以強韌估測器偵測GNSS系統多重路徑之影響

Abstract

本論文中，我們基於強韌估測器(R-Estimation)提出一個新的定位方法，以便偵測GNSS/GPS系統中的多重路徑的影響，其中我們將GNSS/GPS的定位問題視為一個非線性回歸問題，並指出傳統以最小平方法(Least Squares)所得的定位結果，對於非直射(Non-Line-Of-Sight, NLOS)訊號在偽距(Pseudorange)量測上造成的異常值(Outliers)很敏感，所以我們採用強韌估測器中的比序方法(Rank-based Approach)來得到較好的強韌性。 在新的方法中，我們將Wilcoxon norm當作是新的目標函數(Objective Function)，同時也使用梯度下降法(Gradient Decent Method)來最小化Wilcoxon目標函數。我們將透過分析二維空間中的例子，來完整討論Wilcoxon目標函數的特性，與傳統2-norm所構成的目標函數相比，Wilcoxon目標函數並不會受到接收機鐘差的影響。 我們也將以最小化2-norm目標函數後，所得殘差(Residuals)的標準差，用來探討使用比序方法的時機，同時透過雙GNSS衛星群的模擬，討論比序方法的偵測效能，其結果顯示本論文的方法有較好的效能來抵抗較大的異常值(Larger Outliers)。

In this dissertation, a new positioning method based on the robust estimation (R-estimation) is proposed to detect the multipath effect in GNSS/GPS system. We reorganize the GNSS/GPS positioning problem as a nonlinear regression problem and point out the positioning result of the traditional least squares approach is sensitive to the pseudorange measurement outliers caused by the non-line-of-sight (NLOS) signal. The new rank-based approach from the R-estimator is adopted here to provide better robustness. The Wilcoxon norm is used as a new objective function in this new approach. The numerical method, called the gradient decent method, is provided to minimize the Wilcoxon objective function. The properties of this new objective function will be thoroughly discussed in our dissertation by analyzing 2-dimension cases. Comparing with the 2-norm objective function, the new Wilcoxon objective function will not be changed with the variation of the receiver clock bias. The timing of applying the rank-based approach will be discussed in terms of the standard deviation of the residuals with respect to the minimized 2-norm objective function. The performance of detecting the satellites corrupted by the multipath effect will be provided through the simulation of dual GNSS constellations. The results show the proposed approach has better performance against larger outliers.