An updated guide to GNSS, and INS, and solutions to real-worldGNSS/INS problems with Kalman filtering Written by recognized authorities in the field, this thirdedition of a landmark work provides engineers, computer scientists,and others with a working familiarity of the theory andcontemporary applications of Global Navigation Satellite Systems(GNSS), Inertial Navigational Systems, and Kalman filters.Throughout, the focus is on solving real-world problems, with anemphasis on the effective use of state-of-the-art integrationtechniques for those systems, especially the application of Kalmanfiltering. To that end, the authors explore the various subtleties,common failures, and inherent limitations of the theory as itapplies to real-world situations, and provide numerous detailedapplication examples and practice problems, including GNSS-aidedINS (tightly and loosely coupled), modeling of gyros andaccelerometers, and SBAS and GBAS. Drawing upon their many years of experience with GNSS, INS, andthe Kalman filter, the authors present numerous design andimplementation techniques not found in other professionalreferences. The Third Edition includes: * Updates on the upgrades in existing GNSS and other systemscurrently under development * Expanded coverage of basic principles of antenna design andpractical antenna design solutions * Expanded coverage of basic principles of receiver design and anupdate of the foundations for code and carrier acquisition andtracking within a GNSS receiver * Expanded coverage of inertial navigation, its history, itstechnology, and the mathematical models and methods used in itsimplementation * Derivations of dynamic models for the propagation of inertialnavigation errors, including the effects of drifting sensorcompensation parameters * Greatly expanded coverage of GNSS/INS integration, includingderivation of a unified GNSS/INS integration model, itsMATLAB® implementations, and performance evaluation undersimulated dynamic conditions The companion website includes updated background material;additional MATLAB scripts for simulating GNSS-only and integratedGNSS/INS navigation; satellite position determination; calculationof ionosphere delays; and dilution of precision.
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ACRONYMS AND ABBREVIATIONS
1.2 GNSS OVERVIEW
1.3 INERTIAL NAVIGATION OVERVIEW
1.4 GNSS/INS INTEGRATION OVERVIEW
2 FUNDAMENTALS OF SATELLITE NAVIGATION SYSTEMS
2.1 NAVIGATION SYSTEMS CONSIDERED
2.2 SATELLITE NAVIGATION
2.3 TIME AND GPS
2.4 EXAMPLE: USER POSITION CALCULATIONS WITH NO ERRORS
3 FUNDAMENTALS OF INERTIAL NAVIGATION
3.1 CHAPTER FOCUS
3.2 BASIC TERMINOLOGY
3.3 INERTIAL SENSOR ERROR MODELS
3.4 SENSOR CALIBRATION AND COMPENSATION
3.5 EARTH MODELS
3.6 HARDWARE IMPLEMENTATIONS
3.7 SOFTWARE IMPLEMENTATIONS
3.8 INS PERFORMANCE STANDARDS
3.9 TESTING AND EVALUATION
4 GNSS SIGNAL STRUCTURE, CHARACTERISTICS, AND INFORMATION UTILIZATION
4.1 LEGACY GPS SIGNAL COMPONENTS, PURPOSES, AND PROPERTIES
4.2 MODERNIZATION OF GPS
4.3 GLONASS SIGNAL STRUCTURE AND CHARACTERISTICS
5 GNSS ANTENNA DESIGN AND ANALYSIS
5.2 GNSS ANTENNA PERFORMANCE CHARACTERISTICS
5.3 COMPUTATIONAL ELECTROMAGNETIC MODELS (CEMS) FOR GNSS ANTENNA DESIGN
5.4 GNSS ANTENNA TECHNOLOGIES
5.5 PRINCIPLES OF ADAPTABLE PHASED-ARRAY ANTENNAS
5.6 APPLICATION CALIBRATION/COMPENSATION CONSIDERATIONS
6 GNSS RECEIVER DESIGN AND ANALYSIS
6.1 RECEIVER DESIGN CHOICES
6.2 RECEIVER ARCHITECTURE
6.3 SIGNAL ACQUISITION AND TRACKING
6.4 EXTRACTION OF INFORMATION FOR USER SOLUTION
6.5 THEORETICAL CONSIDERATIONS IN PSEUDORANGE, CARRIER PHASE, AND FREQUENCY ESTIMATIONS
6.6 HIGH-SENSITIVITY A-GPS SYSTEMS
6.7 SOFTWARE-DEFINED RADIO (SDR) APPROACH
6.8 PSEUDOLITE CONSIDERATIONS
7 GNSS DATA ERRORS
7.1 DATA ERRORS
7.2 IONOSPHERIC PROPAGATION ERRORS
7.3 TROPOSPHERIC PROPAGATION ERRORS
