Inertial navigation systems with geodetic applications

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Title:

Personal Author:

Jekeli, Christopher, 1953-

Publication Information:

Berlin : Walter de Gruyter, 2000

ISBN:

9783110159035

Subject Term:

Earth -- Figure -- Measurement

Inertial navigation -- Mathematics

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010080127	QB283 J44 2000	Open Access Book	Book	Searching... Unknown

This book covers all aspects of inertial navigation systems (INS), including the sensor technology and the estimation of instrument errors, as well as their integration with the Global Positioning System (GPS) for geodetic applications. Complete mathematical derivations are given. Both stabilized and strapdown mechanizations are treated in detail. Derived algorithms to process sensor data and a comprehensive explanation of the error dynamics provide not only an analytical understanding but also a practical implementation of the concepts. A self-contained description of GPS, with emphasis on kinematic applications, is one of the highlights in this book.

The text is of interestto geodesists, including surveyors, mappers, and photogrammetrists; to engineers in aviation, navigation, guidance, transportation, and robotics; and to scientists involved in aerogeophysics and remote sensing.

1 Coordinate Frames and Transformations	p. 1
1.1 Introduction	p. 1
1.2 Coordinate Frames	p. 3
1.2.1 Inertial Frame	p. 3
1.2.2 Earth-Centered-Earth-Fixed Frame	p. 6
1.2.3 Navigation Frame	p. 6
1.3 Transformations	p. 9
1.3.1 Direction Cosines	p. 10
1.3.2 Euler Angles	p. 11
1.3.3 Quaternions	p. 13
1.3.4 Axial Vectors	p. 18
1.3.5 Angular Rates	p. 19
1.4 Differential Equation of the Transformation	p. 20
1.5 Specific Coordinate Transformations	p. 22
1.6 Fourier Transforms	p. 27
2 Ordinary Differential Equations	p. 31
2.1 Introduction	p. 31
2.2 Linear Differential Equations	p. 32
2.3 General Solution of Linear Differential Equations	p. 33
2.3.1 Homogeneous Solution	p. 35
2.3.1.1 An Example	p. 38
2.3.1.2 Fundamental Set of Solutions	p. 39
2.3.2 Particular Solution	p. 40
2.3.2.1 The Example, Continued	p. 42
2.4 Numerical Methods	p. 44
2.4.1 Runge-Kutta Methods	p. 45
2.4.2 Numerical Integration of Functions	p. 50
3 Inertial Measurement Units	p. 51
3.1 Introduction	p. 51
3.2 Gyroscopes	p. 53
3.2.1 Mechanical Gyroscopes	p. 54
3.2.1.1 SDF Gyro	p. 56
3.2.1.1.1 Principal Error Terms	p. 63
3.2.1.2 TDF Gyro	p. 65
3.2.2 Optical Gyroscopes	p. 70
3.2.2.1 Ring Laser Gyro	p. 73
3.2.2.1.1 RLG Error Sources	p. 77
3.2.2.2 Fiber-Optic Gyro	p. 81
3.2.2.2.1 FOG Error Sources	p. 85
3.3 Accelerometer	p. 86
3.3.1 Accelerations in Non-Intertial Frames	p. 89
3.3.2 Force-Rebalance Dynamics	p. 90
3.3.3 Pendulous Accelerometer Examples	p. 93
3.3.4 Vibrating Element Dynamics	p. 96
3.3.5 Error Sources	p. 99
4 Intertial Navigation System	p. 101
4.1 Introduction	p. 101
4.2 Mechanizations	p. 104
4.2.1 Space-Stabilized Mechanization	p. 106
4.2.2 Local-Level Mechanization	p. 106
4.2.2.1 Schuler Tuning	p. 107
4.2.2.2 Wander Azimuth Mechanization	p. 110
4.2.3 Strapdown Mechanization	p. 112
4.2.3.1 Numerical Determination of the Transformation Matrix	p. 114
4.2.3.1.1 A Second-Order Algorithm	p. 115
4.2.4.1.2 A Third-Order Algorithm	p. 118
4.2.3.2 Specializations	p. 122
4.3 Navigation Equations	p. 123
4.3.1 Unified Approach	p. 124
4.3.2 Navigation Equations in i-Frame	p. 126
4.3.3 Navigation Equations in e-Frame	p. 126
4.3.4 Navigation Equations in n-Frame	p. 126
4.3.5 Navigation Equations in w-Frame	p. 131
