合作式定位之低維度最小方差演算法

Abstract

隨著無線通訊的發展，定位的研究已成為重要的議題。近年來，藉由待測物之間彼此相互通訊的合作式定位更是目前發展的重點。在合作式定位系統中，多個待測目標之間額外的合作量測可以有效提升其定位的精準度；但由於待測目標的增加，因此演算法的複雜度相較於傳統定位法更是困難許多。在諸多演算法中，高斯-牛頓法被廣泛的應用在定位的問題中，效能也與Cramer-Rao Lower Bound (CRLB) 相當；然而其牽涉到反矩陣的運算，使得伴隨而來的複雜度相當高。我們試著藉由降低矩陣的維度使反矩陣的運算量降低，進而達到降低複雜度的目標。在論文中，我們設定一個待測物為目標待測物，並試著尋找其餘附屬待測物與目標待測物之間的位置關係，藉此來達到降低運算度的目的，並維持其定位準確度。因此，我們提出了聯合式、平行式與序列式三種預先線性化的方法使附屬待測物的位置座標轉化成目標待測物的線性函式。接著再利用此線性函式使原來的多待測物問題降階成一個目標待測物的估計問題並利用低維度高斯-牛頓法來估計。其中平行式與序列式的演算法運算複雜度順利的被簡化。另外，基於目標待測物的位置估計的影響，我們更進一步提出目標待測物的選擇機制，進而增進定位的效能；另一方面，根據待測物的不確定性，我們對於權重也做了額外的補償。電腦模擬驗證了目標待測物的選擇機制及權重補償能夠提高定位準確度；另外也比較了高斯-牛頓法與我們提出的預先線性法，證明在不失定位準度的情況下，減少了運算複雜度。

Cooperative localization has received extensive interest from the robotic, optimization, and wireless communication. In addition to the range measurements from the mobile and BSs with known position, the extra information among mobiles is added to improve the accuracy of position in cooperative localization. The Gauss-Newton (GN) method can be used to solve the cooperative positioning problem with good performance, but its computational complexity is quite high due to the matrix inversion. However, if the dimension is reduced, the complexity of algorithm is reduced as well. In this thesis, a target mobile is selected as reference mobile, we want to find the relationship between auxiliary mobiles and the target mobile. Therefore, we propose three pre-linear methods, joint, parallel and sequential methods, which can reduce dimension of the unknown parameters by searching the linear mapping relations from auxiliary mobiles to target mobile. With the pre-linear mapping function, the dimension-reduced GN method of target mobile is derived based on the conventional GN method. The total computational cost can be reduced greatly in parallel and sequential methods. Moreover, the choice of target mobile and compensation of inaccurate mobiles are discussed to enhance the localization accuracy. Simulations validate the enhancement of accuracy. In addition, we also compare performance of RMSE and total computation cost for low-complexity pre-linear methods with GN method.