7.4 THE MULTIPATH PROBLEM
7.5 METHODS OF MULTIPATH MITIGATION
7.6 THEORETICAL LIMITS FOR MULTIPATH MITIGATION
7.7 EPHEMERIS DATA ERRORS
7.8 ONBOARD CLOCK ERRORS
7.9 RECEIVER CLOCK ERRORS
7.10 SA ERRORS
7.11 ERROR BUDGETS
8 DIFFERENTIAL GNSS
8.2 DESCRIPTIONS OF LOCAL-AREA DIFFERENTIAL GNSS (LADGNSS), WIDE-AREA DIFFERENTIAL GNSS (WADGNSS), AND SPACE-BASED AUGMENTATION SYSTEM (SBAS)
8.3 GEO WITH L1L5 SIGNALS
8.4 GUS CLOCK STEERING ALGORITHM
8.5 GEO ORBIT DETERMINATION (OD)
8.6 GROUND-BASED AUGMENTATION SYSTEM (GBAS)
8.7 MEASUREMENT/RELATIVE-BASED DGNSS
8.8 GNSS PRECISE POINT POSITIONING SERVICES AND PRODUCTS
9 GNSS AND GEO SIGNAL INTEGRITY
9.2 SBAS AND GBAS INTEGRITY DESIGN
9.3 SBAS EXAMPLE
9.5 FUTURE: GIC
10 KALMAN FILTERING
10.2 KALMAN FILTER CORRECTION UPDATE
10.3 KALMAN FILTER PREDICTION UPDATE
10.4 SUMMARY OF KALMAN FILTER EQUATIONS
10.5 ACCOMMODATING TIME-CORRELATED NOISE
10.6 NONLINEAR AND ADAPTIVE IMPLEMENTATIONS
10.7 KALMAN–BUCY FILTER
10.8 HOST VEHICLE TRACKING FILTERS FOR GNSS
10.9 ALTERNATIVE IMPLEMENTATIONS
11 INERTIAL NAVIGATION ERROR ANALYSIS
11.1 CHAPTER FOCUS
11.2 ERRORS IN THE NAVIGATION SOLUTION
11.3 NAVIGATION ERROR DYNAMICS
11.4 INERTIAL SENSOR NOISE
11.5 SENSOR COMPENSATION ERRORS
11.6 SOFTWARE SOURCES
12 GNSS/INS INTEGRATION
12.1 CHAPTER FOCUS
12.2 GNSS/INS INTEGRATION OVERVIEW
12.3 UNIFIED MODEL FOR GNSS/INS INTEGRATION
12.4 PERFORMANCE ANALYSIS
12.5 OTHER INTEGRATION ISSUES
APPENDIX A: SOFTWARE
A.1 SOFTWARE SOURCES
A.2 SOFTWARE FOR CHAPTER 3
A.3 SOFTWARE FOR CHAPTER 4
A.4 SOFTWARE FOR CHAPTER 7
A.5 SOFTWARE FOR CHAPTER 10
A.6 SOFTWARE FOR CHAPTER 11
A.7 SOFTWARE FOR CHAPTER 12
A.8 ALMANAC/EPHEMERIS DATA SOURCES
APPENDIX B: COORDINATE SYSTEMS AND TRANSFORMATIONS
B.1 COORDINATE TRANSFORMATION MATRICES
B.2 INERTIAL REFERENCE DIRECTIONS
B.3 APPLICATION-DEPENDENT COORDINATE SYSTEMS
B.4 COORDINATE TRANSFORMATION MODELS
B.5 NEWTONIAN MECHANICS IN ROTATING COORDINATES
End User License Agreement
Table of Contents
U.S. Ground-Launched Missile Projects Begun in 1946
A Sampling of Inertial Sensor Types
2 FUNDAMENTALS OF SATELLITE NAVIGATION SYSTEMS
Example with Four Satellites
3 FUNDAMENTALS OF INERTIAL NAVIGATION
Performance Grades for Gyroscopes
INS and Inertial Sensor Performance Ranges
4 GNSS SIGNAL STRUCTURE, CHARACTERISTICS, AND INFORMATION UTILIZATION
Components of Ephemeris Data
Algorithm for Computing Satellite Position
Key Galileo Signals and Parameters
Key QZSS Signals and Parameters
7 GNSS DATA ERRORS
Representative Kalman Filter Parameter Values
8 DIFFERENTIAL GNSS
Worldwide SBAS System Coverage
Code-Carrier Coherence Results
Cases Used in Geometry-per-Station Analysis
9 GNSS AND GEO SIGNAL INTEGRITY
List of SBAS Error Sources
10 KALMAN FILTERING
Essential Kalman Filter Equations
Linearized Kalman Filter Equations
Extended Kalman Filter Equations
Kalman–Bucy Filter Equations
Vehicle Dynamic Models for GNSS Receivers
Filter Models for Unknown Vehicle Dynamics
Statistical Parameters of Host Vehicle Dynamics
Comparison of Alternative GNSS Filters on 1.5-km Figure-8 Track Simulation
Summary Implementation of Schmidt–Kalman Filter
Implementation Equations for Serial Measurement Update
Compatible Methods for Solving the Riccati Equation
11 INERTIAL NAVIGATION ERROR ANALYSIS
List of Symbols and Approximations
State Variables for the Nine Core INS Errors
Dynamic Coefficient Submatrix Sources
Equation References for Dynamic Coefficient Submatrices
APPENDIX B: COORDINATE SYSTEMS AND TRANSFORMATIONS
Multiplication of Quaternion Basis Matrices
MOHINDER S. GREWAL
ANGUS P. ANDREWS
CHRIS G. BARTONE
Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved
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Published simultaneously in Canada
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Library of Congress Cataloging-in-Publication Data:
Grewal, Mohinder S.