4.3.6 Numerical Integration of Navigation Equations	p. 134
5 System Error Dynamics	p. 139
5.1 Introduction	p. 139
5.2 Simplified Analysis	p. 140
5.3 Linearized Error Equations	p. 147
5.3.1 Error Dynamics Equations in i-Frame	p. 151
5.3.2 Error Dynamics Equations in e-Frame	p. 152
5.3.3 Error Dynamics Equations in n-Frame	p. 153
5.4 Approximate Analysis	p. 157
5.4.1 Effects of Accelerometer and Gyro Errors	p. 159
5.4.2 Vertical Velocity and Position Error Effects	p. 161
5.4.3 Essential Error Modes	p. 162
6 Stochastic Processes and Error Models	p. 165
6.1 Introduction	p. 165
6.2 Probability Theory	p. 165
6.2.1 Gaussian Distribution	p. 170
6.3 Stochastic Processes	p. 172
6.3.1 Covariance Functions	p. 173
6.3.2 Power Spectral density	p. 175
6.3.3 Ergodic Processes	p. 176
6.4 White Noise	p. 177
6.5 Stochastic Error Models	p. 179
6.5.1 Random Constant	p. 180
6.5.2 Random Walk	p. 181
6.5.3 Gauss-Markov Model	p. 182
6.6 Gravity Models	p. 186
6.6.1 Normal Gravity Field	p. 186
6.6.2 Deterministic Gravity Models	p. 190
6.6.3 Stochastic Gravity Models	p. 192
6.7 Examples of IMU Error Processes	p. 195
7 Linear Estimation	p. 197
7.1 Introduction	p. 197
7.2 Bayesian Estimation	p. 199
7.2.1 Optimal Estimation Criteria	p. 200
7.2.2 Estimation with Observations	p. 202
7.2.2.1 A Posteriori Density Function	p. 203
7.2.2.2 A Posteriori Estimate and Covariance	p. 205
7.3 Discrete Kalman Filter	p. 207
7.3.1 Observation Model	p. 209
7.3.2 Optimal State Vector Estimation	p. 210
7.3.2.1 Prediction	p. 212
7.3.2.2 Filtering	p. 213
7.3.2.3 Smoothing	p. 215
7.4 Discrete Linear Dynamics Model	p. 220
7.5 Modifications	p. 223
7.5.1 Augmented State Vector	p. 223
7.5.2 Closed-Loop Estimation	p. 225
7.6 A Simple Example	p. 227
7.7 Continuous Kalman Filter	p. 230
7.7.1 Covariance Function	p. 233
7.7.2 Solution to Matrix Ricatti Equation	p. 235
7.7.2.1 Constant Coefficient Matrices	p. 235
7.7.2.2 No System Process Noise	p. 236
7.7.2.3 No Observations	p. 237
8 INS Initialization and Alignment	p. 238
8.1 Introduction	p. 238
8.2 Coarse Alignment	p. 240
8.3 Fine Alignment and Calibration	p. 243
8.3.1 Acceleration Observations	p. 244
8.3.2 Velocity and Azimuth Observations	p. 246
8.3.3 Kinematic Alignment	p. 252
9 The Global Positioning System (GPS)	p. 255
9.1 Introduction	p. 255
9.2 Global Positioning System	p. 259
9.2.1 Clocks and Time	p. 259
9.2.2 GPS Signals	p. 261
9.2.3 GPS Receiver	p. 263
9.3 GPS Observables	p. 266
9.4 GPS Errors	p. 269
9.5 Combinations of Observations	p. 273
9.5.1 Dual-Frequency Pseudorange and Phase	p. 275
9.5.2 Single and Double Differences	p. 278
9.6 Kinematic Positioning	p. 282
9.6.1 Dynamics Model	p. 284
9.6.2 Observation Equations	p. 287
9.6.3 Single-Receiver Case	p. 288
9.6.4 Multiple-Receiver Case	p. 292
10 Geodetic Application	p. 295
10.1 Introduction	p. 295
10.2 Inertial Survey System	p. 297
10.2.1 Historical Developments	p. 297
10.2.2 Estimation Methods	p. 300
10.2.2.1 Models and Observations	p. 300
10.2.2.2 Parameter Estimation	p. 302
10.2.3 Final Adjustments	p. 303
10.2.4 Typical Results	p. 305
10.3 GPS/INS Integration	p. 306
10.3.1 Integration Modes	p. 308
10.3.1.1 Decentralized Integration	p. 310
10.3.1.2 Centralized Integration	p. 314
10.3.2 Cycle Ambiguity Determination	p. 318
10.4 Moving-Base Gravimetry	p. 320
10.4.1 Gravitation from Inertial Positioning	p. 323
10.4.2 Gravitation from Accelerometry	p. 327
10.4.2.1 Kalman Filter Approaches	p. 330
10.4.2.2 Scalar Gravimetry	p. 334
References	p. 336
Index	p. 343

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