GPS Speed Calculation
Harvey Gratt
accurate. Is the Garmin able to obtain this accuracy from the GPS
position estimates considering that they may be noisy and have a time
varying clock drift?
Or does the device somehow make use of Doppler information obtained from
satellite transmissions?
Thanks,
Harvey
Harvey Gratt
since it would only yield speed along the vehicle-satellite line of
sight. I guess then that the position data is accurate enough to yield a
smoothed velocity estimate.
Holger Issle
On Sat, 26 Dec 2009 20:56:32 -0600, Harvey Gratt wrote:
>I guess then that the position data is accurate enough to yield a
>smoothed velocity estimate.
You will at some time figure there is a (one off) significant position
error in the log of your trips. ususally that comes when you enter a
region with poor reception (such as a house) and just sit still in
there. With that you will see the maximum speed being _very_ high,
just good enough to go from that sigle one off point to the real
position. Calculate speed for that position error yourself... you will
figure a pretty good match to the reading on the unit.
In my mind, that can only be by the device doing the same calculation
as you did. I do not see why the doppler speed measurement would
always lead to that same result since that would mean that all (at
least 4) doppler shifts are measured incorrect along the same vector!
--
Ciao,
Holger (GUS-KOTAL, GUS#1100, GRR#51)
90-92 Honda CB400 10 Mm | 93-95 Yamaha TDM 850 26 Mm
95-97 KTM 620 LC4 13 Mm | seit 97 BMW R1100GS 69 Mm (Die Renndrecksau!)
cu @ http://www.issle.de
H@n Zijsp@n
According to my GPSmap 60CSx I once rode Mach 2.5 on my bicycle....
Most of the time, however my Garmin speed is VERY accurate.
Holger Issle
>According to my GPSmap 60CSx I once rode Mach 2.5 on my bicycle....
Cool, what type of bike is that? ;-)
IF you still have a log of that trip, I bet the position logged is WAY
off where you really were.
frijoli
> On Sun, 27 Dec 2009 06:26:40 -0800 (PST), "H@n Zijsp@n" wrote:
>
>> According to my GPSmap 60CSx I once rode Mach 2.5 on my bicycle....
>
> Cool, what type of bike is that? ;-)
> IF you still have a log of that trip, I bet the position logged is WAY
> off where you really were.
I took mine on an airplane once and was clocked at 7826 mph!
It's funny too because it went from 550 to 289, then to
7000+ then back to 550.
:)
H@n Zijsp@n
> On Sun, 27 Dec 2009 06:26:40 -0800 (PST), "H@n Zijsp@n" wrote:
> >According to my GPSmap 60CSx I once rode Mach 2.5 on my bicycle....
>
> Cool, what type of bike is that? ;-)
> IF you still have a log of that trip, I bet the position logged is WAY
> off where you really were.
That was the problem indeed. I had switched of after entering the
building where I work, meaning after loosing satellite contact. I
assume it kept speed and direcion the same as as it behaves in a
tunnel. When I went home at the end of the day the thing was somewhere
in the south of France instead of the Netherlands.
On my way home it sort of hurried back to me. ;-)
Holger Issle
>When I went home at the end of the day the thing was somewhere
>in the south of France instead of the Netherlands.
>On my way home it sort of hurried back to me. ;-)
Pretty quick travel, though :-)
I bet you wished to have had that speed really, didn't you?
Darren Dunham
Yes.
The GPS solution spills out position, velocity, and time information.
Doppler information may only be for line-of-sight, but when you
integrate it over all the satellite angles, you still get good
information.
The unit will then probably take the raw position and velocity figures
and put them into a Kalman filter for calculating what it will display
for a speed measurement.
Even if you were to only use multiple position figures, it would still
work very well at greater speeds (driving or flying) because the error
in position at each measurement will tend to be overwhelmed by the
actual change in position. So the speed calculation becomes quite
accurate.
--
Darren
Gene E. Bloch
simple trigonometry can convert it to speed along the line of travel.
Although that wouldn't work if the slope of the road wasn't known. But
even that can be figured from a vertical component of the Doppler
shift...However, with a car speeding along at 88 ft/sec or so, and a
satellite crawling along at 25000 ft/sec or so, the accuracy might be
insufficient...
