pseudorange

Pseudorange is the distance-like measurement between a Global Navigation Satellite System (GNSS) receiver and a satellite, derived from the time-of-flight of the satellite signal and scaled by the speed of light. It is called pseudorange because the receiver’s clock is not synchronized with the GNSS time, so the measurement includes an unknown receiver clock bias and does not equal the true geometric range.

Principle and measurement. The receiver correlates the incoming PRN code with a locally generated copy to determine the code phase and the time of reception. Multiplying the measured time-of-flight by the speed of light yields the pseudorange value. The measurement is affected by ionospheric and tropospheric delays, multipath, receiver hardware delays, and satellite clock errors, in addition to random noise. Civil receivers typically use C/A code for single-frequency pseudorange measurements, while more precise measurements can be obtained with P code or dual-frequency processing.

Observation model. A common form of the pseudorange observation equation is P_i = ρ_i + c·Δt_r + ε_i, where P_i is the measured pseudorange to satellite i, ρ_i is the geometric range between receiver and satellite i computed from approximate positions and satellite ephemeris, Δt_r is the receiver clock bias (in seconds), c is the speed of light, and ε_i represents residual errors including atmospheric delays and noise. Since Δt_r is unknown, measurements from at least four satellites are used to solve for the three spatial coordinates and the receiver clock offset.

Applications and accuracy. Pseudorange observations enable GNSS positioning and time transfer. The basic code-based pseudorange is typically accurate to several meters in open sky, with higher precision achievable through corrections, dual-frequency processing, and augmentation systems.