cribbagepeg
Sorry for any lack of clarity. Differential GPS is well-known strategy for correcting the effects of local-ish GPS errors when calculating
absolute positions. I was pointing out that when you calculate
relative positions the local GPS errors cancel out anyway, so no such correction is required.
As I stated:
There are lots of causes of GPS inaccuracy; such as deliberate encoding, atmospheric effects, and engineering imperfections. However these effects are similar for two GPS readings taken at positions close in space and time. ...
This effect is used in the various differential GPS systems in operation, in which base stations broadcast correction factors.
As you state, this base station needs to be at a
known location, so that the [local] GPS error can be measured, and transmitted to interested parties. These parties can then apply this as a correction to their readings to get first-order correction for their GPS errors [if they are close enough].
However if you want to know the
difference in altitude between your wingtips you are interested in
relative not
absolute positions. You may know that there is a local GPS error, but you don't actually need to worry about its value. As the error is the same for all local GPS measurements, its value disappears when you take differences.
So I repeat:
For measuring aircraft attitude its even easier -- the error is surely [almost entirely] canceled when you take the difference between two GPS readings; e.g. the difference in altitude of the two wingtips.
So for the measurement of absolute positions differential-GPS is far more accurate than normal GPS (as it removes the effect of local GPS errors). While for the measurement of relative positions the two systems provide the same high accuracy (as local GPS errors have no impact). Making the accurate measurement of aircraft attitude, based on civilian GPS technology, a very real possibility.
Again:
I'm not advocating such a system, just commenting on its engineering feasibility. ... [But] I feel that the accurate statements previously made about GPS absolute accuracy give a misleading impression of the utility of present GPS systems for measuring civilian aircraft attitude.
Regards, Peter
If you prefer an algebraic argument.
Let the altitude of the left and right wingtips - as measured by their GPS receivers - be l & r.
Let the altitude component of the GPS correction required locally be c (perhaps as transmitted by a friendly neighbourhood differential base station).
The corrected altitudes of the wingtips are (l+c) and (r+c).
The corrected altitude of left wingtip relative to the corrected altitude of the right wingtip is then ( (l+c) - (r+c) ) = (l-r).
Which is, of course, the same as the simple difference in GPS readings (l-r); as any differential GPS correction simply cancels out in the calculation.