112.215 Modern NavigationThomas Herring ([email protected]),MW 10:30-12:00 Room 54-322http://geoweb.mit.edu/~tah/12.21509/09/2009 12.215 Modern Naviation 2Course Overview• The development of the Global Positioning System (GPS) startedin the 1960s, and the system became operational in 1992.• The system has seen many diverse applications develop in thelast few years with the accuracy of positioning ranging from 100meters (the civilian restricted accuracy requirement) to 1millimeter (without the need for a security clearance!)• In this course we will apply many of basic principles of scienceand mathematics learnt at MIT to explore the applications andprinciples of GPS and contrast it to conventional navigation.• We also use GPS and other equipment in the class (and outsideon Campus) to demonstrate the uses of this system209/09/2009 12.215 Modern Naviation 3Class Expectations• We will have some lab sessions during the course and there willbe homework once every few weeks.• There will be an open book final exam.• Grading will be from the homework (70%), final exam (20%) andclass participation (10%).• It will be acceptable in this course to work together on homeworkwith the aim of better understanding the material and to refer toother books and published material provided that these additionalmaterials are cited appropriately in the homework.• Each student should complete the homework separately.• It is not acceptable to simply copy the homework of anotherstudent.09/09/2009 12.215 Modern Naviation 4Course Topics: Coordinate Systems• General Areas:– Coordinate systems on a deformable, non-spherical Earth.– Concepts of latitude and longitude as determined by thedirection of gravity (astronomical latitude and longitude) anddetermined by the normal to an ellipsoidal shape (geodeticlatitude and longitude).– Relationships between coordinates; concepts of polar motionand changes in the rotation rate of the Earth; rotations andtranslations between coordinate systems. Effects that need tobe considered for different accuracy results and theaccuracies that are achievable with GPS.309/09/2009 12.215 Modern Naviation 5Course Topics: Navigation and Maps• Principles of Navigation.• Dead-reckoning, true and magnetic bearings• Use of celestial bodies for navigation• Common map projections• Metrics for relating curvi-linear coordinates• Spherical trigonometry09/09/2009 12.215 Modern Naviation 6Course topics: GPS• Principles of GPS.– Pseudorange and phase measurements.– Spread spectrum signal structure; basic concepts of signalanalysis. Contributions of pseudorange and phase (geometricpositions, clock errors, propagation medium, cycles ambiguityfor phase).– Simple atmospheric and ionospheric delay models; use ofdispersive properties of plasmas (ionosphere).– Use of differencing techniques in the analysis of GPS data.– Security systems on GPS satellites (selective availability andanti-spoofing) and their effects on navigation and precisepositioning.409/09/2009 12.215 Modern Naviation 7Course Topics: Statistics andEstimation• Estimation procedures– Stochastic and mathematical models– Correlations and their interpretation– Statistical descriptions of dynamic systems– Propagation of covariance matrices– Statistics in least-squares estimation.09/09/2009 12.215 Modern Naviation 8Course Topics: Applications• Examples of applications:– aircraft navigation using GPS (comparison withlaser profiling)– examination of real data to assess the limits ofaccuracy obtainable with GPS– applications in a variety of areas including precisionfarming; and intelligent vehicle navigation systems.509/09/2009 12.215 Modern Naviation 9Course Topics• Selection of topics is based on applying principles andmathematics to actual problems• Each of the mathematical topics covered will be usedin understanding how GPS works and how the systemcan be used.• Homework exercises and data collection sessions inclass will be examples of how these concepts areused09/09/2009 12.215 Modern Naviation 10Specific Schedule (see web page)Dead reckoning and conventional navigation7Almanacs paper and on-line6Motion of Sun/Earth and astronomical positiondetermination5Spherical trigonometry4Height Definition3Latitude and Longitude definition2Introduction; coordinate systems (this lecture)1Topic#609/09/2009 12.215 Modern Naviation 11Specific Schedule (see web pageCorrelations14Propagation of variances13Basic statistics need for estimation12Map projections11Sextant results. Analysis of results previouslycollected10Linear algebra (as applied to transformations)9Use of sextant and measurements in class(determine latitude and longitude of class room)8Topic#09/09/2009 12.215 Modern Naviation 12Specific Schedule (see web pageSatellite motions21Dispersive propagation delays20Neutral atmosphere propagation19GPS carrier phase measurements18Geometry of GPS measurements andaccuracy17Basics of GPS pseudo range16Electronic distance measurement15Topic#709/09/2009 12.215 Modern Naviation 13Specific Schedule (see web pageReview26Applications of GPS in different fields25GPS outside the classroom24Basics of hand held GPS23Class before Thanks Giving22Topic#09/09/2009 12.215 Modern Naviation 14Notes on Schedule• Specific dates of some activities will depend on theweather conditions and the schedule may change• Last yearʼs lecture will be left on-line (updatedversions will have 2009 date).• Reference material for the class– During the lectures, web-based materials andbooks will be referred to.– The topics covered in this course are sufficientlydiverse that no single text book is recommended.– All materials for the course will be made availableelectronically809/09/2009 12.215 Modern Naviation 15Electronic Materials• The class notes are made available in three formats:– Microsoft Power Point documents (original format)– PDF in black and white for printing– HTML web format (The exact look of thesedocuments will depend on your Browser and OS.Even MS internet Explorer does not render MS htmldocuments uniformly.• Links in documents are only active in the power pointand html versions.09/09/2009 12.215 Modern Naviation 16Coordinate Systems• Navigation: knowing where you are, where you wantto go, and how to get there– Also useful: knowing how long it will take– To achieve these goals in a general way; acoordinate system is needed that allow quantitativecalculations (Claudius Ptolemy,