Global navigation satellite systems, inertial navigation, and integration / Mohinder S. Grewal, Angus P. Andrews, Chris G. Bartone. – Third edition.
Originally published under title: Global positioning systems, inertial navigation, and integration.
ISBN 978-1-118-44700-0 (cloth);
1. Global Positioning System. 2. Inertial navigation. 3. Kalman filtering. I. Andrews, Angus P. II. Bartone, Chris G. III. Title.
M.S.G. dedicates this book to the memory of his parents, Livlin Kaur and Sardar Sahib Sardar Karam Singh Grewal.
A.P.A. dedicates his contributions to his wife, Jeri, without whom it never would have happened.
C.G.B dedicates this work to his wife, Shirley, and two sons, Christopher and Stephen, for their never-ending support over the years.
This book is intended for people who need a working knowledge of global navigation satellite systems (GNSSs), inertial navigation systems (INSs), and the Kalman filtering models and methods used in their integration. The book is designed to provide a usable, working familiarity with both the theoretical and practical aspects of these subjects. For that purpose, we include “real-world” problems from practice as illustrative examples. We also cover the more practical aspects of implementation: how to represent problems in a mathematical model, analyze performance as a function of model parameters, implement the mechanization equations in numerically stable algorithms, assess the computational requirements, test the validity of results, and monitor performance in operation with sensor data from GNSS (GPS) and INS. These important attributes, often overlooked in theoretical treatments, are essential for effective application of theory to real-world problems.
The accompanying companion website (www.wiley.com/go/globalnavigation) contains MATLAB® m-files to demonstrate the workings of the navigation solutions involved. It includes Kalman filter algorithms with GNSS and INS data sets so that the reader can better discover how the Kalman filter works by observing it in action with GNSS and INS. The implementation of GNSS, INS, and Kalman filtering on computers also illuminates some of the practical considerations of finite-word-length arithmetic and the need for alternative algorithms to preserve the accuracy of the results. If the student wishes to apply what she or he learns, then it is essential that she or he experience its workings and failings—and learn to recognize the difference.
The book is organized for use as a text for an introductory course in GNSS technology at the senior level or as a first-year graduate-level course in GNSS, INS, and Kalman filtering theory and applications. It could also be used for self-instruction or review by practicing engineers and scientists in these fields.
This third edition includes advances in GNSS/INS technology since the second edition in 2007, as well as many improvements suggested by reviewers and readers of the second edition. Changes in this third edition include the following:
Updates on the upgrades in existing GNSS systems and on other systems currently under development
Expanded coverage of basic principles of antenna design and practical antenna design solutions
Expanded coverage of basic principles of receiver design, and an update of the foundations for code and carrier acquisition and tracking within a GNSS receiver
Expanded coverage of inertial navigation, its history, its technology, and the mathematical models and methods used in its implementation
Derivations of dynamic models for the propagation of inertial navigation errors, including the effects of drifting sensor compensation parameters
Greatly expanded coverage of GNSS/INS integration, including derivation of a unified GNSS/INS integration model, its MATLAB implementations, and performance evaluation under simulated dynamic conditions
The accompanying website has also been augmented to include updated background material and additional MATLAB scripts for simulating GNSS-only and integrated GNSS/INS navigation. These routines include satellite position determination, calculation of ionospheric delays, and dilution of precision.
Chapter 1 provides an overview of navigation, in general, and GNSS and inertial navigation, in particular. These overviews include fairly detailed descriptions of their respective histories, technologies, different implementation strategies, and applications.
Chapter 2 covers the fundamental attributes of satellite navigation systems, in general, and the technologies involved, how the navigation solution is implemented, and how satellite geometries influence errors in the solution.
Chapter 3 covers the fundamentals of inertial navigation, starting with its nomenclature and continuing through to practical implementation methods, error sources, performance attributes, and development strategies.
Chapters 4–9 cover basic theory of GNSS for a senior-level class in geomatics, electrical engineering, systems engineering, and computer science. Subjects covered in detail include basic GNSS satellite signal structures, practical receiver antenna designs, receiver implementation structures, error sources, signal processing methods for eliminating or reducing recognized error sources, and system augmentation methods for improving system integrity and security.
Chapter 10 covers the fundamental aspects of Kalman filtering essential for GNSS/INS integration: its mathematical foundations and basic implementation methods, and its application to sensor integration in general and to GNSS navigation in particular. It also covers how the implementation includes its own performance evaluation and how this can be used in the predictive design of sensor systems.
Chapter 11 covers the basic errors sources and models for inertial navigation, including the effects of sensor noise and errors due to drifting inertial sensor error characteristics, how the resulting navigation errors evolve over time, and the resulting models that enable INS integration with other sensor systems.
