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:

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

Special case: [(P)] is rational: In this solution formula we can carry out the indicated integrations in literal form in the case in which [(P)] is rational. In our work, we deal in practical way only with rational,sn, and, so this function will be rational if D(p)is rational This will be true of every desired operation except predictor. Thus except in the case of prediction, the above