Error in Niell tropo function calculation ? #99

[jonathanmuller]

Hi,

There is a common pattern I see in all implementations of the Niell tropo across github :

The implementation is always the same :

(1+a / ... ) / (sinel +b / ...) while I believe it should be (sinel +b / ...) / (1+a / ... ) (the opposite)

For example in the code :

cssrlib/src/cssrlib/gnss.py

Line 1410 in 4843cc7

return (1.0+a/(1.0+b/(1.0+c)))/(sinel+(a/(sinel+b/(sinel+c))))

def mapf(el, a, b, c):
    """ simple tropospheric mapping function """
    sinel = np.sin(el)
    return (1.0+a/(1.0+b/(1.0+c)))/(sinel+(a/(sinel+b/(sinel+c))))

However, original paper ( https://safe.nrao.edu/wiki/pub/Main/RefBendDelayCalc/Niell_Global.pdf ) list "equation 4" as :

So the form is (1/(1+a / ... )) / (1+1/(sinel +b / ...))
As (1/y)/(1/x) can be rewritten as x/y
Then the calculation above can be simplified as (sinel +b / ...) /(1+a / ... )
There can be no ambiguity as later it is used directly as follow, without further division or calculation directly as height correction :

cssrlib/src/cssrlib/gnss.py

Line 1439 in 4843cc7

dm = (1.0/np.sin(el)-mapf(el, aht[0], aht[1], aht[2]))*hgt*1e-3

This is the same (wrong?) implementation as RTKLib and any other commonly used RTK library I could find on github.
Am I just wrong about the understanding of the calculation, or is everyone copy-pasting the same error ?

[hirokawa]

Thank you for your comment.
The Neil mapping function is also described in the ESA Navipedia:
https://gssc.esa.int/navipedia/index.php/Mapping_of_Niell

The current implementation of CSSRlib (and RTKLIB) is compatible with the Navipedia. Based on the original paper, I don't know what is wrong with your understanding.

[hirokawa]

I also checked some famous book "GPS: Theory and Practice 5th", p.114, the equation in CSSRlib/RTKLIB is correct. The original paper is Herring (1992), "Modeling atmospheric delays in the analysis of space geodetic data".

[jonathanmuller]

You fully convinced me that you -and the code- where right
Thank you a lot for the details !