squares collocation and quadric surfaces fitting.

Key words: least squares collocation, height anomaly, quadric surfaces, residual value, precision

CLC Number:

P228

Lü Jianwei, ZHANG Zhihua, ZHANG Xinxiu, LIU Zuyu. Application of combination model of quadric surfaces and least squares collocation in GPS height anomaly fitting[J]. Bulletin of Surveying and Mapping, 2020, 0(5): 127-129,133.

References

[1] 沙月进. 最小二乘配置法在GPS高程拟合中的应用[J]. 测绘信息与工程,2000(3):3-5.
[2] 刘玉婵,王延霞,李鹏. 最小二乘配置模型在GPS高程拟合中的应用[J]. 测绘与空间地理信息,2015,38(8):67-69.
[3] 杜红飞,谢绍峰,孙昌瑜. 最小二乘配置法在GPS高程异常值推估中的应用[J].河南科学,2013(2):208-211.
[4] 雷伟伟,郑红晓. 二次曲面拟合法在区域似大地水准面精化中的应用[J]. 测绘与空间地理信息,2008,31(6):38-42.
[5] 王明孝,张之孔. 基于组合模型的高程拟合方法及精度分析[J]. 测绘工程,2013,22(2):1-4.
[6] 张腾旭,刘立龙,周淼,等. 基于最小二乘配置法的高程拟合及精度评定方法[J]. 桂林理工大学学报,2014,34(4)728-731.
[7] 孙正明,高井祥,李丽华,等. 最小二乘配置法在GPS高程异常推估中的应用[J]. 测绘科学,2007,32(6):102-103.
[8] 王小辉,王琪洁,丁元兰,等. 基于二次曲面和BP神经网络组合模型的GPS高程异常拟合[J]. 大地测量与地球动力学,2012,32(6):103-105.
[9] 郭辉. 组合模型的GPS高程转换及精度分析[J]. 测绘科学,2018,43(2):34-37.
[10] 毕航权,石杏喜,刘玮. LS-SVM/BP神经网络组合模型在GPS高程转换中的应用[J]. 公路与汽运,2016(177):133-136.
[11] 沈雪峰,高成发,潘树国. 基于最小二乘配置法的BP神经网络GPS高程异常拟合方法研究[J]. 测绘工程,2011,20(4):14-17.
[12] 张勤,张菊清,岳东杰. 近代测量数据处理与应用[M]. 北京:测绘出版社,2011.
[13] 邱卫宁,陶本藻,姚宜斌,等. 测量数据处理理论与方法[M]. 武汉:武汉大学出版社,2008.
[14] 李建章,陈海鹰,纪凤仙,等. 测量数据处理程序设计[M]. 北京:国防工业出版社,2012.
[15] 李成仁,岳东杰,金保平. 协方差函数的选择对GPS高程拟合精度的影响研究[J]. 大地测量与地球动力学,2012,32(4):82-85.
[16] 魏玉明,张永志. 基于抗差最小二乘配置法的GPS高程拟合[J]. 工程勘察,2017(3):40-43.