# Lecture Notes

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## Lecture Notes

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- Pages:
- 25
- School:
- Massachusetts Institute of Technology
- Course:
- 12 215 - Modern Navigation

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12 215 Modern Navigation Thomas Herring Summary of last class Ionospheric delay effects in GPS Look at theoretical development from Maxwell s equations Refractive index of a low density plasma such as the Earth s ionosphere Most important part of today s class Dual frequency ionospheric delay correction formula using measurements at two different frequencies Effects of ionospheric delay are large on GPS 10 s of meters in point positioning 1 10ppm for differential positioning Largely eliminated with a dual frequency correction most important thing to remember from this class at the expense of additional noise and multipath Residual errors due to neglected terms are small but can reach a few centimeters when ionospheric delay is large 12 01 2004 12 215 Modern Naviation L21 2 Satellite Orbits Treat the basic description and dynamics of satellite orbits Major perturbations on GPS satellite orbits Sources of orbit information SP3 format from the International GPS service Broadcast ephemeris message Accuracy of orbits and health of satellites 12 01 2004 12 215 Modern Naviation L21 3 Dynamics of satellite orbits Basic dynamics is described by F Ma where the force F is composed of gravitational forces radiation pressure drag is negligible for GPS and thruster firings not directly modeled Basic orbit behavior is given by r 12 01 2004 GM e r 3 r 12 215 Modern Naviation L21 4 Simple dynamics GMe 3986006x108 m3s 2 The analytical solution to the central force model is a Keplerian orbit For GPS these are elliptical orbits Mean motion n in terms of period P is given by n 2 3 P a For GPS semimajor axis a 26400km 12 01 2004 12 215 Modern Naviation L21 5 Solution for central force model This class of force model generates orbits that are conic sections We will deal only with closed elliptical orbits The orbit plane stays fixed in space One of the foci of the ellipse is the center of mass of the body These orbits are described Keplerian elements 12 01 2004 12 215 Modern Naviation L21

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