摘要
已有加乘性混合误差模型参数估计方法能达到二阶精度,但精度评定方法只能达到一阶精度,若通过传统泰勒级数展开近似函数法来获取参数估值的二阶精度信息,由于加乘性混合误差模型中参数估值与观测值为一个复杂的非线性关系,必然需要复杂的求导运算。针对该问题,本文使用一种无须求导、无须了解非线性函数构成的比例无迹变换(scaled unscented transformation,SUT)法来计算参数估值的二阶精度信息。通过算例分析表明,利用SUT法求解加乘性混合误差模型能够有效避免复杂的求导运算,所求得的参数估值及其协方差阵均能达到二阶精度,从而验证了本文方法的可行性和优势。
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.
作者
王乐洋
陈涛
WANG Leyang;CHEN Tao(Faculty of Geomatics,East China University of Technology,Nanchang 330013,China;Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake,Ministry of Natural Resources,Nanchang 330013,China;School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China)
出处
《测绘学报》
EI
CSCD
北大核心
2022年第11期2303-2316,共14页
Acta Geodaetica et Cartographica Sinica
基金
国家自然科学基金(42174011,41874001)
东华理工大学研究生创新专项资金(DHYC-202020)。
关键词
加乘性混合误差模型
加权最小二乘
非线性函数
SUT法
精度评定
mixed additive and multiplicative random error model
weighted least squares
nonlinear function
SUT method
precision estimation
