Precise Real-Time Positioning Using Network RTK - Global Navigation Satellite Systems: Signal,Theory and Applications - page 172

Typically in FKP, two planes are computed for each satellite, centred at each reference
station, one plane for the dispersive and another for the non-dispersive corrections. The
corrections at the rover are determined through interpolation using the inclination
parameters of the correction planes. Results of Euler et al ., 2002, showed that the plane
surface model gave good results when modelling the regional trends of the correction
differences. Although low-order (linear-plane) surface models are usually utilised, longer
baselines between reference stations may require polynomials of a higher order.

The surface area model was discussed in several publications, e.g. Varner, 2000, Fotopoulos
and Cannon, 2001 and Wübbena and Bagge, 2002. An example is given by the latter study
for generation of FKP, where the errors are computed as follows:

δr o (t) = 6.37 ( FKP N (φ − φ R ) + FKP E (λ − λ R ) cos(φ R )) (t) (13)

δr I (t) = 6.37 α ( FKP N I (φ − φ R ) + FKP E I (λ − λ R ) cos(φ R )) (t) (14)

α = 1+ 16 (0.53 - θ/π) 3 (15)

Where:

δr

estimated non-dispersive geometric (orbital and tropospheric) error

δr I

estimated dispersive ionospheric error

FKP N I

The FKP parameter in north-south direction for the ionospheric signal “narrow
lane” in ppm

FKP E I

The FKP parameter in east-west direction for the ionospheric signal “narrow lane”
in ppm

FKP N

The FKP parameter in north-south direction for the geometric signal “ionosphere-
free” in ppm

FKP E

The FKP parameter in east-west direction for the geometric signal “ionosphere-
free” in ppm

θ the satellite elevation angle in radians

After interpolating the dispersive and non-dispersive errors, they are combined to generate
the range residuals for L1 and L2 frequency observations, which read:

δr δr δr I

(16)

δr δr δr I

(17)

Where:
δ r , δ r total measurement errors for the frequencies f 1 and f 2 .
f 2 , f 1 frequencies of L 1 and L 2 signals.
Finally, the range R, derived from the carrier-phase measurements are corrected as follows:

R R δ r

(18)

R R δ r

(19)