The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.

隨著WiFi訊號在都市的涵蓋率逐漸普及，基於WiFi訊號強度值的定位方法逐漸發展。WiFi匹配定位(Matching Positioning)是透過參考點坐標與WiFi訊號強度(Received Signal Strength Indicator, RSSI)的蒐集，以最小二乘法(Least Squares, LS)計算RSSI模型參數；然後，利用模型參數與使用者位置的WiFi訊號強度，推估出使用者的位置。然而WiFi訊號強度容易受到環境因素影響，例如降雨、建物遮蔽、人群擾動等因素，皆會使訊號強度降低，若以受影響的訊號強度進行定位，將使定位成果與真實位置產生偏移。 為了降低訊號強度的錯誤造成定位結果的誤差，本研究嘗試透過具有穩健性的最小一乘法( Least Absolute Deviation, LAD)結合WiFi匹配定位，去克服WiFi訊號易受環境影響的特性，期以獲得較精確的WiFi定位成果。研究首先透過模擬資料的建立，測試不同粗差狀況最小一乘法WiFi匹配定位之表現，最後再以真實WiFi訊號進行匹配定位的演算，並比較最小一乘法WiFi匹配定位與最小二乘法WiFi匹配定位的成果差異，探討二種方法的特性。 根據本研究成果顯示，於模擬資料中，最小一乘法WiFi匹配定位相較於最小二乘法WiFi匹配定位，在面對參考點接收的AP訊號與檢核點接收的AP訊號強度含有粗差的情形皆能有較好的穩健性，且在參考點接收的AP訊號含有粗差的情況有良好的偵錯能力。而於真實環境之下，最小一乘法WiFi匹配定位之精度也較最小二乘法WiFi匹配定位具有穩健性；在室外資料的部份，最小一乘法WiFi匹配定位之精度為8.46公尺，最小二乘法WiFi匹配定位之精度為8.57公尺。在室內資料的部份，最小一乘法WiFi匹配定位之精度為2.20公尺，最小二乘法WiFi匹配定位之精度為2.41公尺。 / Because of the extensive coverage of WiFi signal, the positioning methods by the WiFi signal are proposed. WiFi Matching Positioning is a method of WiFi positioning. By collecting the WiFi signal strength and coordiates of reference points to calculate the signal strength transformation parameters, then, user’s location can be calculated with the LS (Least Squares). However, the WiFi signal strength is easily degraded by the environment. Using the degraded WiFi signal to positioning will produce wrong coordinates. Hence this research tries to use the robustness of LAD (Least Absolute Deviation) combining with WiFi Matching Positioning to overcome the sensibility of WiFi signal strength, expecting to make the result of WiFi positioning more reliable. At first, in order to test the ability of LAD, this research uses simulating data to add different kind of outliers in the database, and checks the performance of LAD WiFi Matching Positioning. Finally, this research uses real data to compare the difference between the results of LAD and LS WiFi Matching Positioning. In the simulating data, the test result shows that LAD WiFi Matching Positioning can not only have better robust ability to deal with the reference and check points AP signal strength error than LS WiFi Matching Positioning but also can detect the outlier in the reference points AP signal strength. In the real data, LAD WiFi Matching Positioning can also have better result. In the outdoor situation, the RMSE (Root Mean Square Error) of LAD WiFi Matching Positioning and LS (Least Squares) WiFi Matching Positioning are 8.46 meters and 8.57 meters respectively. In the indoor situation, the RMSE (Root Mean Square Error) of LAD WiFi Matching Positioning and LS (Least Squares) WiFi Matching Positioning are 2.20 meters and 2.41 meters respectively.