Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 318

For elevation angles other than 90°, the model in (7.28) does, in general, not
apply. To account for the elevation angle of the satellite, for example, so-called map-
ping functions may be introduced in the equation:

∆ S =⋅ md +⋅ md

tropo d dry w et

or (7.29)

( )

∆ S =⋅ md + d

tropo dry wet

where:

m d = dry-component mapping function

m w = wet-component mapping function

m = general mapping function

Existing mapping functions can be divided into two groups: the geodetic survey-
oriented applications and the navigation-oriented applications [24]. An example of
the geodetic survey-oriented group is the Niell mapping function as described in
[25]. Navigation-oriented mapping functions include both analytical models and
more complex forms such as the fractional form introduced by [26]. The advantage
of the analytical forms is that it is not computationally intensive to determine the
mapping function values. An example of analytical models is Black and Eisner's
mapping function, which is a function of the satellite's elevation angle, E :

1001
0002001

.

()

mE =

()

2

. + sin E

A more accurate, but more complex, model that may be used for the mapping
function has the following continued fractional form [26]:

a

1 +

i

b

1 +

i

c

1 +

i

1 + K

()

mE =

i

a

sin E +

i

b

sin E +

i

c
E

sin E +

i

sin + K

where E is the elevation angle; a i , b i , and c i are the mapping function parameters; and
i represents either the dry or wet component. Note that the term in the numerator
normalizes the mapping function with respect to zenith. The parameters a i , b i , and c i
can be estimated from ray-tracing delay values at various elevation angles. Exam-
ples of mapping functions that describe the troposphere delay accurately down to a