本文選題：總體最小二乘 + 相關(guān)觀測(cè)　； 參考：《測(cè)繪學(xué)報(bào)》2017年08期

【摘要】：Partial errors-in-variables(Partial-EIV)模型作為EIV模型的擴(kuò)展形式,其構(gòu)造方式更有規(guī)律,解算方法更為簡(jiǎn)便,能有效應(yīng)用于實(shí)際情況。針對(duì)已有Partial EIV模型方法未考慮觀測(cè)向量和系數(shù)矩陣存在相關(guān)性這一情況,通過提取觀測(cè)向量和系數(shù)矩陣組成的增廣矩陣中非重復(fù)出現(xiàn)的隨機(jī)元素,構(gòu)建更具一般適用性的Partial EIV模型,在該模型的基礎(chǔ)上,將特殊假定條件擴(kuò)展到不限定觀測(cè)數(shù)據(jù)相關(guān)性的一般情況,詳細(xì)推導(dǎo)了觀測(cè)向量和系數(shù)矩陣元素相關(guān)且不等精度情況下的加權(quán)總體最小二乘方法,通過算例試驗(yàn),并與目前已有的解決EIV模型相關(guān)觀測(cè)情況下的方法進(jìn)行了比較分析,研究表明本文方法可以提高計(jì)算效率,更具一般性,特別是對(duì)于觀測(cè)向量和系數(shù)矩陣中存在常數(shù)元素和重復(fù)元素的情況。
[Abstract]:As an extended form of EIV model, the Partial errors-in-variables-Partial-Eve) model is constructed in a more regular manner, and its solution method is simpler and can be effectively applied to the actual situation. In view of the fact that the existing Partial EIV model methods do not consider the correlation between the observation vector and the coefficient matrix, the augmented matrix composed of the observation vector and the coefficient matrix is extracted. A more general applicable Partial EIV model is constructed. Based on the model, the special assumptions are extended to the general case of unqualified correlation of observed data. In this paper, the weighted population least square method with variable precision and correlation between the observation vector and coefficient matrix elements is derived in detail. The method is compared with the existing methods for solving the related observation of EIV model through an example. The results show that the proposed method can improve the computational efficiency and be more general, especially in the case of constant elements and repeated elements in the observation vector and coefficient matrix.
【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(guó)家測(cè)繪地理信息局重點(diǎn)實(shí)驗(yàn)室;江西省數(shù)字國(guó)土重點(diǎn)實(shí)驗(yàn)室;武漢大學(xué)測(cè)繪學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(41664001;41204003) 江西省杰出青年人才資助計(jì)劃項(xiàng)目(20162BCB23050) 國(guó)家重點(diǎn)研發(fā)計(jì)劃(2016YFB0501405) 江西省教育廳科技項(xiàng)目(GJJ150595)~~
【分類號(hào)】：P207

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1 歐吉坤;相關(guān)觀測(cè)情況的可靠性研究[J];測(cè)繪學(xué)報(bào);1999年03期

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