Chapter 12 covers the essential mathematical foundations for GNSS/INS integration, including a unified navigation model, its implementation in MATLAB, evaluations of the resulting unified system performance under simulated dynamic conditions, and demonstration of the navigation performance improvement attainable through integrated navigation.
Appendix A contains brief descriptions of the MATLAB software on the CD-ROM, including formulas implementing the models developed in the different chapters and used for demonstrating how they work. Appendix B contains background material on coordinate systems and transformations implemented in the software, including derivations of the rotational dynamics used in navigation error modeling and GNSS/INS integration.
For instructors that wish to cover the fundamental aspects of GNSS, Chapters 1, 2, and 4–9 are recommended. Instructors of courses covering the fundamental concepts of inertial navigation can cover Chapters 1, 3, 10, and 11. A more advanced course in GNSS and INS integration should include Chapter 12, as well as significant utilization of the software routines provided for computer-based GNSS/INS integration projects.
MOHINDER S. GREWAL, PH.D., P.E.California State University at Fullerton
ANGUS P. ANDREWS, PH.D.Rockwell Science Center (retired)Thousand Oaks, California
CHRIS G. BARTONE, PH.D., P.E.Ohio University, Athens, Ohio
We acknowledge Professors John Angus of Claremont Graduate University, Jay A. Farrell of the University of California, Riverside, and Richard B. Langley of the University of New Brunswick for assistance and inspiration on the outline of this edition. We acknowledge the assistance of Mrs. Laura A. Cheung of the Raytheon Company for her expert assistance in reviewing Chapter 8 (“Differential GNSS”) and with the MATLAB® programs. Special thanks go to Dr. Larry Weill of California State University, Fullerton, for his contribution to Chapter 7 on multipath mitigation algorithms.
A. P. A. thanks Andrey Podkorytov at the Moscow Aviation Institute for corrections to the Schmidt–Kalman filter, Randall Corey from Northrop Grumman, and Michael Ash from C. S. Draper Laboratory for access to the developing Draft IEEE Standard for Inertial Sensor Technology; Dr. Michael Braasch at GPSoft, Inc. for providing evaluation copies of the GPSoft INS and GPS MATLAB® Toolboxes; Drs. Jeff Schmidt and Robert F. Nease, former Vice President of Engineering and Chief Scientist at Autonetics, respectively, for information on the early history of inertial navigation; Edward H. Martin for information on the very early history of GPS/INS integration; and Mrs Helen Boltinghouse for access to the personal memoirs of her late husband, Joseph C. Boltinghouse.
C. G. B. would like to thank Ohio University and many of its fine faculty, staff, and students with whom he has had the pleasure to interact in his research and teaching over the years. Such a rich environment has enabled him to develop a wide variety of classes and research efforts that these writings draw upon. Thanks also goes to Pat Fenton and Samantha Poon from NovAtel, Dave Brooks from Sensor Systems, James Horne from Roke, and Herbert Blaser from u-blox for providing antenna information.
3rd Generation Partnership Project
Accumulated delta range
Automatic dependent surveillance
Automatic gain control
Attitude and heading reference system
Akaike information-theoretic criterion
Advanced Inertial Reference Sphere
Atmospheric loss factor
Autonomous landing systemalt
Alternate binary offset carrier
Age of data word, ephemeris
Atlantic Ocean Region East (WAAS)
Atlantic Ocean Region West (WAAS)
Applied Physics Laboratory, Johns Hopkins University
Autoregressive moving average
Antenna reference point
Aeronautical radio navigation services
Amplitude spectral density
Application-specific integrated circuit
Application-Specific Qualification Facility (EGNOS)
Air traffic control
Band pass filter
bits per second
Binary offset carrier
Binary phase-shift keying
Coarse acquisition (channel or code)
Correction and verification (WAAS)
Code-division multiple access
Computational electromagnetic model
Circular error probable, or circle of equal probability
Code noise and multipath
Conterminous United States, also Continental United States
Continuously operating reference station
Acronym from transliterated Russian title “Cosmicheskaya Sistyema Poiska Avariynich Sudov,” meaning “Space System for the Search of Vessels in Distress”
Chips per second
Cyclic redundancy check
Controlled reception pattern antenna
Charles Stark Draper Laboratory
Digital differential analyzer
Distance measurement equipment
Department of Defense (United States)
Dilution of precision
Earth-centered, earth-fixed (coordinates)
Earth-centered inertial (coordinates)
European (also Geostationary) Navigation Overlay System
Effective isotropic radiated power
European Space Agency
Electrically Supported Gyro Navigator
EGNOS Wide-Area (communication) Network (EGNOS)
Federal Aviation Administration (United States)
Frequency division multiple access
Forward error correction
Finite impulse response
Final prediction error (Akaike’s)
Free-space loss factor
GPS & GEO Augmented Navigation (India)
Ground-based augmentation system
GEO Communication and Control Segment
Geometric dilution of precision
Geostationary earth orbit
GPS Earth Station COMSAT
GNSS Integrity Channel
Galileo In-Orbit Validation Element
GPS Infrared Positioning System
Geographic Information System(s)
Grid ionosphere vertical error
