What a GNSS fix actually costs

A GNSS receiver reports a position to a few metres. The satellites it is listening to are twenty thousand kilometres away, moving at roughly four kilometres a second, and the entire measurement rests on knowing when a signal was sent to within a few nanoseconds.

Getting from there to a dot on a map involves more corrections than most people who consume the output realise, and each one has a failure mode worth knowing.

The measurement is a clock comparison

A satellite transmits a signal stamped with the time it left. The receiver notes the time it arrived, differences the two, multiplies by the speed of light, and obtains a range.

Except the receiver’s clock is a cheap oscillator and the satellite’s is an atomic standard. The receiver clock is wrong, so every range is wrong by the same distance — hence pseudorange. That shared error is why you need four satellites rather than three: three for position, one to solve for the clock offset.

A microsecond of clock error is 300 metres of range error. The system is a timing instrument that happens to output coordinates.

Everything the signal passes through

The ionosphere is the largest correctable error. Free electrons delay the signal, and the delay is frequency-dependent — which is the saving grace. A dual-frequency receiver observes the same signal at two frequencies and solves for the delay directly. A single-frequency receiver cannot, and instead applies a broadcast model — Klobuchar’s, still in use — that removes roughly half the error on average. Under an ionospheric storm it removes considerably less.

The troposphere is smaller but harder, because the delay is not frequency-dependent and cannot be eliminated by dual-frequency observation. It is modelled, typically with a Saastamoinen-type formulation, and the wet component — water vapour — is the stubborn residual.

Multipath is the one that defeats models. A signal reflecting off a building arrives later than the direct path and the receiver may track the reflection. This is not a bias you can subtract; it depends on the geometry of the surroundings and changes as you move. In urban canyons it dominates the error budget.

Geometry multiplies everything

Given the same measurement quality, position accuracy depends on where the satellites are in the sky. Satellites clustered together produce a poorly conditioned solution; spread across the sky produce a well conditioned one.

This is summarised as dilution of precision, and it multiplies your ranging error into a position error. Same receiver, same corrections, twice the DOP and twice the position error. It is a property of the sky at that moment, not of the equipment.

The datum problem

A coordinate is meaningless without the reference frame it is expressed in, and this is where GNSS output most often goes wrong downstream.

GPS broadcasts positions in WGS84. Many national mapping systems use their own datum — NAD83 in North America, ETRS89 across Europe. These were aligned at epoch and have since diverged, because the tectonic plates they are tied to keep moving. The difference between WGS84 and NAD83 is now on the order of a metre or more in parts of North America.

A receiver reporting centimetre precision in one frame, plotted against a basemap in another, gives you a confidently wrong answer. Precision and accuracy come apart exactly here, and no amount of better hardware fixes it.

What this means for anything built on positions

• Accuracy is a distribution, not a number. Ask what conditions produced the figure.
• Sub-metre claims usually imply differential or RTK correction, which means a nearby reference station and a working correction link. Without those, the claim is about the hardware’s potential, not its output.
• Always record the datum and epoch alongside the coordinate. A position without a frame is not a position.
• Vertical accuracy is typically two to three times worse than horizontal, because the satellites are all above you and the geometry is one-sided.

None of this makes GNSS unreliable. It makes it an instrument with a characterised error budget, which is a different thing — and treating a reported coordinate as ground truth rather than as a measurement with structure is where most downstream errors start.

References

1. P. Misra, P. Enge. Global Positioning System: Signals, Measurements, and Performance, 2nd ed. Ganga-Jamuna Press, 2011. The standard text on the measurement itself.
2. E. D. Kaplan, C. J. Hegarty (eds.). Understanding GPS/GNSS: Principles and Applications, 3rd ed. Artech House, 2017.
3. J. A. Klobuchar. “Ionospheric Time-Delay Algorithm for Single-Frequency GPS Users.” IEEE Transactions on Aerospace and Electronic Systems, AES-23(3), 1987. The broadcast correction model.
4. J. Saastamoinen. “Atmospheric Correction for the Troposphere and Stratosphere in Radio Ranging of Satellites.” In The Use of Artificial Satellites for Geodesy, AGU, 1972.
5. J. Iliffe, R. Lott. Datums and Map Projections, 2nd ed. Whittles, 2008. On reference frames and why they diverge.
6. UCAR/COMET, Global Navigation Satellite Systems training programme.