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)

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 two middle terms are zero: fort>lo,n(t) and are uncorrelated becauset) is white(impulse correlation function) For=, n() has a finite effect on x()because n() is white. But the integral of a finite quantity over one point is zero

Solution in the Free Configuration Non-Real-Time Filter Case The applicable condition in this important case is:

For the differential system characterized by its equations of state,specialization to invariance means that the system matrices A, B,C are constants

Note n, s enter the system at the same place F is fixed. We design(and perhaps B). We must stabilize F if it is given as unstable