The SUT method for precision estimation of mixed additive and multiplicative random error model

被引：0
|
作者：
Wang L. [1 ,2 ]
Chen T. [1 ,3 ]
机构：
[1] Faculty of Geomatics, East China University of Technology, Nanchang
[2] Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake, Ministry of Natural Resources, Nanchang
[3] School of Geodesy and Geomatics, Wuhan University, Wuhan
来源：
Cehui Xuebao/Acta Geodaetica et Cartographica Sinica | 2022年 / 51卷 / 11期
基金：
中国国家自然科学基金;
关键词：
mixed additive and multiplicative random error model; nonlinear function; precision estimation; SUT method; weighted least squares;
D O I：
10.11947/j.AGCS.2022.20200514
中图分类号：
学科分类号：
摘要：
The existing parameter estimation method of mixed additive and multiplicative random error model can achieve second-order precision, but the precision estimation method can only achieve first-order precision. If the traditional Taylor series expansion approximate function method is used to obtain the second-order precision information of parameter estimations, it will inevitably require complicated derivation operation due to the complex nonlinear relationship between parameter estimations and observations in the mixed additive and multiplicative random error model. Aiming at this problem, this paper uses the scaled unscented transformation method, which does not require derivative operation and understand the composition of nonlinear function, to obtain the second-order precision information of parameter estimations. The results of experiments show that using the SUT method to solve the mixed additive and multiplicative random error model can effectively avoid complicated derivation operation, and the obtained parameter estimations and covariance matrix can both achieve second-order precision, thus verifies the feasibility and advantages of the proposed method in this paper. © 2022 SinoMaps Press. All rights reserved.
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页码：2303 / 2316
页数：13
相关论文
共 47 条
  • [1] JIANG Yong, Application of least square method and its extension method in surveying and mapping, (2016)
  • [2] TEUNISSEN P J G, KNICKMEYER E H., Nonlinearity and least-squares [J], CISM Journal ASCGC, 42, 4, pp. 321-330, (1988)
  • [3] SHI Yun, XU Peihang, PENG Junhuan, Multiplicative error models
  • [4] an applications-oriented review of parameter estimation methods and statistical error analysis [J], Geotechnical Investigation & Surveying, 42, 6, pp. 60-66, (2014)
  • [5] SHI Yun, XU Peiliang, PENG Junhuan, An overview of adjustment methods for mixed additive and multiplicative random error models, Proceedings of 2015 International Association V! Hotine-Marussi Symposium on Mathematical Geodesy, 142, pp. 283-290, (2015)
  • [6] XU Peiliang, SHI Yun, PENG Junhuan, Et al., Adjustment of geodetic measurements with mixed multiplicative and additive random errors [J], Journal of Geodesy, 87, 7, pp. 629-643, (2013)
  • [7] SHI Yun, XU Peiliang, Adjustment of measurements with multiplicative random errors and trends, IEEE Geoscience and Remote Sensing Letters, 18, 11, pp. 1916-1920, (2021)
  • [8] WANG Leyang, CHEN Tao, Virtual observation iteration solution and A-optimal design method for ill-posed mixed additive and multiplicative random error model in geodetic measurement, Journal of Surveying Engineering, 147, 4, (2021)
  • [9] XU Peiliang, SHIMADA Seiichi, Least squares parameter estimation in multiplicative noise models [J], Communications in Statistics - Simulation and Computation, 29, 1, pp. 83-96, (2000)
  • [10] SHI Yun, Least squares parameter estimation in additive/multiplicative error models for use in geodesy, Geomatics and Information Science of Wuhan University, 39, 9, pp. 1033-1037, (2014)
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