從最近過去的時間序列相位殘差分析 估計非模式化GPS誤差與改正

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謝吉修(Chi-Hsiu Hsieh) 查詢紙本館藏

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土木工程學系

論文名稱

從最近過去的時間序列相位殘差分析估計非模式化GPS誤差與改正
(The estimation and mitigation of unmodeled GPS biases from the recent time-series phase residuals analysis)

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摘要(中)

眾所周知，GPS電碼和載波相位測量在差分模式下的偏差，諸如多路徑效應是一個主要的誤差來源，它抑制了實現最高精度層級的定位成果。類多路徑特徵的信號是在動態衛星量測中，一個小區域內與空間相關且緩慢變化的訊號誤差，且無法平均此偏差。在不同的衛星、位置及時間這些偏移量誤差皆不同特徵，就如臉譜是獨一無二。唯有依據最近每天時間序列殘差估值重複的相關性，這種關係可以經濟地降低此多路徑誤差。
本研究開發一種創新技術，包括希爾伯特-黃變換(Hilbert-Huang Transform, HHT)的經驗模態分解(Empirical Mode Decomposition, EMD)，以分析時間序列的載波相位殘差。分解後由統計顯著性檢測門檻值百分95的邊界線，進行檢測識別幾個短週期分量成份為白噪聲，以此消除高頻分量。本研究展示如何選擇最佳的門檻值。同時，增加了一個源於灰色關聯分析(Grey Relational Analysis, GRA)的外推技術，以預測偏差並糾正這種非系統性偏差的定位。實用上可通過上述模式的功能和灰色建模，再由傳統最小二乘平差與參數加權獲得產生更精確的三維定位坐標。
研究結果顯示，此改正技術是必要的程序。由此程序可更可靠地解相位模稜(Ambiguity)，且糾正後可以顯著地改善GPS的動態定位與大地監測的精度。

摘要(英)

It is well-known that unmodeled biases, such as the multipath effect, are a major source of errors in GPS code and carrier phase measurements in the differential mode, which can hinder the achievement of the highest levels of accuracy. An alike multipath-characterized signal is spatially correlated within a small area that introduces slow varying errors in the measurements due to satellite dynamics, whose biases cannot be averaged out. These offset biases are unique, much like a portrait. According to the correlation between day-to-day time series residual estimates in the recent past, this relationship can be widespread and economically exploited to mitigate multipath errors.
In this study an innovative method, which involves empirical mode decomposition (EMD) in the Hilbert-Huang transform (HHT), is employed to analyze time-series phase residuals. After decomposition, statistical significance testing using a 95 percentile boundary line can identify a few short period components, whiles the white noise is determined using a threshold to eliminate the high frequency component. In this study show how to choose the best threshold. An extrapolation technique, which is rooted in grey relational analysis (GRA), is simultaneously utilized to predict the biases for the current positioning task and thus to correct for such systematic biases. When technically supported by the above-mentioned mode functions and grey modeling, classical least-squares adjustment with parametric weighting can yield more accurate three-dimensional coordinates.
The results also show that this mitigation technique is a necessary procedure, which allows the ambiguity solutions to become more reliable so that after correction there is a over 50% improvement in GPS kinematic OTF positioning and geodetic monitoring accuracy.

關鍵字(中)

★ 全球衛星定位系統
★ 經驗模態分解
★ 灰色關聯分析
★ 希爾伯特-黃變換
★ 相位殘差分析

關鍵字(英)

★ GPS
★ Empirical Mode Decomposition
★ Grey Relational Analysis
★ Hilbert-Huang Transform
★ Phase Residuals Analysis

論文目次

中文摘要 I
ABSTRACT II
ACKNOWLEDGEMENTS IV
CONTENTS V
LIST OF FIGURES VII
LIST OF TABLES XI
LIST OF ABBREVIATIONS XII
CHAPTER 1. INTRODUCTION 1
1.1 Motivation 3
1.2 Research objectives and scope 4
1.3 Contribution 5
1.4 Structure of the dissertation 5
CHAPTER 2. LITERATURE REVIEW 7
2.1 Functional description of a GNSS receiver 7
2.2 GPS observables and error sources 10
2.2.1 Satellite-based errors 13
2.2.2 Signal propagation errors 13
2.2.3 Receiver-based errors 16
2.3 Unmodeled GPS biases such as the multipath phenomenon 16
2.4 Phase residual analysis 19
2.4.1 Fourier transform 20
2.4.2 Wavelet transform 22
2.4.3 Hilbert-Huang transform 23
CHAPTER 3. ALGORITHM METHOD 26
3.1 Time-series SD phase residuals 28
3.2 Resolution of the GPS constellation orbit periods 38
3.3 Phase residual analysis 39
3.4 Bias forecasting using the GM(1,1) approach of GRA 50
3.5 Reduction algorithm with forecast bias parameters 56
CHAPTER 4. EXPERIMENTS AND RESULTS 59
4.1 Case 1: Baseline SPP0−SP3A 60
4.2 Case 2: Baseline CSRF−NTPU 73
CHAPTER 5. CONCLUSIONS AND FUTURE WORK 82
5.1 Conclusions 82
5.2 Limitations 83
5.3 Future Work 84
BIBLIOGRAPHY 85
APPENDIX 95
A. Least-squares parameter estimation of , and 95
B. Tactics for estimation of the variance component 97
CURRICULUM VITAE 98

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指導教授

吳究(Joz Wu)

審核日期

2014-7-22

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