- 期刊
貝氏統計應用於GPS定位與其信賴區域之研究
GPS Positioning and Its Confidence Regions Based on Bayesian Inference
摘要
全球定位系統提供全天候的觀測量與高精度的定位成果。然而，利用載波相位觀測量進行定位時，會產生整數與實數之混合型態未知參數的問題。本研究利用貝氏統計所推導之相位模稜的邊際後驗密度函數，以最大後驗法求定整數相位模稜及實數幾何參數之估計值。此外，基於約制模稜之先驗分布與真實資料狀況並不符合的概念，本文利用貝氏方法所推導之決策運作指標，即時判定是否擴大模稜搜尋空間以求正確模稜估計值。本研究目的即爲利用貝氏統計的方法與決策運作指標進行GPS近即時定位，以及藉由貝氏推論所導之定位估計值與協方差矩陣，以蒙地卡羅數值法獲取定位參數之信賴區域。實驗成果顯示，利用決策指標判別是否擴大模稜搜尋空間的方法，可即時且自動化地判斷模稜搜尋空間是否恰當，並找出正確的整數解以提升整體的定位精度，且蒙地卡羅數值法可即時以視覺化的方法呈現定位參數之信賴區域。
並列摘要
GPS provides all-weather observations, and highly accurate positions. With a GPS model using carrier-phase observations containing integer-valued and real-valued unknown parameters, this paper presents a near-real-time data processing technique based on Bayesian statistics. The Bayesian approach takes the maximum-likelihood posterior solution of positioning parameters as the estimator with highest posterior density function of ambiguity. Moreover, for the sake of the fact that restricting the prior distribution of ambiguities is not consistent with the real data in Bayesian view, a theory of mixture model based on Bayesian inference was advanced and the index for decision-making was derived. The index was used here to determine whether the ambiguity search space is expanded or not. The main aims of this research are to perform the GPS positioning by using the Bayesian approach with the index for decision-making and determine the confidence regions for positioning parameter by using a Monte Carlo method based on the Bayes estimation and covariance matrix. The experimental results show that the correct solution can be obtained and the accuracy of positioning results can be improved in real time and automatically by using the Bayesian approach. Furthermore, the confidence regions for GPS positioning parameter can be determined by using the Monte Carlo method.