Global Orbiting Navigation Satellite System
Global navigation satellite system
Global Positioning System
GEO uplink subsystem
GEO uplink subsystem type 1
Horizontal dilution of precision
Highly-inclined elliptical orbit
Hazardously misleading information
High precision navigation signal (i.e., for GLONASS)
Hemispheric resonator gyroscope
International Civil Aviation Organization
Ionospheric correction computation
Interface control document
Independent Data Verification (of WAAS)
Interferometric fiber-optic gyroscope
Inclined geosynchronous orbit
Ionospheric grid point (for WAAS)
International GNSS Service
Instrument landing system
Inertial measurement unit
International Mobile (originally “Maritime”) Satellite Organization
Inertial navigation system
Issue of data
Issue of data clock
Issue of data ephemeris
Inertial reference unit
Inertial sensor assembly
International Terrestrial Reference Frame
International Telecommunications Union
Joint precision approach and landing system
Joint Tactical Information Distribution System
Klystron Power Amplifier
Local-Area Augmentation System
Local-area differential GPS
Least-squares ambiguity decorrelation adjustment
Lunar Excursion Module
Left-hand circularly polarized
Local Information Network Communication System
Land Information Systems
Line of sight
Lateral positioning with vertical guidance
Least significant bit
Local tangent plane
Mission/Master Control Center (EGNOS)
million chips per second
Multipath-estimating delay-lock loop
Medium earth orbit
Mobile station (i.e., cell phone)
Maximum-likelihood estimation (or estimator)
Mueller Mechanical Integrating Accelerometer
Minimum mean-squared error (estimator)
Multipath mitigation technology
Minimum Operational Performance Standards
MTSAT Satellite-based Augmentation System (Japan)
Most significant bit
Multifunctional Transport Satellite (Japan)
Minimum variance distortionless response
Minimum-variance unbiased estimator
Momentum wheel gyroscope
National Airspace System
Navigation system with time and ranging
Numerically controlled oscillator
National Geodetic Survey (United States)
Navigation Land Earth Station(s) (EGNOS)
National Oceanic and Atmospheric Administration
National Spatial Reference System
National Satellite Test Bed
Orbit analysis simulation software
Old but active data
Online Positioning User Service (of NGS)
Open Service (of Galileo)
Performance Assessment and Checkout Facility (EGNOS)
portable document format
Predetection integration interval
Position dilution of precision
Proportional and integral (controller)
Process input data (of WAAS); proportional, integral, and differential (control)
Pendulous integrating gyroscopic accelerometer
Position Location and Reporting System (U.S. Army)
Pacific Ocean Region
Precise point positioning
Precise Positioning Service
Pulse per second
People’s Republic of China
Pseudorandom noise or pseudorandom number (=SVN for GPS)
Public Regulated service (of Galileo)
Power spectral density
Quadrature phase shift keying
Quasi-Zenith Satellite System
right ascension of ascending node
Receiver antenna gain (relative to isotropic)
Receiver autonomous integrity monitoring
Right-hand circularly polarized
Ranging and Integrity Monitoring Station(s) (EGNOS)
Receiver independent exchange format (for GPS data)
Ring laser gyroscope
Reliability, maintainability, availability
Root mean square; reference monitoring station
Radio navigation satellite service
Radio Technical Commission for Aeronautics
Radio Technical Commission for Maritime Service
Real-time operating system
Rotational vibratory coriolis gyroscope
Selective availability (also abbreviated “S/A”)
Submeter accuracy with integrity function (in QZSS)
Space adaptive processing
Synthetic Aperture Radar or Search and Rescue (Galileo service)
Standards and Recommended Practices (Japan)
Search and rescue satellite—aided tracking
Surface acoustic wave
Space-based augmentation system
Space-based infrared low earth orbit
Scripps coordinate update tool
Satellite Correction Processing (of WAAS)
Space-frequency adaptive processing
Specific force information receiver
Signal in space
Satellite Navigation Augmentation System (China)
Safety of Life Service (of Galileo)
Standard precision navigation signal (i.e., for GLONASS)
Standard Positioning Service
symbols per second
Ship Submersible Ballistic Nuclear (US)
Space–time adaptive processing
Signal Task Force (of Galileo)
State transition matrix
Space vehicle number (=PRN number for GPS)
Standing wave ratio
Terrestrial communications subsystem (for WAAS)
Temperature-compensated Xtat (crystal) oscillator
Time difference of arrival
Time dilution of precision
Total electron content
Total electron content units
Terrestrial Communication Network
Test Loop Translator
Time of arrival
Time of week
Time to alarm
Time to first fix
User differential range error
User-equivalent range error
User range error
United States Air Force
United States Navy
Universal Time, Coordinated (or Coordinated Universal Time)
Universal Transverse Mercator
Vertical alert limit
Vibratory Coriolis gyroscope
Vertical dilution of precision
Very high frequency (30–300 MHz)
VHF omnirange (radionavigation aid)
Velocity random walk
Wide-Area Augmentation System (United States)
Wide-area differential GPS
World Geodetic System
WAAS Message Processor
Wide-area master station
WAAS network time
Wide-area reference equipment
Wide-area reference station
Zero-Lock Gyroscope (“Zero Lock Gyro” and “ZLG” are trademarks of Northrop Grumman Corp.)
