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課程來源:MIT
     

12.215 現代導航(2002年秋季)

12.215 Modern Navigation, Fall 2002

 

翻譯:栦哢

編輯:陳盈,馬景文

Figure showing 24 GPS satellites orbiting the Earth.

至少有24顆全球定位系統(GPS)衛星在11,000英里(大約20,000km)的高空環繞地球,能夠為世界上任何地方、任何天氣情況下的用戶提供精確的位置、速度和時間信息。(圖片由美國聯邦航空局提供.)

 

課程重點

本課程包括詳細的課堂講稿和作業。

課程描述

20世紀60年代,全球定位系統(GPS)開始研發,1992年投入使用。在最近的幾年,此系統從100m(民用限制精度要求)的定位精度降至1mm(無需安全許可!),引發許多不同形式的應用。這門課程會應用大量在麻省理工學院學到的科學和數學基本原理,以探索全球定位系統的應用與原理。我們也在堂上和校園使用全球定位系統和其他設備,以示範如何使用該系統。

技術需求

本課程的網頁上的.f文件可以用很多開發工具來編譯並運行。具體指引或建議請參考課程內容。
MATLAB®軟件是運行本課程網頁.m文件的必備軟件。

 

教學大綱

1.變形的、非球體的地球坐標系統。依照重力方向(天文經緯度)和橢球形狀標準(大地經緯度)兩方面來闡述經緯度的概念。不同坐標之間的關係;極移的概念和地球自轉速率的變化;坐標系統之間的相互轉換。對不同精度結果和全球定位系統所能達到的精度需要考慮的影響。

2. 導航原理;盲航推算,真實的磁象限角;天體的應用,定位割線法應用。一般地圖投影概論;不同的地圖投影的應用。球面三角學向量法。

3. 全球定位系統原理;偽距和相位測量。擴頻訊號結構;訊號解析基本原理。偽距和相位(幾何位置,時鐘誤差,傳播媒介,相位整周模糊度)的作用。簡化的大氣層和電離層延時模型;電離層散射影響。差分技術在全球定位系統數據分析中的運用。全球定位系統衛星的安全系統(選擇可用性,反電子誘騙)及其對導航和精確定位的影響。

4.估算程序;隨機和數學模型;動態系統的統計描述;協方差矩陣最小二乘估計傳播。

5. 飛機導航使用全球定位系統的實例(與激光成型比較);檢核全球定位系統取得的真實數據,以估算其可以達到的精度極限;在眾多領域的應用,包括精耕農業;智能汽車導航系統。

課程有實驗課,每幾周有一次家庭作業。有一次期末開卷考試。成績將由以下部分組成:家庭作業(60%),期末考試(30%),出勤率(10%)。

為了更好理解內容,大家可以在一起討論作業,也可以參考其他書目和已發表的材料,但要在作業恰當註明這些額外資料的出處。學生必須單獨完成作業。抄襲他人絕不允許。

課本

Hofmann-Wellenhof, B., H. Lichtenegger和J. Collins.《全球定位系統理論和實踐》GPS Theory and Practice. New York: Springer-Verlag, Wein, 1992, pp. 326.

Strang, G.和K. Borre.《線性代數、測地學與全球定位系統》Linear Algebra, Geodesy, and GPS. Wellesley, MA: Wellesley-Cambridge Press, 1997, pp. 526. (Gilbert Strang教授的網頁)

 

教學時程,課堂講稿,作業

課程單元

1

緒論
Introduction

 

概論及坐標系
Introduction and Coordinate Systems (英PDF)

2

經緯度的定義
Latitude and Longitude Definition

 

不同類型經緯度的定義;與Cartesian直角坐標的數學關係;影響經緯度定義的地球轉軸運動
Definitions of the Types of Latitude and Longitude; Mathematical Relationship Between These and Cartesian XYZ; Motion of the Rotation Axis which Effects Determination of Latitude and Longitude (英PDF)

3

高程的定義
Height Definition

 

高程的概念,測定高程的方法,水準測量和三角測量;大地水準高度及其測定
Height Definitions, Methods for Determining Heights, Spirit Leveling and Trigonometric Leveling; Geoid Heights and their Determination (英PDF)

4

球面三角學
Spherical Trigonometry

 

球面三角學。產生及應用範例
Spherical Trigonometry. Derivations and Examples on How to Use (英PDF)

