GPS Observables Today's class we start discussing the nature of GPS observables and the methods used to make range and phase measurements Start with idea of remotely measuring distances

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

Potential field based coordinates: -Astronomical latitude and longitude -Orthometric heights (heights measured about an equipotential surface, nominally mean-sea-level

Gravitational potential In spherical coordinates: need to solve

Coordinate Systems Today we cover: Definition of coordinates - Conventionalrealization of coordinates Modern realizations using spaced based geodetic systems (such as GPS)

Class expectations This is a graduate level class. There is no final exam Grading in the class is based on homework (75%) and on a final written report(25%) The report will be revised during semester and should be 2000-3000 words(8-10 double spaced pages)

The quantity K2 is known as the Kalman gain. It is the optimum gain in the mean squared error sense. Substitute it into the expression for

If the system reaches a statistical steady state the covariance matrix would be constant. The system would have to be invariant

The estimate of x based on N data points can then be made without reprocessing the first N, points. Their effect can be included simply by starting with pseudo observation which is equal to the estimate based on the first N points having a variance equal to the variance of the estimate based on N The same is true of the variance of the estimate based on N

This means that in the cascade of Ho(s) with F(s), the effect of the RHP zero on the amplitude of the product is cancelled out, but the effect on the phase is not In fact, the phase lag due to the RHP zero is doubled in the product. Note: