Satellite navigation solution for the receiver's position (geopositioning) involves an algorithm.
In essence, a GNSS receiver measures the transmitting time of GNSS signals emitted from four or more GNSS satellites (giving the pseudorange) and these measurements are used to obtain its position (i.e., spatial coordinates) and reception time.
The following are expressed in inertial-frame coordinates.
i
is the orbital eccentric anomaly of satellite
is the mean anomaly,
is the eccentricity, and
δ
clock
δ
clock,sv
δ
orbit-relativ
{\displaystyle \scriptstyle \delta t_{{\text{clock}},i}(t_{i},\,E_{i})\;=\;\delta t_{{\text{clock,sv}},i}(t_{i})\,+\,\delta t_{{\text{orbit-relativ}},i}(E_{i})}
cos
cos
{\displaystyle \scriptstyle {\begin{pmatrix}t_{i}\\E_{i}\\\end{pmatrix}}\leftarrow {\begin{pmatrix}t_{i}\\E_{i}\\\end{pmatrix}}-{\begin{pmatrix}1&&0\\{\frac {{\dot {M}}_{i}(t_{i})}{1-e_{i}\cos E_{i}}}&&-{\frac {1}{1-e_{i}\cos E_{i}}}\\\end{pmatrix}}{\begin{pmatrix}\Delta t_{i}\\\Delta M_{i}\\\end{pmatrix}}}