5

太陽/地球運動以及天文位置的測定
Motion of Sun/Earth and Astronomical Position Determination

 

利用天文學方法定義經緯度
Determination of Latitude and Longitude using Astronomical Methods (英PDF)

6

書面和在線年鑑
Almanacs Paper and On-line

 

書面和電子形式的年鑑
Almanacs in both Paper and Electronic Forms (英PDF)

 

作業1 (英PDF)

7

盲航和傳統的導航
Dead Reckoning and Conventional Navigation

 

盲航推算法和六分儀。講稿用到以下的網站
Dead Reckoning and Sextants. The Following Web Sites are Used in the Notes. (英PDF)

 

指向磁北極的道路The Road to the Magnetic North Pole
地球兩磁極的磁場線Field Lines for a Magnetic Dipole
雙磁場Dipole Field
北磁極North Magnetic Pole
船員和輔助領航的近海領航Coastal Piloting for Boat Crew and AuxNav
介紹和高級近海導航法學生學習指南Presentations & Advanced Coastal Navigation Student Study Guide(連結失效)
遊標卡尺Vernier

8

六分儀的使用方法和測量法則
Use of Sextant and Measurements

 

六分儀測量法
Sextant Measurements (英PDF)

9

線性代數
Linear Algebra

 

複習線性代數,涉及向量和矩陣,求解線性方程, 向量空間,特徵值和向量,矩陣轉置
Review of Linear Algebra Covering Vectors and Matrices, Solving Linear Equations, Vector Spaces, Eigenvalues and Vectors, Rotation Matrices (英PDF)

10

六分儀數據結果分析
Analysis of Sextant Results

 

經檢驗的作業2解答和可用於表達所獲測量結果的非線性模型
Examined HW 02 Solution and the Non-Linear Model that can be Used to Represent the Measurements Taken (英PDF)

 

作業2 (英PDF)
*數據文件*Data file (TXT)

11

地圖投影
Map Projections

 

不同類型的地圖投影和一些投影背後的數學
Map Projections of Different Types and the Mathematics Behind Some Projections (PDF)

 

此課使用的網頁:
地圖投影概論Map Projection Overview
美國地質勘探局:變化世界的科學USGS - Science for a Changing World
圓的地球,平的地圖Round Earth, Flat Maps
地圖投影 Map Projection

12

初等統計學和誤差傳播
Basic Statistics and Propagation of Variances

 

統計學和協方差矩陣傳播
Statistics and Propagation of Variance-Covariance Matrices (英PDF)

13

最小二乘估算
Least Squares Estimation

 

超定估計,包括最小二乘和加權最小二乘的近似線性系統
Estimation of Over-Determined, Nearly Linear Systems Including Least and Weighted Least Squares (英PDF)

14

相關度
Correlations

 

利用逐次估計和誤差橢圓法完成估算;檢查隨機時間序列的相關度(課堂的時間序列和相關值圖像由cross.f生成)
Finish Estimation with Sequential Estimation and Error Ellipses; Examine Correlations Between Random Time Series (The Time Series and Correlation Values Plotted in this Lecture were generated with cross.f) (英PDF)

 

作業3 (英PDF)

15

電子距離測量
Electronic Distance Measurement

 

電磁波測距法(EDM)。傳統儀器及其操作理論
Electromagnetic Distance Measurement (EDM). Conventional Instruments and Theory of their Operation (英PDF)

16

全球定位系統偽距的基礎
Basics of GPS Pseudo Range

 

全球定位系統偽距測量和全球定位系統基本原理. 這堂課利用MATLAB® 代碼GPSSim.mxcor.m
GPS Pseudo-range Measurements and Basic Principals of GPS. We also use the MATLAB® code GPSSim.m and xcor.m in this class (英PDF)

17

全球定位系統測量的幾何學及精度
Geometry of GPS Measurements and Accuracy

 

全球定位系統訊號跟蹤,軌道幾何學,具體訊號結構,相位測量和數據
GPS Signal Tracking, Orbit Geometry, Specific Signal Structure, Phase Measurements and Data (英PDF)

18

全球定位系統載波相位測量法
GPS Carrier Phase Measurements

 

GPS偽距和相位測量,基本處理方法,精度測量的影響因素
GPS Pseudo Range and Phase Measurements, Basic Processing Methods, Dilution of Precision Measures (英PDF)

 

作業4 (英PDF)

