本文選題：PEIV模型 + 總體最小二乘��； 參考：《武漢大學(xué)學(xué)報(信息科學(xué)版)》2017年06期

【摘要】：針對觀測向量和系數(shù)矩陣權(quán)分配不合理、驗(yàn)前隨機(jī)模型不準(zhǔn)確的情況,以部分誤差變量(partial errors-in-variables,PEIV)模型為基礎(chǔ),推導(dǎo)了附有相對權(quán)比的總體最小二乘平差算法;通過在平差準(zhǔn)則中加入相對權(quán)比,自適應(yīng)調(diào)整觀測向量和系數(shù)矩陣隨機(jī)元素對模型參數(shù)估計的貢獻(xiàn),給出了確定相對權(quán)比的驗(yàn)前單位權(quán)方差法和判別函數(shù)最小化迭代算法,該算法普遍適用于一般性的系數(shù)矩陣和權(quán)矩陣。通過直線擬合和坐標(biāo)轉(zhuǎn)換模擬算例的比較分析,發(fā)現(xiàn)當(dāng)觀測值和系數(shù)矩陣的驗(yàn)前單位權(quán)方差已知,且較準(zhǔn)確時,驗(yàn)前單位權(quán)方差法確定相對權(quán)比和參數(shù)估計的效果較好;而以s訐礯1(ε,ε_a)=ε~Tε+ε_a~Tε_a作為判別函數(shù)是判別函數(shù)最小化迭代算法中效果最好的。
[Abstract]:In view of the unreasonable weight allocation of the observation vector and coefficient matrix and the inaccuracy of the prior random model, based on the partial error variable partial errors-in-variablesl PEIVs model, the total least square adjustment algorithm with relative weight ratio is derived. By adding the relative weight ratio to the adjustment criterion and adjusting the contribution of the observation vector and the random elements of the coefficient matrix to the parameter estimation of the model, a priori unit weight variance method for determining the relative weight ratio and an iterative algorithm for minimizing the discriminant function are presented. The algorithm is generally applicable to general coefficient matrix and weight matrix. Through the comparison and analysis of straight line fitting and coordinate transformation simulation examples, it is found that when the prior unit weight variance of observation value and coefficient matrix is known and more accurate, the result of relative weight ratio and parameter estimation by prior unit weight variance method is better. However, it is the best iterative algorithm to minimize the discriminant function by using the discriminant function as a discriminant function.
【作者單位】： 東華理工大學(xué)測繪工程學(xué)院;流域生態(tài)與地理環(huán)境監(jiān)測國家測繪地理信息局重點(diǎn)實(shí)驗(yàn)室;武漢大學(xué)測繪學(xué)院;
【基金】：國家自然科學(xué)基金(41664001,41204003) 江西省杰出青年人才資助計劃項(xiàng)目(20162BCB23050) 國家重點(diǎn)研發(fā)計劃(2016YFB0501405) 測繪地理信息公益性行業(yè)科研專項(xiàng)(201512026) 江西省教育廳科技項(xiàng)目(GJJ150595) 流域生態(tài)與地理環(huán)境監(jiān)測國家測繪地理信息局重點(diǎn)實(shí)驗(yàn)室項(xiàng)目(WE2015005) 對地觀測技術(shù)國家測繪地理信息局重點(diǎn)實(shí)驗(yàn)室項(xiàng)目(K201502) 東華理工大學(xué)博士科研啟動金(DHBK201113)~~
【分類號】：P207.2

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