02 / WHY IT WORKS

Why “pseudo” range?

The observation contains geometric range plus clock and propagation effects. Calling it pseudorange prevents us from treating the raw timing result as a perfectly measured straight-line distance. The receiver also needs satellite positions and satellite-clock corrections from navigation data.

Four observations are a minimum, not a guarantee

In the basic single-system model, unknowns are x, y, z and receiver clock bias. At least four independent observations are needed. Nearly dependent directions make the solution weak. More observations support a least-squares solution, but additional biases may require a richer model.

03 / UNDER THE SURFACE

From intuition to a model

The code observation model

The receiver estimates unknowns after applying available corrections. The sign of clock terms depends on the convention; this equation uses receiver minus satellite clock offset. Linearization around an approximate position leads to a system whose rows contain line-of-sight directions and a clock term.

ρ=r+c(δtr−δts)+I+T+ε\begin{aligned}\rho &= r+c\left(\delta t_r-\delta t_s\right)\\&\quad+I+T+\varepsilon\end{aligned}

ρ, r, I, T, ε: meters; c = 299,792,458 m/s; δtr, δts: seconds. I and T are code delays due to ionosphere and troposphere; ε collects remaining effects.

04 / A WORKED EXAMPLE

A tiny clock offset, a large range offset

A receiver clock offset of +1 microsecond contributes +299.792458 m to every pseudorange in this simplified model. Move the clock slider from 0 to +1 μs and watch all range constraints expand. This does not mean the receiver position error is exactly 300 m: position and clock are solved together. Reset the offset before comparing geometry.

Return to the experiment and try it ↑

05 / PUT IT TO WORK

Try it in GNSS View

  1. Open the observatory and select one constellation to isolate the basic geometry.
  2. Compare visible count and DOP at several times.
  3. Remember that this site predicts directions; it does not ingest pseudorange observations to solve your receiver position.
Open the observatory ↗

06 / COMMON QUESTIONS

Does the receiver transmit to the satellites?

Ordinary GNSS reception is one-way: navigation signals travel from satellites to the receiver. Internet assistance or correction services are separate links.

Why not use three satellites for three coordinates?

The unknown receiver-clock offset adds another parameter unless external constraints are available.

Does a phone measure light-speed delays directly?

It correlates received codes and applies timing and navigation models. Noise, clock offsets and propagation effects make the resulting observation a pseudorange.

07 / FURTHER READING

An original GNSS View explanation. These references document the models, terminology and system context.

ESA Navipedia · GNSS Basic Observables ↗ESA Navipedia · Positioning Error ↗GPS.gov · Space segment ↗