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velocity calculations from a GPS

 
 
DWilson
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      11-30-2007, 07:22 AM
Hi all,
Does anyone know internally how the GPS unit derives the velocity
measurements?
Is it straight differencing of subsequent lat/long positions or is it via
some sort of Doppler
on the received frequency of the L1 signal?

I have heard the latter, but that would not explain why the velocity
measurments tend to get noisier as soon as you stop, but the signal to noise
ratio improves rapidly once you are moving, even if only at a walking pace.
That would indicate differencing with a possible Kalman filter type
correction.

Also the differential velocity for Doppler is, of course, extremely small
for many applications (e.g. walking/car/marine).


 
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SamSvL
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      11-30-2007, 09:26 AM
Hi Dave,

I guess the answer is yes, yes. Although not confirmed by the manufacturer
I am pretty sure the some receivers do it by differencing position while
others use either delta carrier (delta over 1 sec, or shorter) or Doppler
(which usually is nothing more than delta cattier over 20msec, 1 nav bit.

I found his by calculating velocity from delta carrier and/or Dopper
and comparing the results by the receiver calculated values.

Internal receiver filtering (whenever possible I switch it off) obscures
the comparison indeed.

Hope this helps,

Sam



"DWilson" <(E-Mail Removed)> wrote in
news:fiodoj$5e4$(E-Mail Removed):

> Hi all,
> Does anyone know internally how the GPS unit derives the velocity
> measurements?
> Is it straight differencing of subsequent lat/long positions or is it
> via some sort of Doppler
> on the received frequency of the L1 signal?
>
> I have heard the latter, but that would not explain why the velocity
> measurments tend to get noisier as soon as you stop, but the signal to
> noise ratio improves rapidly once you are moving, even if only at a
> walking pace. That would indicate differencing with a possible Kalman
> filter type correction.
>
> Also the differential velocity for Doppler is, of course, extremely
> small for many applications (e.g. walking/car/marine).
>
>
>


 
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claudegps
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      11-30-2007, 12:18 PM
On 30 Nov, 08:22, "DWilson" <(E-Mail Removed)> wrote:
> Hi all,
> Does anyone know internally how the GPS unit derives the velocity
> measurements?
> Is it straight differencing of subsequent lat/long positions or is it via
> some sort of Doppler
> on the received frequency of the L1 signal?
>
> I have heard the latter, but that would not explain why the velocity
> measurments tend to get noisier as soon as you stop, but the signal to noise
> ratio improves rapidly once you are moving, even if only at a walking pace.
> That would indicate differencing with a possible Kalman filter type
> correction.
>
> Also the differential velocity for Doppler is, of course, extremely small
> for many applications (e.g. walking/car/marine).


As far as I know, velocity measurementes are derived from both
depending on the situations.
Doppler is absolutely the most used for "relatively high" speeds, ok
for car application for example.
If the speed is below a thresold (like in pedestrian navigation) there
is many filtering (like static filters) and the velocity is derived
also from delta-position.
The contrubutes(doppler or delta-pos) can be also weighted to have
informations from both source.
Filters are quite complex and it's not possible to have a unique
answer to your question :-)

Hope to have helped

claudegps
www.claudegps.altervista.org
 
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utilsea@gmail.com
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      11-30-2007, 05:30 PM
Hi,
at the beginning of GPS the speed was derivated from the postion.
But now doppler is used (except for RTK receiver) the algorithm is
more or less using the position and time and recomputing the doppler
for each satellite then make the difference with measured and computed
value.

http://utilsea.free.fr


 
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Sam Wormley
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      11-30-2007, 05:51 PM
DWilson wrote:
> Hi all,
> Does anyone know internally how the GPS unit derives the velocity
> measurements?
> Is it straight differencing of subsequent lat/long positions or is it via
> some sort of Doppler
> on the received frequency of the L1 signal?
>
> I have heard the latter, but that would not explain why the velocity
> measurments tend to get noisier as soon as you stop, but the signal to noise
> ratio improves rapidly once you are moving, even if only at a walking pace.
> That would indicate differencing with a possible Kalman filter type
> correction.
>
> Also the differential velocity for Doppler is, of course, extremely small
> for many applications (e.g. walking/car/marine).
>
>


Ref: Misra & Enge "GPS: Signals, Measurements, and Performance" (2001)

Sec. 5.2.1 (pgs 196-197) Velocity Estimation

"The relative motion of a satellite and the user results in changes in
the observed frequency of the satellite signal. This Doppler shift is
measured routinely in the carrier tracking loop of a GPS receiver
[Section 9.6]. Given the satellite velocity, the Doppler shift can be
used to estimate the user velocity. The Doppler shift, or equivalently,
the range rate [Section 1.3.3], can be written as a projection of the
relative velocity vector on the satellite line-of-sight vector. The
measurement, however, is biased by the receiver clock bias rate (i.e.,
frequency offset), and what's actually measured is the pseudorange
rate.