As you might guess, I doubt that Doppler is used. I agree more with
what Darren Dunham said, within the limits of my knowledge. All I know
about Kalman is that it's a Hungarian name, at least if you put an
accent on each 'a' :-)
On 12/26/09, Harvey Gratt posted:
--
Gene Bloch 650.366.4267 lettersatblochg.com
H@n Zijsp@n
> Pretty quick travel, though :-)
> I bet you wished to have had that speed really, didn't you?
You can say so! I once was head of security at Fokker and also had a
commerical pilot's license. Fokker was bulding F16's for our dutch
airforce and also de Danish. I had arranged to join on a delivery
flight of a two-seater tot Danmark. It gave the possibility to go
supersonic over the North Sea.
Unfortunately my pregnant wife got ill so I had more important things
to do. I don't blame her, but that was my one and only change to fly
supersonic and even handle the stick myself.
Off topic regards,
H@n Zijsp@n
Darren Dunham
> Although the Doppler effect would indeed be along the line of sight,
> simple trigonometry can convert it to speed along the line of travel.
> Although that wouldn't work if the slope of the road wasn't known. But
> even that can be figured from a vertical component of the Doppler
> shift...However, with a car speeding along at 88 ft/sec or so, and a
> satellite crawling along at 25000 ft/sec or so, the accuracy might be
> insufficient...
From other posts, it appears that most of the speed value does in fact
come from the doppler information. It has less noise than the
position information. Here's some:
http://groups.google.com/group/sci.geo.satellite-nav/browse_thread/thread/4ab44f4f56e5ab78/882706ddb6739829?q=#882706ddb6739829
http://groups.google.com/group/sci.geo.satellite-nav/browse_thread/thread/9e66ba9651c794aa/81def8a0517cb2ca?lnk=gst&q=doppler+kalman#81def8a0517cb2ca
> As you might guess, I doubt that Doppler is used. I agree more with
> what Darren Dunham said, within the limits of my knowledge. All I know
> about Kalman is that it's a Hungarian name, at least if you put an
> accent on each 'a' :-)
Such filters are discussed above (and on the OP's question of how it
correlates the information to reduce the impact of noise). Just
imagine that it's some math that is looking at both the position and
the velocity information coming from the receiver and correlating
their information over time to make the reported answer more accurate.
--
Darren
Harvey Gratt
It still seems to me that Doppler would only provide velocity info along
the LOS from the satellites to the receiver, It also appears that one
would need to know the satellite velocities accurately and one would
also need to be able to calculate angle rates of the LOS to the
satellites in order to get the transverse velocity components.
It's not clear how much this would help with the vehicle velocity
estimate since the angle rate calculation would be noisy - although it
does contain some added information by way of the range rate (Doppler)
component.
While all this information would be used as the observables in a Kalman
Filter (actually, an Extended Kalman Filter(EKF) ), if the derived
transverse velocities (obtained from LOS angle rate info)is too noisy,
the EKF will put little weighting on it.
I'm guessing that this would only be used in advanced (military)
applications utilizing better (more expensive) hardware, not in civilian
use.
Thanks for the comments,
Harvey
Gene E. Bloch
Thanks for the references. I stand informed and corrected.
I admit that I'm not going to buy Gelb or Grewal & Andrews, however :-)
Gene E. Bloch
The velocity of the car along its direction of travel is the component
of the line-of-sight velocity due to the car's motion divided by the
cosine of the angle between the satellite's direction and the car's
direction of motion.
Marc Auslander
>
> The velocity of the car along its direction of travel is the component
> of the line-of-sight velocity due to the car's motion divided by the
> cosine of the angle between the satellite's direction and the car's
> direction of motion.
>
> --
> Gene Bloch 650.366.4267 lettersatblochg.com
I don't think they use just one doppler shift. Rather, think of this
as a system of equations for time, x, y, z, dx, dy, dz using both the
sattelite time delays and doppler shifts. I expect they kalman filter
the thing since the solution is overdetermined if you have more than
four sattelites. In the end you get true velocity - that is speed in
the direction of travel.
