Practical stuff

1. 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

2. Data weighting & a priori model values How and when?

3. 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).

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

7. Residuals as f(elevation)

8. The usual trick: run LS once, calculate the std of the pfr Then weight by that std.

9. Options: If the non-gaussian distribution of the residuals is caused by a model defect, you can (and should) improve your model. But if the problem is intrinsic to your data, you should pick a weight function that corresponds to the distribution of your residuals

10. Calculate standard deviations in bins

11. Data weighting schemes - How do you pick?

12. Lets use 1/sineE

13. 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

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

17. Standard deviations

19. Compared to what we had originally

20. 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.

21. Why are the pseudorange errors so non-gaussian?

22. A priori model values