How accurate is my speed?

I have just purchased an iPaq running the TOMTOM software covering the
UK. The speed dispalyed on the iPAQ differs by about 5 mph at 70 mph.
i.e. 70 mph on the speedmoter registers as 65 on the iPAQ. Which is
likely to be closer to my true speed?

David

Mine is spot on against a digital Speedo
"David Steward" <david@steward4.freeserve.co.uk> wrote in message
news:david-FB072A.17294807072003@slb-newsm1.svr.pol.co.uk...
> I have just purchased an iPaq running the TOMTOM software covering the
> UK. The speed dispalyed on the iPAQ differs by about 5 mph at 70 mph.
> i.e. 70 mph on the speedmoter registers as 65 on the iPAQ. Which is
> likely to be closer to my true speed?
>
> David

David Steward wrote:
> I have just purchased an iPaq running the TOMTOM software covering the
> UK. The speed dispalyed on the iPAQ differs by about 5 mph at 70 mph.
> i.e. 70 mph on the speedmoter registers as 65 on the iPAQ. Which is
> likely to be closer to my true speed?

At steady speeds the GPS receiver should be very accurate (well
within a mph of true speed). But most GPS receivers do some
filtering/averaging to make the reported speed more stable so
they can be off if you're braking or accelerating.

David Steward wrote:
>
> I have just purchased an iPaq running the TOMTOM software covering the
> UK. The speed dispalyed on the iPAQ differs by about 5 mph at 70 mph.
> i.e. 70 mph on the speedmoter registers as 65 on the iPAQ. Which is
> likely to be closer to my true speed?
>
> David

Keep in mind that most GPS receivers employ "smoothing filters" and so
instantaneous velocity reading during acceleration is not necessarily
accurate. However at constant velocity (and assuming no obstruction of
signals), the GPS receiver will likely measure velocity to an accuracy
of 0.2 m/s (0.45 mph) 2drms.

There are those that will argue (probably correctly) that steady state
velocity accuracy is even better by a factor of two or so.

>
> There are those that will argue (probably correctly) that steady state
> velocity accuracy is even better by a factor of two or so.

My feeling is that speed only is measured horizontally, going up- or
downhill will reduce the GPS-speed?

/aw (Garmin Venture)

Anders Wiklund wrote:
>
> >
> > There are those that will argue (probably correctly) that steady state
> > velocity accuracy is even better by a factor of two or so.
>
> My feeling is that speed only is measured horizontally, going up- or
> downhill will reduce the GPS-speed?
>
> /aw (Garmin Venture)

True...

The measured speed will be cos(incline) times total velocity
For a steep grade of 5% the reported velocity will be 0.9992
of the total.

On Mon, 7 Jul 2003 13:46:39 -0500, "Blair" <bfonville1@hotmail.com>
wrote:

>Actually, no. The direction of the velocity won't make any difference.

I agree with Anders. Can you explain your view?

Blair wrote:
>
> >My feeling is that speed only is measured horizontally, going up- or
> >downhill will reduce the GPS-speed?
>
> Well, first off, maybe I'm wrong. But here is what I was thinking:
>
> Horizontal with respect to what? The relative motion of a satellite and a
> user is what determines the frequency shift (Doppler) that is the basis for
> the receiver velocity calculation. So, how could the incline of a road
> possibly matter? The incline of a road is different from the viewpoint of
> one satellite to another and the velocity solution requires at least four
> satellites.
>
> Blair
>

Horizontal (perpendicular to the line going
throught the GPS receiver and ECEF coordinates
of (0,0,0)).

A minimum of four GPS NAVSTAR satellites (more can
be used in overdetermined PVT solutions) are used
to determine three position dimensions and time.
Position dimensions are computed by the receiver in
Earth-Centered, Earth-Fixed X, Y, Z (ECEF XYZ)
coordinates. Most receivers compute (and store)
positions in geodetic coordinates (datum WGS-84)
latitude, longitude and height above the ellipsoid
(HAE).

On Mon, 7 Jul 2003 19:38:53 -0400, "Chip Orange"
<acorange@comcast.net> wrote:

>The speed data as it comes from GPS is in knots, not MPH, so could this be
>the explanation (I don't know TomTom).

Well, this depends on the GPS and how you have it set up. If you have
it set up to display nautical miles, then your speed will be in knots;
if it's set up for statute miles, it'll display in statute miles per
hour.