19

中性大氣傳播
Neutral Atmosphere Propagation

 

溫習作業4. 大氣延遲效應
Review HW 4. Atmosphere Delay Effects (英PDF)

20

色散傳播延遲
Dispersive Propagation Delays

 

電離層和散射性全球定位系統延遲糾正(雙頻電離層延時糾正)

Ionosphere and Dispersive GPS Delay Correction (Dual Frequency Ionospheric Delay Corrections) (英PDF)

21

非正式問答課
Informal Question and Answer Session

 

 

22

衛星的運動
Satellite Motions

 

衛星軌道描述和軌道訊息來源
Satellite Orbit Representation and Sources of Information about Orbits (英PDF)

23

手提全球定位系統接收器基礎
Basics of Hand Held GPS

 

手提全球定位系統接收器的基本知識
Basics of Hand Held GPS Receivers (英PDF)

24

全球定位系統課外實習
GPS Outside the Classroom

 

 

25

不同領域中全球定位系統的實用方面及其應用
Practical Aspects of GPS and Applications of GPS in Different Fields

 

全球定位系統應用
Applications of GPS (英PDF)

 

12.215 Modern Navigation, Fall 2002


A minimum of 24 GPS satellites orbit the Earth at an altitude of approximately 11,000 miles providing users with accurate information on position, velocity, and time anywhere in the world and in all weather conditions. (Image courtesy of FAA.)

課程重點

This course includes detailed lecture notes and assignments.

課程描述

The development of the Global Positioning System (GPS) started in the 1960s, and the system became operational in 1992. The system has seen many diverse applications develop in the last few years with the accuracy of positioning ranging from 100 meters (the civilian restricted accuracy requirement) to 1 millimeter (without the need for a security clearance!) In this course we will apply many of basic principles of science and mathematics learnt at MIT to explore the applications and principles of GPS. We also use GPS and other equipment in the class (and outside on Campus) to demonstrate the uses of this system.

Technical Requirements

Any number of development tools can be used to compile and run the .f files found on this course site. Please refer to the course materials for any specific instructions or recommendations.
MATLAB® software is required to run the .m files found on this course site.

教學大綱

 Topics to be Covered in the Course

1. Coordinate systems on a deformable, non-spherical Earth. Address concepts of latitude and longitude as determined by the direction of gravity (astronomical latitude and longitude) and determined by the normal to an ellipsoidal shape (geodetic latitude and longitude). Relationships between coordinates; concepts of polar motion and changes in the rotation rate of the Earth; rotations and translations between coordinate systems. Effects that need to be considered for different accuracy results and the accuracies that are achievable with GPS.

2. Principles of Navigation. Dead-reckoning, true and magnetic bearings; use of celestial bodies, use of secants for position fixes. Introduction common map projections; uses of different map projections. Vector approach to spherical trigonometry.

3. Principles of GPS. Pseudorange and phase measurements. Spread spectrum signal structure; basic concepts of signal analysis. Contributions of pseudorange and phase (geometric positions, clock errors, propagation medium, cycles ambiguity for phase). Simple atmospheric and ionospheric delay models; use of dispersive properties of plasmas (ionosphere). Use of differencing techniques in the analysis of GPS data. Security systems on GPS satellites (selective availability and anti-spoofing) and their effects on navigation and precise positioning.

4. Estimation procedures; Stochastic and mathematical models; statistical descriptions of dynamic systems; propagation of covariance matrices least-squares estimation.

5. Examples of aircraft navigation using GPS (comparison with laser profiling); examination of real data to assess the limits of accuracy obtainable with GPS; applications in a variety of areas including precision farming; and intelligent vehicle navigation systems.

We will have some lab sessions during the course and there will be homework once every few weeks. There will be an open book final exam. Grading will be from the homework (60%), final exam (30%) and class participation (10%).

It will be acceptable in this course to work together on homework with the aim of better understanding the material and to refer to other books and published material provided that these additional materials are cited appropriately in the homework. Each student should complete the homework separately. It is not acceptable to simply copy the homework of another student

Texts

Hofmann-Wellenhof, B., H. Lichtenegger, and J. Collins. GPS Theory and Practice. New York: Springer-Verlag, Wein, 1992, pp. 326.

