本文關(guān)鍵詞：多元總體最小二乘問題的牛頓解法　出處：《測(cè)繪學(xué)報(bào)》2016年04期 　論文類型：期刊論文

  更多相關(guān)文章： 多元總體最小二乘 牛頓法 協(xié)因數(shù)傳播律 仿射變換

【摘要】：為提高多元總體最小二乘問題參數(shù)估值的解算效率,推導(dǎo)了基于牛頓法的多元加權(quán)總體最小二乘算法;分析比較了基于牛頓法的多元加權(quán)總體最小二乘解和基于拉格朗日乘數(shù)法多元加權(quán)總體最小二乘解之間的關(guān)系,根據(jù)協(xié)因數(shù)傳播律給出了多元總體最小二乘平差的16種協(xié)因數(shù)陣的近似計(jì)算公式。新算法能夠解決觀測(cè)矩陣和系數(shù)矩陣元素具有相關(guān)性的問題,并且可以把觀測(cè)矩陣和系數(shù)矩陣的隨機(jī)元素和常數(shù)元素納入到一個(gè)協(xié)因數(shù)陣中進(jìn)行處理。算例結(jié)果表明,本文提出的多元總體最小二乘問題的牛頓解法可行且收斂速度更快。
[Abstract]:In order to improve the calculation efficiency of parameter estimation of multivariate total least squares problem, multivariate weighted total least squares algorithm based on Newton method is derived; analysis and comparison of the multivariate weighted total least squares solutions of the Newton method and Lagrange multiplier method multivariate weighted total least two by the relationship between the solutions based on covariance propagation law is given according to the approximate calculation formula of multiple general least squares 16 variance covariance matrix. The new algorithm can solve the problem of correlation between the observation matrix and the coefficient matrix elements, and can also incorporate the random elements and constant elements of the observation matrix and the coefficient matrix into a covariate matrix. The results of the example show that the Newton solution of the multivariate general least square problem proposed in this paper is feasible and the convergence speed is faster.
【作者單位】： 東華理工大學(xué)測(cè)繪工程學(xué)院;流域生態(tài)與地理環(huán)境監(jiān)測(cè)國家測(cè)繪地理信息局重點(diǎn)實(shí)驗(yàn)室;江西省數(shù)字國土重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金(41204003;41161069;41304020;41464001) 測(cè)繪地理信息公益性行業(yè)科研專項(xiàng)(201512026) 江西省自然科學(xué)基金(20151BAB203042) 江西省教育廳科技項(xiàng)目(GJJ150595;KJLD12077;KJLD14049) 流域生態(tài)與地理環(huán)境監(jiān)測(cè)國家測(cè)繪地理信息局重點(diǎn)實(shí)驗(yàn)室開放基金(WE2015005) 東華理工大學(xué)博士科研啟動(dòng)金(DHBK201113);東華理工大學(xué)研究生創(chuàng)新專項(xiàng)資金(DHYC-2015005) 江西省研究生創(chuàng)新專項(xiàng)資金(YC2015-S266;YC2015-S267) 對(duì)地觀測(cè)技術(shù)國家測(cè)繪地理信息局重點(diǎn)實(shí)驗(yàn)室開放基金(K201502)~~
【分類號(hào)】：P207
【正文快照】： 總體最小二乘(total least squares,TLS)方法是近30多年來發(fā)展起來的一種能同時(shí)顧及觀測(cè)值誤差和模型系數(shù)矩陣誤差的數(shù)學(xué)方法,其理論及應(yīng)用研究是目前國內(nèi)外研究的熱點(diǎn)問題[1]。文獻(xiàn)[2]首次提出總體最小二乘概念,隨著變量誤差模型(errors-in-variables,EIV)由單變量模型擴(kuò)展到，

本文編號(hào)：1339089