Fred McKenzie
Harvey Gratt <hgr...@verizon.net> wrote:
Harvey-
When you first turn on your GPS, it downloads a table of orbital
parameters for all satellites in the constellation. This establishes
the exact locations of the satellites at any given time. Your GPS also
synchronizes its time with the atomic clocks in the satellites
It is my understanding that GPS position calculations are based on
triangulation using time-of-arrival of signals from all visible
satellites.
Then, a position calculation is made each second. Knowing the
difference in location since the previous calculation, speed can be
calculated.
Assuming that the same errors (doppler, et cetera) will exist for
several consecutive locations, that the GPS clock drifts very slowly,
and that speed is relatively constant, the calculation can be quite
accurate.
Fred
Harvey Gratt
O.K., I've looked at several of the references and have given this some
more thought.
Since one has access to at least 4 satellites, as some have stated,
there should be some Doppler info for all three vehicle velocity
components. As Gene Bloch has pointed out, if one can calculate a unit
vector representing the vehicle direction of motion (assume Cartesian
components), then the dot product of the vehicle velocity along this
"track" with the unit LOS vector to a given satellite, is the range rate
measured by the Doppler shift. The vehicle velocity magnitude could then
be calculated from the Doppler velocity component and the enclosed angle
as previously posted.
What is not clear (to me anyway) is how accurate the "track" has to be.
Conversely, if a sufficiently accurate "track" is calculated from
smoothed position data, could an accurate velocity calculation be
obtained by appropriately differentiating the smoothed position data
(thus no real need for Doppler info).
Still, within the context of using a full blown EKF, the additional
Doppler info utilizing the derived vehicle velocity components as
outlined above (as pointed out by Gene) might be an effective set of
additional measurements. I still think this would be have some drawbacks:
1, EKF's can have issues when poorly initialized
2. Computationally complex - especially if one chooses to update the EKF
in the measurements natural coordinate frame (spherical) and then
extrapolate in the local level Cartesian frame (a lot of coordinate
frame transformations are needed for the states (position, velocity,
clock drifts, equivalent spherical states) and covariance matrices
3. May not be as robust as algebraically solving 4 psuedo-range/time
equations as originally outlined
Thanks for all the comments,
Harvey
Gene E. Bloch
Of course I agree with you. I was just trying to point out that the
basic idea is simple, and so I left out such complicating (but of
course necessary) details as other satellite vectors and Dopplers.
Harvey Gratt then ran with our ideas; I think his reply to your same
post is interesting and informative. And we're all apparently on the
same wavelength (sorry!) now.
Bu
wrote:
Just to add my five cents.
I do not believe that commercial everyday GPS receivers use the
doppler effect to calculate the speed.
At last not the doppler from the carrier frquency. If this was the
case the receiver needs to be very complex. Besides processing the
data (demodulating the high frequency signal) then it also needs to
establish the frequency shift for every satellite based on the speed.
Moreover it needs to establish the direction vector and the vector to
every individual locked GPS satellite and convert all this data.
As 'byproduct' the Kalman filter establishes the change in change of
the pseudo code of every satellite. And this is converted into speed.
And i would not call this doppler effect.
Bu
Darren Dunham
> I do not believe that commercial everyday GPS receivers use the
> doppler effect to calculate the speed.
> At last not the doppler from the carrier frquency. If this was the
> case the receiver needs to be very complex. Besides processing the
> data (demodulating the high frequency signal) then it also needs to
> establish the frequency shift for every satellite based on the speed.
It already has to do this. It wouldn't be able to receive the signal
unless it corrected for the doppler. That's why a GPS with no
position info can take a while to lock on. Besides having to shift
the code to match phase in the correlator, it has to shift the doppler
correction as well. This "2D" search can take much longer than a
simple "1D" code space search. Once the signal is locked-on, the
doppler correction is maintained with a PLL.
> Moreover it needs to establish the direction vector and the vector to
> every individual locked GPS satellite and convert all this data.
Yes. But since it has to do this to receive the data in the first
place, this isn't a hardship.