Strang, G., and K. Borre. Linear Algebra, Geodesy, and GPS. Wellesley, MA: Wellesley-Cambridge Press, 1997, pp. 526. (Home Page of Prof. Gilbert Strang)

教學時程

CLASS # 課程單元
1 Introduction
2 Latitude and Longitude Definition
3 Height Definition
4 Spherical Trigonometry
5 Motion of Sun/Earth and Astronomical Position Determination
6 Almanacs Paper and On-line
7 Dead Reckoning and Conventional Navigation
8 Use of Sextant and Measurements
9 Linear Algebra
10 Analysis of Sextant Results
11 Map Projections
12 Basic Statistics and Propagation of Variances
13 Least Squares Estimation
14 Correlations
15 Electronic Distance Measurement
16 Basics of GPS Pseudo Range
17 Geometry of GPS Measurements and Accuracy
18 GPS Carrier Phase Measurements
19 Neutral Atmosphere Propagation
20 Dispersive Propagation Delays
21 Informal Question and Answer Session
22 Satellite Motions
23 Basics of Hand Held GPS
24 GPS Outside the Classroom
25 Practical Aspects of GPS and Applications of GPS in Different Fields

課堂講稿

Any number of development tools can be used to compile and run the .f files in this section.
MATLAB® software is required to view and run the .m files in this section. 課 課程單元
1 Introduction and Coordinate Systems (PDF)
2 Definitions of the Types of Latitude and Longitude; Mathematical Relationship Between These and Cartesian XYZ; Motion of the Rotation Axis which Effects Determination of Latitude and Longitude (PDF)
3 Height Definitions, Methods for Determining Heights, Spirit Leveling and Trigonometric Leveling; Geoid Heights and their Determination (PDF)
4 Spherical Trigonometry. Derivations and Examples on How to Use (PDF)
5 Determination of Latitude and Longitude using Astronomical Methods (PDF)
6 Almanacs in both Paper and Electronic Forms (PDF)
7

Dead Reckoning and Sextants. The Following Web Sites are Used in the Notes. (PDF)
The Road to the Magnetic North Pole
Field Lines for a Magnetic Dipole
North Magnetic Pole
Coastal Piloting for Boat Crew and AuxNav
Presentations & Advanced Coastal Navigation Student Study Guide
Vernier

8 Sextant Measurements (PDF)
9 Review of Linear Algebra Covering Vectors and Matrices, Solving Linear Equations, Vector Spaces, Eigenvalues and Vectors, Rotation Matrices (PDF)
10 Examined HW 02 Solution and the Non-Linear Model that can be Used to Represent the Measurements Taken (PDF)
11 Map Projections of Different Types and the Mathematics Behind Some Projections (PDF)
Web Pages Used in Class:
Map Projection Overview
USGS - Science for a Changing World
Round Earth, Flat Maps
Map Projection
12 Statistics and Propagation of Variance-Covariance Matrices (PDF)
13 Estimation of Over-Determined, Nearly Linear Systems Including Least and Weighted Least Squares (PDF)
14 Finish Estimation with Sequential Estimation and Error Ellipses; Examine Correlations Between Random Time Series (The Time Series and Correlation Values Plotted in this Lecture were generated with cross.f) (PDF)
15 Electromagnetic Distance Measurement (EDM). Conventional Instruments and Theory of their Operation (PDF)
16 GPS Pseudo-range Measurements and Basic Principals of GPS. We also use the MATLAB® code GPSSim.m and xcor.m in this class (PDF)
17 GPS Signal Tracking, Orbit Geometry, Specific Signal Structure, Phase Measurements and Data (PDF)
18 GPS Pseudo Range and Phase Measurements, Basic Processing Methods, Dilution of Precision Measures (PDF)
19 Review HW 4. Atmosphere Delay Effects (PDF)
20 Ionosphere and Dispersive GPS Delay Correction (Dual Frequency Ionospheric Delay Corrections) (PDF)
  Informal class of Question and Answers. No lecture notes for this class
21 Satellite Orbit Representation and Sources of Information about Orbits (PDF)
22 Basics of Hand Held GPS Receivers (PDF)
  Class outside using GPS
23 Applications of GPS (PDF)

作業

作業 DUE
Homework 1 (PDF) Lec #6
Homework 2 (PDF)
*Data file (TXT)
Lec #10
Homework 3 (PDF) Lec #14
Homework 4 (PDF) Lec #18

*(Note: To copy the data file, display it in your browser and then select all the text and copy to a working document. A directly saved the data file may not look like a text file depending on the system you are using.)


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