利用遺傳演算法最佳化模糊控制器之GPS定位權重最小平方法

Abstract

GPS 接收機的定位精度對於使用者而言相當重要，在定位的過程中，定位精度與數個因子之間具有某種程度的關連性。本文所提出的歸一化精確度稀釋鬆弛值(Normalized Dilution of Precision Slackness Value, NDSV) 衍生自精確度稀釋值(Dilution of Precision, DOP)，此一因子代表單一衛星之幾何誤差。NDSV、訊號雜訊比(Signal-to-Noise Ratio, SNR)及衛星仰角(elevation angle)，三者和定位誤差具微妙且相互矛盾的關係。當我們所觀測到的衛星數大於四，即可以此三項因子為基準，透過模糊控制器(Fuzzy Controller)決定每個衛星之訊號在權重型最小平方法(Weighted-Least-Square, WLS)中的權重，進而提昇定位精度。 傳統上以試誤法所設計之模糊控制器的效能不甚理想。為了要提昇模糊控制器的效能，本文提出了一種以遺傳演算法(Genetic Algorithms, GAs)將模糊控制器的三個部份作最佳化，卻不違反常見之歸屬函數設計準則的新方法。這其中包括了歸屬函數之最佳化、歸屬函數之數量最佳化與模糊規則最佳化。在此同時，歸屬函數之數量亦透過適應函數之設計而獲得最簡化。 一旦我們得到最佳化之模糊控制器，權重型最小平方法即可同時計算出較準確之位置與速度。將此估測量納入卡門濾波器(Kalman filter)中，定位精度即可獲得進一步的提升。 數值結果證實，權重型最小平方法的定位結果優於最小平方法，且引入權重型最小平方法之卡門濾波器，其所估測之位置與速度亦優於引用最小平方法之結果。經本文提出之方法所訓練出的模糊控制器，由於具備效能最佳化、結構最簡化之特性，故此一模糊控制器具實現於低階GPS接收機之潛力。

The positioning accuracy of the GPS receiver is essential to users. During positioning, several factors are related to positioning accuracy. NDSV (Normalized Dilution of Precision Slackness Value) proposed here is derived from DOP (Dilution of Precision) and represents the relationship of geometric error to a single satellite. There are tradeoffs among NDSV, SNR and elevation angle to positioning error. If the number of observed satellites is above four, the WLS (Weighted-Least-Square) method which considers three factors (NDSV, SNR, elevation angle) to determine the weighting of the measurement of each satellite through fuzzy controller is applied to enhance the positioning accuracy. However, the fuzzy controller is difficult to be optimized through trial-and-error method. To solve this problem, we proposed a new approach to design fuzzy controller in three stages (membership functions (mfs), the number of mfs, rules) via GAs (Genetic Algorithms) without violating the common design antecedent of mfs. At the same time, the number of mfs is optimized and optimally reduced through fitness function design. The optimized fuzzy controller can be used to determine position and velocity through WLS method simultaneously. Furthermore, we can include the more precise estimated position and velocity from WLS into Kalman filter as measurement to further improve positioning accuracy. The numerical results show that the positioning using WLS method is improved in comparison with LS method. The Kalman filter which includes the estimated position and velocity from WLS as measurements can further improved the positioning accuracy in comparison with including the estimated position and velocity from LS. Due to its performance and simplified structure, the trained fuzzy controller may be potentially used on a low-cost GPS receiver.