--
Darren
Mike Coon
> ... Once the signal is locked-on, the
> doppler correction is maintained with a PLL.
How is that possible, given that 4-12 satellites are being received, each
with its own, different, doppler shift?
Mike.
--
If reply address is invalid, remove spurious "@" and substitute "plus"
where needed.
Thibaud Taudin Chabot
> Darren Dunham wrote:
>> ... Once the signal is locked-on, the
>> doppler correction is maintained with a PLL.
>
> How is that possible, given that 4-12 satellites are being received, each
> with its own, different, doppler shift?
>
> Mike.
difference related to its own radiofrequency it would be a veeeeeery
small relative frequency shift.
Why not the simple calculation using the fix every say 2 seconds?
Mike Lane
Because it would be far too inaccurate. A speed of (say) 30 mph is about 13
metres/second. If the gps position error is around 10 metres (not uncommon)
you can calculate the speed error that would result.
--
Mike Lane
UK North Yorkshire
email: mike_lane at mac dot com
Mike Coon
That assumes that the error (or uncertainty) is varying. If it were constant
the speed calculation would not be impacted. So it is the variability of the
error that matters. And then there is averaging...
Mike Lane
> Mike Lane wrote:
>> Thibaud Taudin Chabot wrote on Jan 5, 2010:
>>> Why not the simple calculation using the fix every say 2 seconds?
>>
>> Because it would be far too inaccurate. A speed of (say) 30 mph is
>> about 13 metres/second. If the gps position error is around 10 metres
>> (not uncommon) you can calculate the speed error that would result.
>
> That assumes that the error (or uncertainty) is varying. If it were constant
> the speed calculation would not be impacted. So it is the variability of the
> error that matters. And then there is averaging...
>
Of course the error varies! If it were constant it could be corrected.
Garmins EPE accuracy figure of 10 metres means 50% of the readings will lie
within a circle of radius 10 metres centred on your true position. They may
be even further away see:
http://gpsinformation.net/main/errors.htm
As for averaging - on a moving platform? Please...!
Mike Russell
> Darren Dunham wrote:
>> ... Once the signal is locked-on, the
>> doppler correction is maintained with a PLL.
>
> How is that possible, given that 4-12 satellites are being received, each
> with its own, different, doppler shift?
>
> Mike.
A PLL per receiver. Phase lock loops are common circuit elements - for
example every FM receiver uses one to demodulate the audio signal.
--
Mike Russell - http://www.curvemeister.com
Mike Coon
> A PLL per receiver. Phase lock loops are common circuit elements -
> for example every FM receiver uses one to demodulate the audio signal.
Very true: *one*. Some radios even say "PLL" on the case (though one wonders
how many people know its relevance!). It would be a different matter trying
to run twelve PLLs tracking twelve frequencies very close to each other and
also shifting about as the geometry changes. I'm not saying it's impossible;
I just don't believe it's done, despite the link recently cited (which also
seemed to think that the doppler was due to the receiver whereas the
satellites travel much faster).
Darren Dunham
> Very true: *one*. Some radios even say "PLL" on the case (though one wonders
> how many people know its relevance!). It would be a different matter trying
> to run twelve PLLs tracking twelve frequencies very close to each other and
> also shifting about as the geometry changes.
I guess I don't see why it's more difficult to do it x12. It's just a
little bit more processing power. You don't have to have a separate
chip for each PLL you want to use.
> I'm not saying it's impossible;
> I just don't believe it's done, despite the link recently cited (which also
> seemed to think that the doppler was due to the receiver whereas the
> satellites travel much faster).
See this thread where folks mention that even the cheapest garmin
units do it this way. It's got a lot of good discussion.
--
Darren
Bu
<darren...@gmail.com> wrote:
>On Jan 5, 2:45�pm, "Mike Coon" <Mike@@mjcoon.+.com> wrote:
>
>> Very true: *one*. Some radios even say "PLL" on the case (though one wonders
>> how many people know its relevance!). It would be a different matter trying
>> to run twelve PLLs tracking twelve frequencies very close to each other and
>> also shifting about as the geometry changes.
