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.
The solution illustrated
Calculation steps
Notes for above In the field of GNSS, is called pseudorange, where is a provisional reception time of the receiver. is called receiver's clock bias (i.e., clock advance). Standard GNSS receivers output and per an observation epoch. The temporal variation in the relativistic clock bias of satellite is linear if its orbit is circular (and thus its velocity is uniform in inertial frame). The signal time of flight from satellite to receiver is expressed as , whose right side is round-off-error resistive during calculation. The geometric range is calculated as , where the Earth-centred, Earth-fixed (ECEF) rotating frame (e.g., WGS84 or ITRF) is used in the right side and is the Earth rotating matrix with the argument of the signal transit time. The matrix can be factorized as . The line-of-sight unit vector of satellite observed at is described as: . The satellite-navigation positioning equation may be expressed by using the variables and . The nonlinearity of the vertical dependency of tropospheric delay degrades the convergence efficiency in the Gauss–Newton iterations in step 7. The above notation is different from that in the Wikipedia articles, 'Position calculation introduction' and 'Position calculation advanced', of Global Positioning System (GPS).
The GPS case
The GLONASS case The GLONASS ephemerides don't provide clock biases , but .
See also Dilution of precision (navigation)
Least squares adjustment Precise Point Positioning Pseudo-range multilateration Real Time Kinematic Time to first fix
Notes
References
External links PVT (Position, Velocity, Time): Calculation procedure in the open-source GNSS-SDR and the underlying RTKLIB