practical stuff
Post on 20-Jan-2016
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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
d de
viat
ions
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
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