本文選題：AR模型 + 設(shè)計矩陣誤差�。� 參考：《測繪學報》2017年11期

【摘要】：在自回歸模型求解中,設(shè)計矩陣和觀測值均存在誤差,傳統(tǒng)的最小二乘法不能很好地解決這一問題。本文提出了一種顧及設(shè)計矩陣誤差的AR模型新解法,通過引入虛擬觀測值,使觀測向量與設(shè)計矩陣不僅同源而且?guī)д`差的元素個數(shù)相同,然后通過對觀測方程進行等價變換巧妙實現(xiàn)了在最小二乘框架下求解自回歸問題。利用模擬數(shù)據(jù)及實測數(shù)據(jù)分別對新算法進行了內(nèi)符合精度檢驗,并利用實測數(shù)據(jù)對新算法進行外符合精度檢驗,結(jié)果表明新算法得到的結(jié)果顯著優(yōu)于奇異值分解(singular value decomposition,SVD)解法及傳統(tǒng)最小二乘解法,驗證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.
【作者單位】： 武漢大學測繪學院;武漢大學地球空間環(huán)境與大地測量教育部重點實驗室;地球空間信息技術(shù)協(xié)同創(chuàng)新中心;武漢大學中國南極測繪研究中心;
【基金】：國家自然科學基金(41274022;41574028) 湖北省杰出青年科學基金(2015CFA036)~~
【分類號】：P207.2
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本文編號：1769522