機率性方法在室內定位環境下之可行性研究

Abstract

在以信號強度為指紋辨識的室內定位系統中,一般而言相較於決定性方法來說,對於多重路徑,障礙物遮蔽所造成的雜訊,機率性方法有著較佳的適應性,因此期望能在機率性方法下獲得較精確且穩定的定位結果。 在這篇論文中,決定性以及機率性方法分別以歐基里得距離與多變數高斯模型(馬氏距離)來處理信號強度資料。但實際情況並非像上一段所描述,多變數高斯模型所得到的定位誤差大於歐基里德距離方法所得。在進一步探討多變數高斯模型的性質後發現，主要影響多變數高斯模型的關鍵因子在於指數項,也就是馬氏距離上,不僅提供平均向量(歐基里德距離所使用),更以共變數矩陣來描述所有信號源的變動情形。在這邊提出了距離分布的概念,可以將高維信號強度空間的距離分布投影到二維的直方圖,透過這個方法投入多筆信號強度資料組合作觀察，可以詳細地了解到馬氏距離與歐氏距離的差異如何導致不同定位結果。不相似的RSSI向量分布導致共變數矩陣隨著時間改變,不穩定的程度甚高於平均向量。最極端的不相似情形為在訓練階段(training phase)與追蹤階段(tracking phase)的封包接收率有0%與100%的差異,造成了計算馬氏距離發生除零的狀況。除此之外,不穩定的封包接收率也是造成不可靠的共變數矩陣成因之一。因此MTGI,修正版的多變數高斯,以封包接收率來濾除不穩定或不合理的信號源,再代入多變數高斯模型作計算。最後比較三種方法:歐基里德距離(ED),多變數高斯模型(MGI)與修正版多變數高斯模型(MTGI)在兩個不同環境與實驗設置下的定位結果並藉此驗證在論文中的推論。

In fingerprint based localization methods, it is generally believed that compared with deterministic one, there is more robust for probabilistic one against noise result from many possible factors like multipath fading channel, hardware, obstacles shadowing…etc, and more accuracy and stable localization results are also expected. In this work, deterministic and probabilistic methods are implemented as Euclidean Distance and Multivariate Gaussian Inference (Mahalanobis distance) respectively with received signal strength data sets. Not as expected in last paragraph, higher location error happened in MGI than in Euclidean distance. From advance study of MGI, or its dominate item, Mahanobis distance, we learned that it provides not only average RSSI vector used in Euclidean distance but also covariance matrix which provides information about variance and covariance of all signal sources. Distance distribution is proposed here to project high dimension distance distribution to 2-d diagram and thorough these observations, the reason why worse location result in Mahalanobis distance is confirmed by experimenting different training and tracking data combination. Dissimilar RSSI vectors distribution of the same position tells us the instability of covariance matrix varying with time severer than average RSSI vectors. Extreme case of dissimilarity is even happening 100% packet loss in training phase but partially received in tracking phase, resulting zero divided in the calculation of Mahalanobis distance, and MTGI (Multivariate Truncated Gaussian Inference) is proposed to mitigate this situation by filtering packet receive ratio before distance calculation. In the end, two data sets from two testbeds with different environmental characteristic are implied by ED, MGI and MTGI for comparison and verify whole discussion of this work.