其在測(cè)量中的應(yīng)用
(中南工業(yè)大學(xué)資源環(huán)境與建筑工程學(xué)院， 長(zhǎng)沙 410083)
摘 要: 在測(cè)量等許多工程領(lǐng)域中， 存在因函數(shù)模型結(jié)構(gòu)差即設(shè)計(jì)矩陣病態(tài)、 致使未知數(shù)的最小二乘估計(jì)偏差太大且不穩(wěn)定的問題，因此， 研究了使用矩陣 奇異值分解和廣義嶺估計(jì)進(jìn)行數(shù)據(jù)處理的方法。 首先, 簡(jiǎn)述了矩陣奇異值分解及廣義嶺估 計(jì)的理論與性質(zhì); 然后，重點(diǎn)比較研究了它們解算病態(tài)方程的思想、途徑、 對(duì)關(guān)鍵問題 的處理 、適應(yīng)范圍、工作量大小等；最后，通過攝影測(cè)量算例驗(yàn)證了所得結(jié)果。并且指出，奇異值分解方法應(yīng)用于病態(tài)方程的參數(shù)解算, 是一種易于操作、 效果更好的方法， 有 重要的應(yīng)用價(jià)值。
關(guān)鍵字: 奇異值分解 廣義嶺估計(jì) 病態(tài)方程
（College of Resource, Environment and Civil Engineering,Central South University of Technology, Changsha 410083, P. R. China）
Abstract:The methods of data processing in surveying were studied with Singular Value Decomposition(SVD) and Generalized Ridge Estimation(GRE) under the circumstances that the multicollinearity among the columns of the coefficient matrix makes deviation of estimator too great by least squares adjustment. The theory and their properties of SVD and GRE were narrated, then a comparison between these two methods in the thoughts, ways, key problems, amount of work, applicable limits of solving ill-conditioned equation series was made. At last a photogrammetrical example was used to give the verification for the conclusion reached, and the SVD method solving ill-conditioned equation series was pointed out to be easy to handle and effective, therefore SVD method will be of great value to surveying work.
Key words: singular value decomposition(SVD) generalized ridge estimation(GRE)
ill-conditioned equation series