>
>I guess I don't see why it's more difficult to do it x12. It's just a
>little bit more processing power. You don't have to have a separate
>chip for each PLL you want to use.
Keep in mind that you do not only need a PLL per channel but also a
very accurate/stable center frequency. The digitized difference
between the PLL frequency and the center frequency is the doppler. All
in all very complex and not needed (as the Kalman filter provides the
speed as a 'side' product.
Bu
You
Mike Russell <grou...@MOVEcurvemeister.com> wrote:
> A PLL per receiver. Phase lock loops are common circuit elements - for
> example every FM receiver uses one to demodulate the audio signal.
> --
> Mike Russell - http://www.curvemeister.com
Actually NO, every Fm Receiver does NOT use a PLL to demodulate the
audio. You apparently have never heard of a "Discriminator Circuit"
which was the accepted way to recover audio from Fm signals for about 80
years.....
Mike Russell
I stand corrected, then. Which tube does that circuit use, LOL?
Thibaud Taudin Chabot
not to find the speed.
Just switch your garmin on and stay in the same place. If you have trace
on you will see that your gps seems to move. If you look at the speed
you'll also see some speed. This is ofcourse impossible because you are
staying on the same spot, so there is no doppler speed.
This eefect is because the small inaccuracies of the measurements. Your
gps thinks it is at each measurement in a slightly different spot. And
because of that it can calculate a speed.
Thibaud
Darren Dunham
> Keep in mind that you do not only need a PLL per channel but also a
> very accurate/stable center frequency.
That master frequency is the GPS time solution.
> The digitized difference
> between the PLL frequency and the center frequency is the doppler. All
> in all very complex and not needed (as the Kalman filter provides the
> speed as a 'side' product.
It's not needed if the only reason it were there were to produce a
speed output. But it's needed as part of the frequency correction to
gather the GPS signal. Since it's already there, reading the actual
frequency difference isn't much harder, and that gets dumped into the
Kalman as additional data. Having the doppler speed inputs there
reduce the noise in the position output.
--
Darren
Dan Anderson
> There is a simple test to find out whether your garmin uses doppler or
> not to find the speed.
> Just switch your garmin on and stay in the same place. If you have trace
> on you will see that your gps seems to move. If you look at the speed
> you'll also see some speed. This is ofcourse impossible because you are
> staying on the same spot, so there is no doppler speed.
You are not moving only if you are at one of the poles. When you
are standing still relative to the Earth, you are actually
moving very fast in most areas on the planet underneath
the GPS satellites. Almost everything in the system is always
in motion around the center of the Earth.
--
Dan
Personal: www.gpsmap.net
Business:
Western Maps LLC
www.westernmaps.us
Reinhard Zwirner
IMHO 6AK8/6LD12/6T8/DH719 or 6AL5/6D2.
HTH ;-)
Reinhard
Retired VIP
<noE...@noServer.net> wrote:
>Thibaud Taudin Chabot wrote:
>> There is a simple test to find out whether your garmin uses doppler or
>> not to find the speed.
>> Just switch your garmin on and stay in the same place. If you have trace
>> on you will see that your gps seems to move. If you look at the speed
>> you'll also see some speed. This is ofcourse impossible because you are
>> staying on the same spot, so there is no doppler speed.
>
>You are not moving only if you are at one of the poles. When you
>are standing still relative to the Earth, you are actually
>moving very fast in most areas on the planet underneath
>the GPS satellites. Almost everything in the system is always
>in motion around the center of the Earth.
Hmmm....then why doesn't my GPS show my speed as several thousand
miles per hour? No Taudin Chabot is the only one using his head. They
don't use Doppler because the satellites are moving in different
directions and at different speeds, couple that with the fact that you
are moving as the earth turns under the satellites at a speed that
varies depending on how far you are from the equator as well as what
direction you are driving and at what speed. You can see that trying
to use the Doppler shift of the different carrier frequencies would
become impossibly complicated.
Also using a Phase Lock Loop (PLL) circuit to try to determine Doppler
shift would be next to impossible. A PLL circuit jitters a lot, it
works on the error between a frequency standard and the frequency
generated by it's Voltage Controlled Oscillator (VCO) and that error
changes moment by moment as the VCO frequency is corrected by the
circuit.