A book on navigation? Fine reading for a child of six!1
During the European Age of Discovery, in the fifteenth to seventeenth centuries, the word navigation was synthesized from the Latin noun navis (ship) and the Latin verb stem agare (to do, drive, or lead) to designate the operation of a ship on a voyage from A to B—or the art thereof.
In this context, the word art is used in the sense of a skill, craft, method, or practice. The Greek word for it is τεχνυ, with which the Greek suffix -λγια (the study thereof) gives us the word technology.
In current engineering usage, the art of getting from A to B is commonly divided into three interrelated technologies:
refers to the art of determining the current location of an object—usually a vehicle of some sort, which could be in space, in the air, on land, on or under the surface of a body of water, or underground. It could also be a comet, a projectile, a drill bit, or anything else we would like to locate and track. In modern usage,
may refer to the object’s current and intended dynamic
, which can also include its velocity, attitude, or attitude rate relative to other objects. The practical implementation of navigation generally requires observations, measurements, or sensors to measure relevant variables, and methods of estimating the state of the object from the measured values.
refers to the art of determining a suitable trajectory for getting the object to a desired
, which may include position, velocity, attitude, or attitude rate. What would be considered a “suitable” trajectory may involve such factors as cost, consumables and/or time required, risks involved, or constraints imposed by existing transportation corridors and geopolitical boundaries.
refers to the art of determining what actions (e.g., applied forces or torques) may be required for getting the object to follow the desired trajectory.
These distinctions can become blurred—especially in applications when they share hardware and software. This has happened in missile guidance , where the focus is on getting to B, which may be implemented without requiring the intermediate locations. The distinctions are clearer in what is called “Global Positioning System (GPS) navigation” for highway vehicles, where
is implemented by the GPS receiver, which gives the user an estimate of the current location (
) of the vehicle.
is implemented as
, which finds a route (trajectory) from
to the intended destination
, using the connecting road system and applying user-specified measures of route suitability (e.g., travel distance or total time).
is implemented as a sequence of requested driver actions to follow the planned route.
From time immemorial, we have had to solve the problem of getting from A to B, and many solution methods have evolved. Solutions are commonly grouped into five basic navigation modes, listed here in their approximate chronological order of discovery:
essentially relies on recognizing your surroundings to know where you are (
) and how you are oriented relative to where you want to be (
). It is older than human kind.
uses relevant angles between local vertical and celestial objects (e.g., the sun, planets, moons, stars) with known directions to estimate orientation, and possibly location on the surface of the earth. Some birds have been using celestial navigation in some form for millions of years. Because the earth and these celestial objects are moving with respect to one another, accurate celestial navigation requires some method for estimating time. By the early eighteenth century, it was recognized that estimating longitude with comparable accuracy to that of latitude (around half a degree at that time) would require clocks accurate to a few minutes over long sea voyages. The requisite clock technology was not developed until the middle of the eighteenth century, by John Harrison (1693–1776). The development of atomic clocks in the twentieth century would also play a major role in the development of satellite-based navigation.
relies on knowing where you started from, plus some form of heading information and some estimate of speed and elapsed time to determine the distance traveled. Heading may be determined from celestial observations or by using a magnetic compass. Dead reckoning is generally implemented by plotting lines connecting successive locations on a chart, a practice at least as old as the works of Claudius Ptolemy (∼85–168 AD).
relies on radio-frequency sources with known locations, suitable receiver technologies, signal structure at the transmitter, and signal availability at the receiver. Radio navigation technology using land-fixed transmitters has been evolving for nearly a century. Radio navigation technologies using satellites began soon after the first artificial satellite was launched by the former Soviet Union in 1957, but the first global positioning system (GPS) was not declared operational until 1993. Early radio navigation systems relied on electronics technologies, and global navigational satellite system (GNSS) also relies on computer technology and highly accurate clocks. Due to the extremely high speed of electromagnetic propagation and the relative speeds of satellites in orbit, GNSS navigation also requires very precise and accurate timing. It could be considered to be a celestial navigation system using artificial satellites as the celestial objects, with observations using radio navigation aids and high-accuracy clocks.
is much like an automated form of dead reckoning. It relies on knowing your initial position, velocity, and attitude, and thereafter measuring and integrating your accelerations and attitude rates to maintain an estimate of velocity, position, and attitude. Because it is self-contained and does not rely on external sources, it has the potential for secure and stealthy navigation in military applications. However, the sensor accuracy requirements for these applications can be extremely demanding . Adequate sensor technologies were not developed until the middle of the twentieth century, and early systems tended to be rather expensive.
