通常在測量及空間資訊領域，我們以無偏估計來計算未知參數估計值，例如一般慣用的最小二乘法。但若是函數模型的未知參數間會有高度相關時，則在計算出的未知參數估計值的中誤差可能會很大，整個平差系統求解會不穩定甚至無法求解。若以有偏估計為之，則可獲得穩定的解，且其均方誤差會是最小，嶺回歸法就是一種有偏估計法，它可以用來解算參數高度相關的平差問題，且可以得到最佳均方誤差。
嶺回歸數學模型為於法矩陣對角線元素加上一嶺回歸參數k值，形成一有偏估計，此法可降低估計值之MSE值，以提升未知參數估計值求解的精確度。經許多學者之驗證分析，它能穩定和輕易的求解設計矩陣高度相關之平差問題；而以控制點之物空間坐標及其對應之像坐標求解高階有理函式係數時，因受過度參數化之影響，其法矩陣具有高度相關而產生秩虧問題。
高階有理函式係數求解時會有法矩陣秩虧問題，導致無法求逆。因此本研究主要以嶺回歸數學模型，解決高階有理函式係數求解時之秩虧問題，求得最佳嶺回歸參數及最小MSE值。本文以影像等級為Level 1A 之福衛二號衛星影像為實際資料，採用五種不同嶺回歸求解方法:k_HK、k_HKB、k_LW、k_KS、k_AD。並以222個控制點計算嶺回歸成果之MSE值，以最佳成果之k_KS方法於影像坐標x和y方向上之MSE值分別為0.44(pixels)和0.5(pixels)。實驗結果顯示，嶺回歸法對於有理函數的求解是非常有效的。

The Ration Function Model (RFM) is one of the generalized sensor models to　express the relationship between the image space and the object space as a general function. When calculating the third-order Rational Polynomial Coefficients (RPCs) by the least squares method, a rank deficiency problem will exist due to its multicollinearity. In order to overcome this problem, we can add a small value termed as the ridge parameter into the diagonal elements of the normal matrix. Then we obtain a bias estimation based on the ridge regression. The ridge regression can achieve smaller Mean square error (MSE) value than least squares method by increasing a little bias. The results of this research show that the ridge regression indeed solves the multicollinearity problems of the third-order RPCs. In this research, FORMOSAT-II satellite images of Level 1A are used. We use five different Ridge regression methods: k_HK、k_HKB、k_LW、k_KS、k_AD in the research for comparison. In this paper, 222 ground control points are used for checking the quality of the ridge regression methods mentioned above. The k_KS method has the best result and its MSE of image coordinates in x-direction and y-direction are respectively 0.44(pixels) and 0.5(pixels) based on our experiments. The results show that ridge regression is very effective for solving RFM.

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