"The delta pseudoranges obtained from carrier phase measurements are
proportional to the average pseudorange rates or the line-of-sight
velocity of the user relative to the satellite over the time interval.
The model for pseudorange rates can be obtained by differentiating
(5.1). It is left as an exercise to show that

[equation 5.28 is true]

where v_sup(k) [a vector quantity] is the satellite velocity vector,
known from the navigational message broadcast by the satellite; v is
the user velocity vector, to be estimated. Both v_sup(k) and v are
expressed in the ECEF coordinate frame. The user-to-satellite unit
vector 1_sup(k) is determined from an estimate of the user position;
b_dot is the bias of the receiver clock (m/s), and the
epsilon_sub_phi_sup(k) denotes the combined error doe to changes during
the measurement interval in the satellite clock, ionosphere and
troposphere. Note that the velocity of an object attached to the earth
is zero in the ECEF coordinate frame.

"The principal source of error in (5.28) throughout the 1990s was the
satellite clock frequency dithering due to SA. Now with SA gone, the
remaining errors arise from changes in the ionospheric and tropospheric
delays and in multipath, and are generally small. Problems, however,
can arise if the user dynamics are excessive. The delta ranges give
only average velocity over a time interval. High accelerations and
jerks would clearly be problematic. The PPS performance specifications
for velocity estimation (0.1 m/s rms in any direction; 0.2 m/s 2drms)
are based on a constant-velocity scenario [JPO(1991)].

"Equation (5.28) is linear in user velocity components, and can be
rewritten...

the combined set of measurements from K satellites can be written as a
set of equations compactly in matrix notation as

[equation 5.29]

where matrix G characterizes the user-satellite geometry, as defined
previously (5.10). It is interesting that the problem of estimation of
user velocity based on pseudorange rates is identical in structure to
that of estimation of user position from pseudoranges (5.9). A
least-squares solution and the DOP parameters can be defined, as
before, and related to the rms error in these estimates"
 
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utilsea@gmail.com
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      12-01-2007, 10:13 AM
Hi,
solution used by the manufacturer that I know today (I know there is
some other solutions) is not adding a supplementary layer of
complexity but is very simple.
Using the same set of raw data, first of all compute a position
solution then using the position obtained, compute the doppler value
for each satellite on the obtained position to get the theoritical
doppler on this position as a fix position finaly make the difference
between computed and measured value (still doppler due to the rover
movement) and use these values in the same matrix than the used one
for the position to get speed in the 3 axis.
as you can see, only the current solution is used in this method.

In fact, with the GPS using the same frequency for all sv, accuracy is
a little bit less than with GLONASS who is using a different frequency
for each satellite.

After light filtering, accuracy obtained by this method is about 0.1 m/
s.

http://utilsea;free.fr



 
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Alan Browne
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      12-01-2007, 01:33 PM
DWilson wrote:
> Hi all,
> Does anyone know internally how the GPS unit derives the velocity
> measurements?
> Is it straight differencing of subsequent lat/long positions or is it via
> some sort of Doppler
> on the received frequency of the L1 signal?


Doppler. Even when you're standing still, the sats are moving quite
fast. I seem to recall readings in the 100's - low 1000's of Hz for
most sats in view while the receiver was "stationary". Why the quotes?
Well the earth is turning too (unless you're at the poles where there
would be no receiver v component).
 
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Alan Browne
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      12-01-2007, 01:35 PM
http://www.gps-forums.net/(E-Mail Removed) wrote:
> Hi,
> at the beginning of GPS the speed was derivated from the postion.


It evolved?

Really the whole design of GPS is predicated on primary measurements of
PVT (position, velocity, time). Eg: they are each independently
measured by the receiver, not derived.
 
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Alan Browne
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      12-01-2007, 01:38 PM
(E-Mail Removed) wrote:
> Hi,
> solution used by the manufacturer that I know today (I know there is
> some other solutions) is not adding a supplementary layer of
> complexity but is very simple.
> Using the same set of raw data, first of all compute a position
> solution then using the position obtained, compute the doppler value
> for each satellite on the obtained position to get the theoritical
> doppler on this position as a fix position finaly make the difference


Absolutely false. You can't even *track* a satellite without applying
the Doppler shift and offsetting the correlator accordingly for each
sat. This applies to the first 1,2 and 5 channel receivers as much as
to any GPS receiver.
 
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utilsea@gmail.com
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      12-02-2007, 03:43 PM
Hi,
like you said the shift is computed within the correlator for internal
use and not (always) outputed by this one to the PVT. It's why in
those few vulgarisation lines I do not mention this. The solution
explained here is alway working even with RINEX files on wich you
don't have have the doppler value.



 
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