These modes of navigation can be used in combination, as well. The subject of this book is a combination of the last two modes of navigation: GNSS as a form of radio navigation, combined with inertial navigation. The key integration technology is Kalman filtering, which also played a major role in the development of both navigation modes.
The pace of technological innovation in navigation has been accelerating for decades. Over the last few decades, navigation accuracies improved dramatically and user costs have fallen by orders of magnitude. As a consequence, the number of marketable applications has been growing phenomenally. From the standpoint of navigation technology, we are living in interesting times.
There are currently four GNSSs operating or being developed. This section gives an overview; a more detailed discussion is given in Chapter 4.
The GPS is part of a satellite-based navigation system developed by the U.S. Department of Defense under its NAVSTAR satellite program [9, 11, 12, 14–18, 28–31].
The fully operational GPS includes 31 or more active satellites approximately uniformly dispersed around six circular orbits with four or more satellites each. The orbits are inclined at an angle of 55° relative to the equator and are separated from each other by multiples of 60° right ascension. The orbits are nongeostationary and approximately circular, with radii of 26,560 km and orbital periods of one-half sidereal day (≈11.967 h). Theoretically, three or more GPS satellites will always be visible from most points on the earth’s surface, and four or more GPS satellites can be used to determine an observer’s position anywhere on the earth’s surface 24 h/day.
Each GPS satellite carries a cesium and/or rubidium atomic clock to provide timing information for the signals transmitted by the satellites. Internal clock correction is provided for each satellite clock. Each GPS satellite transmits two spread spectrum, L-band carrier signals on two of the legacy L-band frequencies—an L1 signal with carrier frequency f1 = 1575.42 MHz and an L2 signal with carrier frequency f2 = 1227.6 MHz. These two frequencies are integral multiples f1 = 1540f0 and f2 = 1200f0 of a base frequency f0 = 1.023 MHz. The L1 signal from each satellite uses binary phase-shift keying (BPSK), modulated by two pseudorandom noise (PRN) codes in phase quadrature, designated as the C/A-code and P-code. The L2 signal from each satellite is BPSK modulated by only the P(Y)-code. A brief description of the nature of these PRN codes follows, with greater detail given in Chapter 4.
This is one motivation for use of two different carrier signals, L1 and L2. Because delay through the ionosphere varies approximately as the inverse square of signal frequency f (delay ∝ f−2), the measurable differential delay between the two carrier frequencies can be used to compensate for the delay in each carrier (see Ref. 27 for details).
Knowledge of the PRN codes allows users independent access to multiple GPS satellite signals on the same carrier frequency. The signal transmitted by a particular GPS signal can be selected by generating and matching, or correlating, the PRN code for that particular satellite. All PRN codes are known and are generated or stored in GPS satellite signal receivers. A first PRN code for each GPS satellite, sometimes referred to as a precision code or P-code, is a relatively long, fine-grained code having an associated clock or chip rate of 10f0 = 10.23 MHz. A second PRN code for each GPS satellite, sometimes referred to as a clear or coarse acquisition code or C/A-code, is intended to facilitate rapid satellite signal acquisition and handover to the P-code. It is a relatively short, coarser-grained code having an associated clock or chip rate f0 = 1.023 MHz. The C/A-code for any GPS satellite has a length of 1023 chips or time increments before it repeats. The full P-code has a length of 259 days, during which each satellite transmits a unique portion of the full P-code. The portion of P-code used for a given GPS satellite has a length of precisely 1 week (7.000 days) before this code portion repeats. Accepted methods for generating the C/A-code and P-code were established by the satellite developer (Satellite Systems Division of Rockwell International Corporation) in 1991 [10, 19].
The GPS satellite bit stream includes navigational information on the ephemeris of the transmitting GPS satellite and an almanac for all GPS satellites, with parameters providing approximate corrections for ionospheric signal propagation delays suitable for single-frequency receivers and for an offset time between satellite clock time and true GPS time. The navigational information is transmitted at a rate of 50 baud. Further discussion of the GPS and techniques for obtaining position information from satellite signals can be found in .
SA is a combination of methods available to the U.S. Department of Defense to deliberately derate the accuracy of GPS for “nonauthorized” (i.e., non-U.S. military) users during periods of perceived threat. Measures may include pseudorandom time dithering and truncation of the transmitted ephemerides. The initial satellite configuration used SA with pseudorandom dithering of the onboard time reference only , but this was discontinued on May 1, 2000.
Formal, proprietary service PPS is the full-accuracy, single-receiver GPS positioning service provided to the United States and its allied military organizations and other selected agencies. This service includes access to the encrypted P-code and the removal of any SA effects.
SPS provides GPS single-receiver (stand-alone) positioning service to any user on a continuous, worldwide basis. SPS is intended to provide access only to the C/A-code and the L1 carrier.
GPS IIF, GPS IIR-M, and GPS III are being designed under various contracts (Raytheon, Lockheed Martin). These will have a new L2 civil signal and new L5 signal modulated by a new code structure. These frequencies will improve the ambiguity resolution, ionospheric calculation, and C/A-code positioning accuracy.