I would guess that "standard" for handheld GPS units sold for land use
(Garmin Etrex, the Magellans that don't have "Marine" in the name,
etc) are all going to come with MPH standard (as opposed to knots).

Me

steve wrote:
>
> On Mon, 7 Jul 2003 18:57:09 -0500, "Blair" <bfonville1@hotmail.com>
> wrote:
>
> >That's ridiculous. Would you mind posting your reference that reports that a
> >GPS receiver's velocity accuracy is dependent on the hills of road? What am
> >I missing here?
>
> You're missing that the speed that a handheld GPS reports is going to
> be based on two simple things. Distance between a pair of fixes, and
> the time it takes to move between those fixes.
>
>

Ref: http://www.aprs.net/vm/gps_cs.htm

GPS Determination of Course and Speed

br Tom Clark, W3IWI

First -- let me describe how your GPS receiver measures position and velocity.
Your receiver tracks (at least) 4 GPS satellites. The DSP tracking loops built into
the receiver have to lock onto two parts of the signal from each satellite -- the 1.023
Mb/s C/A code and the 1575.42 MHz carrier frequency. The dual DSP operation
involves two tracking loops -- a CLL (Code Locked Loop) for the C/A code, and a
PLL (Phase Locked Loop) tracking the carrier.

The CLL produces the timing of the GPS signal WRT (with respect to) the
receiver's internal clock -- this is normally expressed in distance units called a
Pseudo-Range (PR) and it includes the error in the receiver's internal clock added
to the real geometric range of the satellite. Similarly, the PLL measures the carrier
phase rate (i.e. apparent satellite frequency with respect to the receiver's local
oscillator, usually derived from the same crystal oscillator that is used as the
timing clock) -- this is called the Pseudo-Range Rate (PRR) and includes the
frequency error of the receiver's LO and the contribution from the Doppler shifts
associated with all the motions. The Doppler shift includes the vector sum of the
satellite's ~7 km/sec orbital velocity plus the 400 m/sec (at the equator) rotational
velocity of the earth plus your receiver's motions (in a moving car, ~10-50 m/sec).

In early GPS receivers, four PRs from 4 satellites was converted into a 3-D (XYZ,
Lat/Lon/Hgt or whatever) position plus the calibration of the timing bias of your
receiver, and 4 PRRs were converted into a 3-D velocity plus a measurement of
the frequency error of the oscillator. More modern receivers take all the PR+PRR
data from all the N satellites in view for the past T seconds and feeds the 2*N*T
PR+PRR samples it into a single mathematical "black box" (BB) (usually a Kalman
filter) to produce an over- determined estimate of the same 8 parameters. So in
modern receivers, this BB is using both the combination of past & present PRs and
PRRs from many satellites to improve the Position, Velocity & Time (PVT)
estimate. So Paul's statement about velocities being determined by changes in
position is sorta, partially correct, but (when you look at the equations inside the
BB), the measured "apparent Doppler" frequencies are even more important.

Aside #1: Part of this thread asked about the speed capabilities of the various
Garmin receivers. Garmin has had two generic receiver types. The first, including
the GPS-20, GPS-38, GPS-45, GPS-45XL and the original GPS-II used a slow CPU
to do the DSP+BB+ display functions. The DSP supported only two channels of
receiver, which were sequentially multiplexed amongst the various satellites. The
"Brain Dead" CPU apparently did not have enough horsepower to handle a PRR
"bandwidth" more than that associated with the ~100 MPH speed, so these
receivers have a software "clamp" that makes them useless in airplanes.

The newer Garmins (GPS-25, GPS-48, GPS-12, GPS-12XL, GPS-II+, GPS-III etc)
have a LOT more CPU horsepower; my GPS-III uses an i386ex ! As a result,
Garmin has been able to handle up to 12 satellites simultaneously in the DSP, the
BB can handle airliner speeds, and the GPS-III even supports the neat
highways+land masses mapping.

Now returning to the tutorial -- let's answer the speed/velocity error question. The
errors you get in speed/velocity arise from several sources. The two main ones are
the inherent accuracy of the GPS system (your receiver plus the GPS satellites),
and the added noise from the DoD's aggravation called Selective Availability (SA).

