Re: Speed accuracy

I wonder how I missed the first question: the accuracy in speed of the eTrex
Legend.

Although Dominic quoted:

"Hence even the lowly Garmin eTrex has a stated velocity accuracy of 0.1
knot RMS steady state".
(0.1 Knot = 0.12 MPH = 0.19 KPH)

The specs for the Garmin eTrex *Legend* are at:

http://www.garmin.com/products/etrexLegend/spec.html

Accuracy: Velocity 0.05 m/s steady state = 0.11 MPH = 0.18 KPH

Steady state meaning IMO constant speed. They should also state in which
range of distance, they have this accuracy, because if you travel, say, 10
metres and have an accuracy of 5 metres in position, you'll surely get a big
error in speed.

Although this claim could be biased, coming from the manufacturer, it sets a
reference which could be very difficult to match by any car instruments
manufacturer.

Finally, if velocity is calculated as Distance measured by GPS divided by
time; applying the propagation of error theory, I got the following:

Error in distance = 10 metres in the mile (5 at the starting point; 5 at the
final point)
Error in time = 200 nanoseconds (double as Trimble's GPS, 100 at the start,
100 at the final point); negligible.

Error in Velocity = 0.2 m/s = 0.4 MPH = 0.6 KPH

That is: Velocity = 60.0 + or - 0.4 MPH

You cannot appreciate 0.4 MPH in a normal car speedo.

JV

P.S.: mail me at jdepetare in the server cantv.net, if you are interested
in the details and references for the formula of the propagation of error
using partial derivatives.

To e-mail me substitute "_"s by "e" and "c".

Yes that is what they mean. To produce steady results the receivers use
a Kalman filter system to reduce the effect of 'noise' in the
measurements. Because of this previous solutions can affect the current
solution.


No, the distance is not relevant otherwise speed accuracy would be
dependant upon the inverse of the speed - i.e. for the same position
accuracy the speed accuracy would improve as the receiver travelled
faster.

In reality it is like this. Lets say the receiver travelled 10m between
the two speed readings which were one second apart and the first point
had a position error of 5m. The second point is highly likely to also
have an error very close to 5m.

This is due in part to the Kalman filter used by the receiver to smooth
the errors and in part due to the slow changing nature of the larger
sources of errors in the system. Most of the error comes from the
ionosphere, the satellite clock and the satellite ephemeris data - all
of which are predominantly slow changing.


It isn't!

--

Dominic Sexton

I meant, if it "was" (or "were") calculated... (but as I wasn't sure, due
to my broken English, whether to write "was" or "were", I preferred to write
"is").

I understand, according to your statements, that velocity is calculated
otherwise, but I don't understand your explanation.

If you think that this discussion has gone too far in the Newsgroup, you can
try to explain it or send me a reference to my email: jdepetare (in the
server) cantv.net

Thanks,

JV

That's OK. What you wrote could have the meaning you wanted but I didn't
read it that way.


The GPS receiver computes a PVT (position velocity time) solution for
every sample. It does not compute position and time and then compare to
the previous solution(s) to compute velocity by distance / time.

In order to correctly decode the signals the receiver must take into
account the doppler shift of each signal. The doppler shift is a direct
result of the relative velocity of the transmitter and receiver. The
velocity of the transmitters are known accurately (from the ephemeris
data transmitted by the satellites).

Therefore with enough satellites spread over a reasonable area of the
sky the receiver has enough information to compute its own velocity.

--

Dominic Sexton