How does GPS calculate ground speed?

Velocity drops out of the solution of the GPS equations (along with position, hdop, vdop, etc).

But this is standard old stuff. Not related to IAS, CAS, TAS… GPS GS is also normally very accurate.

It’s derived from Doppler shift in L1 frequency. Since at least 4 satellites are needed for 3D position, there’s plenty of data available for calculations, including satellite positions and ionospheric propagation. I believe googling can easily reveal details on mathematics used.

roznet wrote:

Using the Doppler Shift

Surveyor GPSs use doppler shift and phase shift to get centimetre accuracy without SBAS – but that equipment is stationary when used. Can those techniques really be used for aircraft in flight? I would place my bet on the Kálmán filter.

Every GPS uses Kalman filtering.

AFAIK velocity is done with doppler and is thus very accurate; much more so than say altitude. Funnily enough you see this when using one of the ski apps, clocking you (me) at 95km/hr It tries to adjust GS for the altitude delta and gets it really wrong. I had some comms with the dev on that one.

GPS GS is so accurate that you can calibrate your instruments with it. See threads on ASI calibration.

As Emir wrote you need 4 satellites to give an accurate position in space.
The way it was described to me was as follows as I asked for the primary school version.
A satellite is carrying a very accurate clock.
If someone on that satellite signals the time eg it is 4.31 precisely. On board your aircraft your GPS also has an accurate clock but not as accurate as the one in the satellite and when your GPS hears it is 4.31 looks at its clock and sees that there is a difference in time. It also knows various other information eg that the if the GPS receives 4.31 and 1 second that that satellite is 186,000 miles or 300,000km away from your aircraft. 3 satellites doing the same thing at the same time will give you trigonomically a position in space (sort of ) because the lines may actually cross in 2 places so the 4th satellite is needed to avoid this error.
On top of this both satellite and GPS have other information such as the.exact position in space and its orbit. This information on the satellite along with clock calibration orbit etc.is regularly checked and corrected (almanac and ephirimedes ( something wrong here and spellcheck doesn’t have it) .And of course the time is being sent and received many many times a second and we are talking in differences in time of tiny fractions of a second.
So 2 points in space can be accurately measured and the speed of travel from one point to another calculated. These points can also be compared to points on the ground. In most cases in Europe this is WGS 84 global mapping algorithm/software. So calculating distance on the ground and speed between the is simple maths.
There are several points to remember
a).Not all GPS receivers are created equally
In cheaper models the clocks might be not as good. Although this is not such a big problem nowadays as cheap clocks can be just as accurate as more expensive ones.
The refresh rate of some cheaper GPS receivers will be much longer than say one certified for IFR in an aircraft. For instance one doesn’t need a fast refresh rate if one is using the gps for rambling or orienteering. This does not effect the accuracy.
b) WGS 84 is a total mapping system independent of say Ordinance Survey Maps which means that your GPS position fix of a point on the ground can be very different in terms of latitude and longtitude from that same position on and Ordnance survey map. Sometimes hundreds of metres.

Given the chances of inaccuracy, in aviation, to gain more accuracy at a given point systems such as WAAS and EGNOS have been introduced. These rely on a number of static ground based stations which know exactly where they are and they receive the same information from the satellites calculate any errors and send the offsets to the WAAS or EGNOS satellites (SBAS) which in turn send that information to a GPS capable of using these WAAS or EGNOS offsets.
A ground based master station (GBAS) could also be used to transmit these offsets to the GPS in the aircraft but I’m not sure if there are any GBAS systems operating yet. I don’t recall one in France.