Practical stuff

OH today 12-1:30; also Friday

Never debug longer than 30 minutes

Ask for help! (from me or your classmates)

Reminder: GPS facts to memorize

Phase can be measured to precision of 1mm (or better)

L1 ~ 1.5 GHz, L2 ~ 1.2 GHz

Ionosphere delay ~ TEC/f2

Data weighting & a priori model values

How and when?

The goal of data weighting is to make your uncertainty estimates meaningful (and your estimates more accurate). To do that, you need to remember the rules of least squares:

Assumptions of least squares:

1. you have a model that describes the observations (data)the observations are linearly related to the model

2. postfit residuals are zero mean and randomly distributed

3. you should know your observation errors before you start (or iterate when you do know them).

As I showed on Monday, these postfit residuals “look” Gaussian

Residuals as f(elevation)

The usual trick: run LS once, calculate the std of the pfr

Then weight by that std.

But if the problem is intrinsic to your data, you should pick a weight function that corresponds to the distribution of your residuals

Options:

If the non-gaussian distribution of the residuals is caused by a model defect, you can (and should) improve your model.

Calculate standard deviations in bins

Data weighting schemes - How do you pick?

Lets use 1/sineE

How do we solve the LS problem ?

Model: pfr = C/sineE

The partial of the pfr with respect to C is 1/sineE

A =[1./sind(angles)]; (least squares) C = A\pfr

This is what you get if you don’t use variable data weights

Sta

ndar

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viat

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Compared to what we had originally

Does weighting the data change the solution?

1. If weights are constant (i.e. same for all data), no.

2. If weights are not constant, the answers are different.

Why are the pseudorange errors so non-gaussian?

A priori model values