A second system for global positioning is the GLONASS, placed in orbit by the former Soviet Union, and now maintained by the Russian Republic [21, 22].
GLONASS has 24 satellites, distributed approximately uniformly in three orbital planes (as opposed to six for GPS) of eight satellites each (four for GPS). Each orbital plane has a nominal inclination of 64.8° relative to the equator, and the three orbital planes are separated from each other by multiples of 120° right ascension. GLONASS orbits have smaller radii than GPS orbits, about 25,510 km, and a satellite period of revolution of approximately 8/17 of a sidereal day.
The GLONASS system uses frequency-division multiplexing of independent satellite signals. Its two carrier signals corresponding to L1 and L2 have frequencies f1 = (1.602 + 9k/16) GHz and f2 = (1.246 + 7k/16) GHz, where k = −7, −6, … 5, 6 is the satellite number. These frequencies lie in two bands at 1.598–1.605 GHz (L1) and 1.242–1.248 GHz (L2). The L1 code is modulated by a C/A-code (chip rate = 0.511 MHz) and by a P-code (chip rate = 5.11 MHz). The L2 code is presently modulated only by the P-code. The GLONASS satellites also transmit navigational data at a rate of 50 baud. Because the satellite frequencies are distinguishable from each other, the P-code and the C/A-code are the same for each satellite. The methods for receiving and analyzing GLONASS signals are similar to the methods used for GPS signals. Further details can be found in the patent by Janky . GLONASS does not use any form of SA.
The satellite for the next generation of GLONASS-K was launched on February 26, 2011 and continues to undergo flight tests. This satellite is transmitting a test CDMA signal at a frequency of 1202 MHz.
The Galileo system is the third satellite-based navigation system currently under development. Its frequency structure and signal design is being developed by the European Commission’s (EC’s) Galileo Signal Task Force (STF), which was established by the EC in March 2001. The STF consists of experts nominated by the European Union (EU) member states, official representatives of the national frequency authorities, and experts from the European Space Agency (ESA).
The EU intends the Galileo system to provide the following four navigation services plus one search and rescue (SAR) service.
The OS provides signals for positioning and timing, free of direct user charge, and is accessible to any user equipped with a suitable receiver, with no authorization required. In this respect, it is similar to the current GPS L1 C/A-code signal. However, the OS is expected to be of higher quality, consisting of six different navigation signals on three carrier frequencies. OS performance is expected to be at least equal to that of the modernized Block IIR-M GPS satellites, which began launching in 2005, and the future GPS III system architecture currently being developed. OS applications will include the use of a combination of Galileo and GPS signals, thereby improving performance in severe environments such as urban canyons and heavy vegetation.
The SOL service is intended to increase public safety by providing certified positioning performance, including the use of certified navigation receivers. Typical users of SOL will be airlines and transoceanic maritime companies. The European (also Geostationary) Navigation Overlay System (EGNOS) regional European enhancement of the GPS system will be optimally integrated with the Galileo SOL service to have independent and complementary integrity information (with no common mode of failure) on the GPS and GLONASS constellations. To benefit from the required level of protection, SOL operates in the L1 and E5 frequency bands reserved for the Aeronautical Radionavigation Services.
The CS service is intended for applications requiring performance higher than that offered by the OS. Users of this service pay a fee for the added value. CS is implemented by adding two additional signals to the OS signal suite. The additional signals are protected by commercial encryption and access protection keys are used in the receiver to decrypt the signals. Typical value-added services include service guarantees, precise timing, ionospheric delay models, local differential correction signals for very high-accuracy positioning applications, and other specialized requirements. These services will be developed by service providers, which will buy the right to use the two commercial signals from the Galileo operator.
The PRS is an access-controlled service for government-authorized applications. It is expected to be used by groups such as police, coast guards, and customs. The signals will be encrypted, and access by region or user group will follow the security policy rules applicable in Europe. The PRS will be operational at all times and in all circumstances, including periods of crisis. A major feature of PRS is the robustness of its signal, which protects it against jamming and spoofing.
The SAR service is Europe’s contribution to the international cooperative effort on humanitarian SAR. It will feature near real-time reception of distress messages from anywhere on Earth, precise location of alerts (within a few meters), multiple satellite detection to overcome terrain blockage, and augmentation by the four low earth orbit (LEO) satellites and the three geostationary satellites in the current Cosmitscheskaja Sistema Poiska Awarinitsch-Search and Rescue Satellite (COSPAS-SARSAT) system.
Galileo will provide 10 right-hand circularly polarized navigation signals in three frequency bands. The various signals fall into four categories: F/Nav, I/Nav, C/Nav, and G/Nav. The F/Nav and I/Nav signals are used by the OS, CS, and SOL services. The I/Nav signals contain integrity information, while the F/Nav signals do not. The C/Nav signals are used by the CS, and the G/Nav signals are used by the PRS.
This band, which spans the frequency range from 1164 to 1214 MHz, contains two signals, denoted E5a and E5b
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