摘要
在参数估计中,非线性模型直接精密解算缺乏高效的方法,线性近似存在模型误差,而线性化取高次项导致模型复杂不具实用性。研究表明经典边角网可以不考虑线性近似的模型误差问题,本文以任意旋转角的非线性Bursa-Wolf模型参数解算为例,以不存在模型误差的直接严密解为参照对比,采用线性近似模型的高斯牛顿迭代方法解算非线性模型。试验结果显示,线性化取一次项虽然存在模型误差,但高斯牛顿迭代能以指定精度收敛,可获得更优于非线性严密直接解的精度,该发现对非线性模型解算的研究具有参考价值。
It is very difficult to find an accurate and effective method for solving a nonlinear model directly in parameters estimation.Model errors maybe occur in linearization approximation process.The high order terms make the model complicated and deduce its practicability.Previous studies show that it needs not to consider the model errors in classical triangulateration network adjustment.Based on the nonlinear Bursa-Wolf model of three-dimentional rectangular coordinate transformation with any rotation angle,this paper discussed two algorithms for solving the nonlinear model,Lodrigues direct algorithm and Gauss-Newton iterative method.Though model errors exist in the linearization approximation process,the Gauss-Newton iterative method could converge at an appointed precision.Examples showed the calculation precision of Gauss-Newton iterative algorithm,which bases on the linearization approximation model,would be better than that of Lodrigues direct solution.The discovery has reference value for solving nonlinear model researches.
出处
《测绘科学》
CSCD
北大核心
2014年第5期93-95,共3页
Science of Surveying and Mapping
基金
国家公益性行业科研专项(201111013)
