IONOSPHERIC MODEL |
To aid SPS single receiver real-time GPS navigation, the "Klobuchar model" is often used to compute the zenith time delay to the transmitted L1 signal:
 |
(3.3-2) |
where:
| t | is the local time at receiver (in seconds), |
| t0 | is the local time of maximum ionospheric correction (say 14:00hrs). |
| tzion | is the time delay due to the ionosphere in the zenith direction (in seconds), |
| DC | is the base ionospheric time delay (taken as 5x10-9 s), |
| A | is the amplitude of the ionospheric delay function (in seconds), and |
| P | is the period of the ionospheric delay function (in seconds). |
The quantities A and P are computed from the Navigation Message alpha and beta coefficients:
 |
(3.3-3a) |
 |
(3.3-3b) |
where
om is the geomagnetic latitude of the ionospheric subpoint (expressed in semi-circles):
om
= i + 0.064.cos( i - 1.617) |
(3.3-4) |
i and i are the user's latitude and longitude in
semi-circles. (Multiply "semi-circles" by 2
to obtain the
quantity in units of "radians".) The "alpha" terms are
the coefficients of a cubic equation representing the magnitude of the vertical
delay, and the "beta" terms are the coefficients of a cubic equation
representing the period of the model.
The tzion quantity must be scaled by the mapping function to determine the time delay along the slant direction to the satellite:
| tion = tzion . SF | (3.3-5) |
and
 |
(3.3-6) |
where:
| Elev | is the elevation angle to satellite (in radians), |
| r | is the mean earth radius, and |
| h | is the mean ionospheric height (say 350kms). |
An even simpler approximation is often used within GPS receivers:
| tion = [1 + 16.(0.53 - EL)3] . 5x10-9 | (3.3-7) |
where EL is the elevation angle to satellite in units of semi-circles.
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© Chris Rizos, SNAP-UNSW, 1999