To look at the first of these, let's turn SA off and assume that the GPS satellites are
perfect. The GPS signal carrier wavelength is ~20 cm so with a modest SNR, the
PLL in the receiver can see (measure) the carrier phase to about 1 cm (1/20th of a
cycle or ~20 degrees of electrical phase). For simplicity, we assume that we
measure for 1 second, so I can see ~1 cm/sec of velocity for a given satellite. Since
we don't normally think in these units, 1 cm/sec = 36 meters/hour = ~120 feet/hr =
~0.023 miles/hour. To factor in the geometry and the fact that we see multiple
satellites, we multiply this by HDOP (for horizontal speed) or VDOP (for speed);
since HDOP is rarely > 3, this means that the "system" velocity error is rarely >
~0.07 miles/hour. And note that the fact that we are relying on carrier phase rate to
determine speed, we are measuring the relative L-band carrier frequency (i.e.
Doppler offset) to 1/20th of a Hertz!

Now lets look at SA. In essence, the DoD degrades the performance of the orbiting
atomic clocks on the GPS satellites by putting a programmable line-stretcher in the
output of the (10.23 MHz) clock, and diddling the clock with a magic
pseudo-random sequence that only they know. Our amateur measurements have
shown that they jerk the line stretcher over a wide spectrum of time scales,
ranging from a few seconds to ~1/2 hour, but that the long-term average is zero.
Over longer time scales, the variations affect the timing of the clock signals that
GPS transmits (like the 1.023 Mb/s CA code) so our PR measurements are noisy
and we see our apparent position wander. The DoD has "guaranteed" that the
positional errors due to SA will not exceed ~100 meters (3-sigma, horizontal) for
the range of variations they add, when seen with a reasonable number of satellites
(like with HDOP < 3). We have verified that the SA "dither" is independent on the
different satellites, so viewing more than the minimum=4 satellites not only
improves the geometry, but also reduces SA's effects on position. Since the slowest
SA component is ~1/2 hour in duration, averaging your position over a few hours
of time beats SA's effects down.

This thread really was about speed/velocity, so now let's examine those effects. It is
the rapid variations of the SA "clock dither" that do bad things. In measuring the
power spectrum of SA, we have seen that the largest frequency offset we see on a
given satellite is ~1 Hz at L-band, i.e. a velocity error for that satellite of ~20 cm/sec
= 720 meters/hr = 0.45 MPH. Again multiplying by HDOP translates this into a ~1
MPH peak velocity error when several satellites are used to determine your
velocity.

The final point I wish to make concerns speed versus velocity. Here is the dilema --
K9DOG might say "W3IWI stated that SA averages to zero, and yet my GPS
receiver always says I'm moving a few tenths of a MPH when I'm stopped at a
traffic light.".

These two statements are not in conflict! My assertion was that the VECTOR
velocity averages to zero. It may be north for a while, then east, then west, then
south but I come back "home". K9DOG's statement applied to the indicated
SPEED, ignoring the direction. The speed on your receiver is always positive, so it
can't average out the east-vs-west motions.

Now lets consider the case that we are driving west at a steady 60 MPH. When SA
is north/south, the 1 MPH max changes the apparent direction I am moving by 1
part in 60 (i.e. about one degree), but has little effect on my indicated speed. When
SA is contributing in the east-west direction, my indicated speed varies between 59
& 61 MPH, again adding a noise of one part in 60. And the average error is zero! So
Jon was right -- the effect of SA on apparent SPEED is different when moving
than when stopped. Paul didn't say if he was discussing VECTOR VELOCITY or
SPEED, and he is right ONLY if he is discussing 2-D vector velocities.

[For simplicity, the previous discussion assumed the simplistic 2-D case, and it
assumed that the satellite geometry results in a circular error "footprint". In point
of fact, at mid latitude locations in the northern hemisphere, you see GPS satellites
(nearly, on average) equally in both the east and the west. But the 55 degree
inclination for the GPS satellites mean that you have no satellites in a large region
to the north. Hence "HDOP" (which has no NS vs EW distinction) is an imprecise
description of the geometrical effects. If we broke it down into NSDOP vs
EWDOP, we would see that EWDOP < HDOP < NSDOP. I would note that VDOP
is always bigger than HDOP because you only see satellites above you in the upper
hemisphere.]

Aside #2: For those of you who are mathematically inclined, I have just noted that
when your speed is zero, we have a 2D Gaussian error. When viewed as a one-D
scalar, the resulting errors are Rayleigh distributed at zero speed, and become
Gaussian as the speed gets significantly bigger than error radius. When they are
comparible, a Rice distribution results.