Comparing the corresponding the carrier phase and pseudorange observation we note:

There is one additional and more hidden difference between the equations: The total signal travel time is slightly different for pseudorange and carrier phase measurements because of differences in the ionospheric effect and the equipment delays. As a result, the time argument for the evaluation of the satellite coordinates is also slightly different.

Source: Teunissenn and Kleusberg (1996)

- both contain the geometric distance \(\rho _i^k\left( {t,t - \tau _i^k} \right)\)
- both contain the clock error terms \(c\left[ {d{t_{i\left( t \right)}} - d{t^k}\left( {t - \tau _i^k} \right)} \right]\)
- both contain the tropospheric refraction effect \(T_i^k\)
- the sign of ionospheric refraction effect \(I_i^k\)is reversed
- the pseudorange multipath error \(dm_i^k\)has been replaced by the carrier phase multipath error \(\delta m_i^k\)
- the pseudorange equipment delay terms \(c\left[ {{d_i}\left( t \right) + {d^k}\left( {t - \tau _i^k} \right)} \right]\) have been replaced by the carrier phase equipment delay terms \(c\left[ {{\delta _i}\left( t \right) + {\delta ^k}\left( {t - \tau _i^k} \right)} \right]\)
- the carrier phase observation equation contains the additional terms \(\lambda \left[ {{\phi _0}\left( {{t_0}} \right) - {\phi ^k}\left( {{t_0}} \right)} \right]\) resulting from the non-zero initial phases, and the carrier phase ambiguity term \(\lambda N_i^k\).

There is one additional and more hidden difference between the equations: The total signal travel time is slightly different for pseudorange and carrier phase measurements because of differences in the ionospheric effect and the equipment delays. As a result, the time argument for the evaluation of the satellite coordinates is also slightly different.

Source: Teunissenn and Kleusberg (1996)