顾及设计矩阵误差的AR模型新解法

发布时间：2018-04-18 18:23

  本文选题：AR模型 + 设计矩阵误差　； 参考：《测绘学报》2017年11期

【摘要】：在自回归模型求解中,设计矩阵和观测值均存在误差,传统的最小二乘法不能很好地解决这一问题。本文提出了一种顾及设计矩阵误差的AR模型新解法,通过引入虚拟观测值,使观测向量与设计矩阵不仅同源而且带误差的元素个数相同,然后通过对观测方程进行等价变换巧妙实现了在最小二乘框架下求解自回归问题。利用模拟数据及实测数据分别对新算法进行了内符合精度检验,并利用实测数据对新算法进行外符合精度检验,结果表明新算法得到的结果显著优于奇异值分解(singular value decomposition,SVD)解法及传统最小二乘解法,验证了算法的精度和有效性。
[Abstract]:In solving the autoregressive model, there are errors in both the design matrix and the observed values, but the traditional least square method can not solve this problem well.In this paper, a new method of AR model considering the error of design matrix is proposed. By introducing the virtual observation value, the observation vector is not only homologous to the design matrix, but also has the same number of elements with errors.Then the autoregressive problem is solved under the framework of least square by equivalent transformation of the observation equation.Using the simulated data and the measured data, the new algorithm is tested for the accuracy of internal coincidence, and the new algorithm is tested with the measured data.The results show that the new algorithm is superior to the singular value decomposition-SVD method and the traditional least square method, and the accuracy and validity of the algorithm are verified.
【作者单位】： 武汉大学测绘学院;武汉大学地球空间环境与大地测量教育部重点实验室;地球空间信息技术协同创新中心;武汉大学中国南极测绘研究中心;
【基金】：国家自然科学基金(41274022;41574028) 湖北省杰出青年科学基金(2015CFA036)~~
【分类号】：P207.2
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本文编号：1769522