以遺傳基因演算法爲基礎的符號式迴歸引擎及其於全球定位系統之座標轉換上的應用

A GP-Based Symbolic Regression Engine for the Transformation of GPS Coordinates

周鴻儒(Hung-Ju Chou) ； 吳志宏(Chih-Hung Wu)

《航測及遙測學刊》 12卷4期 (2007/12) Pp. 353-364

https://doi.org/10.6574/JPRS.2007.12(4).7

摘要

全球定位系統之三維座標需要透過複雜的階層式數學計算才可轉換爲二維座標。但是微小的誤差不可避免的會在計算中被累積，使得精準度降低。在本論文中，我們提出一種新的符號式迴歸引擎來產生GPS座標轉換的迴歸方程式。迴歸方程式是透過樹狀結構所定義，再藉由遺傳基因演算法的交配、突變與選擇來改變迴歸方程式的組合來尋找合適的方程式組合。爲了增加迴歸引擎的效率，我們採用了可動態改變機率的機制，加上樹狀修飾來降低公式複雜度，但是仍維持原公式的功能。若能夠得到計算複雜度低的座標轉換公式，就能夠使得定位裝置在獨立電源的環境中，延長待機時間。此方法雖然不能夠降低GPS的系統誤差，但是透過定位資料成功地降低此GPS的統計誤差。此研究的實驗資料採用TWD67的大地座標系統，實驗結果顯示，我們確實能夠使用自行設計的符號式迴歸引擎來取得計算量低的GPS座標轉換公式。

關鍵字

遺傳基因演算法 ； 符號式迴歸 ； 全球定位衛星系統 ； 座標轉換 ； TWD67

並列摘要

Transformation of coordinates usually invokes level-wised processes wherein several sets of complicated equations are calculated. Unfortunately, the accuracy may be corrupted due to the accumulation of inevitable errors between the transformation processes. In this thesis, we present a new symbolic regression engine for generating regressive models for direct transformation from GPS signals to 2-D coordinates. The functional models to be found by the regression engine are represented in tree-based chromosome. Genetic operators like mutation, crossover, and reproduction are applied on such trees. In order to improve the efficiency of the regression process, we design some adaptive mechanisms which adjust the probabilities of applying genetic operations. Methods of trimming and pruning the regressive models for reducing their complexity are also design and implemented. Since target coordinates for a GPS application can be obtained by using simpler transformation formulas, the computational costs and inaccuracy can be reduced. The proposed method, though does not exclude systematic errors due to the imperfection on defining the reference ellipsoid and the reliability of GPS receivers, effectively reduces the statistical errors when the accurate Cartesian coordinates are known from the independent sources. From the experimental results where the target datum TWD67 is investigated, it seems that the proposed method can serve as a direct and feasible solution to the transformation of GPS coordinates.

並列關鍵字

GP ； symbolic regression ； transformation of GPS coordinates ； TWD67