A GPS determines speed as it determines position. The rate of
position change = speed.
Billyb97113
"Thibaud Taudin Chabot" <tch...@dds.nl> wrote in message
news:4b460636$0$22940$e4fe...@news.xs4all.nl...
> Mike Lane schreef:
>> Thibaud Taudin Chabot wrote on Jan 5, 2010:
>>
>>> Mike Coon schreef:
>>>> Darren Dunham wrote:
>>>>> ... Once the signal is locked-on, the
>>>>> doppler correction is maintained with a PLL.
>>>> How is that possible, given that 4-12 satellites are being received,
>>>> each with its own, different, doppler shift?
>>>>
>>>> Mike.
>>> I don't beleive it uses doppler shift. If you look at the frequency
>>> difference related to its own radiofrequency it would be a veeeeeery
>>> small relative frequency shift.
>>> Why not the simple calculation using the fix every say 2 seconds?
>>
>> Because it would be far too inaccurate. A speed of (say) 30 mph is about
>> 13 metres/second. If the gps position error is around 10 metres (not
>> uncommon) you can calculate the speed error that would result.
>>
with your comment that a GPS might be inaccurate 10's of meters. But the
real question is how repeatable is it, even if it is wrong. Over a 2 second
interval it is very repeatable, otherwise your indicated location would be
jumping all over. The repeatability gradually drifts over dozen of seconds
or minutes, but if you are doing your speed calculation every second or two
the drift will not show in each reading. I really don't think they use
Doppler shift in a GPS for speed calculations.
-bill
Mike Lane
> I really don't think they use
> Doppler shift in a GPS for speed calculations.
>
What you think happens is irrelevant.
The article pointed to here (among others) explains how Doppler measurements
are used to compute velocity:
http://gauss.gge.unb.ca/papers.pdf/ionntm2004.serrano.pdf
Thibaud Taudin Chabot
> Billyb97113 wrote on Jan 8, 2010:
>
>> I really don't think they use
>> Doppler shift in a GPS for speed calculations.
>>
>
> What you think happens is irrelevant.
>
> The article pointed to here (among others) explains how Doppler measurements
> are used to compute velocity:
> http://gauss.gge.unb.ca/papers.pdf/ionntm2004.serrano.pdf
>
>
There I explain very clear that doppler cannot be the way to find the
speed. Simple test, simple proof.
Mike Lane
You gave no proof; you just made an assertion that a gps gives a false
velocity reading when stationary. Mine does not. When I am stationary, any
gps unit I have used reads zero velocity.
Fred McKenzie
Mike Lane <mike.lan...@ntlworld.co.uk> wrote:
> The article pointed to here (among others) explains how Doppler measurements
> are used to compute velocity:
Mike-
Use of Doppler for velocity measurements is well known. One example is
use of color shift to determine velocity of stars.
However that simple fact does not prove Doppler is used by GPS for
velocity calculations! It is just one of several sources of error that
must be accounted for when making a position calculation based on
time-of-arrival of signals from the visible satellites.
Fred
Lon
> In article <0001HW.C76C88BB...@news.virginmedia.com>,
> Mike Lane <mike.lan...@ntlworld.co.uk> wrote:
>
>> The article pointed to here (among others) explains how Doppler measurements
>> are used to compute velocity:
>
> Mike-
>
> Use of Doppler for velocity measurements is well known. One example is
> use of color shift to determine velocity of stars.
Color [red] shift is not used to measure velocity, it is used to measure
distance.
Gene E. Bloch
Incorrect.
1. Look into how most of the now known extrasolar planets have been
found.
2. For generations, red (and blue) shifts have been used to measure
stellar masses based on the orbital velocities of double stars.
3. Distances to far galaxies are measured by the correlation between
velocity and distance (the Hubble constant). It is the velocity which
is measured directly from the redshift, from which the distance is then
derived. The distances originally were measured (for the closest
galaxies) by other means, such as the brightness of known star types,
and the researchers noticed serendipitously the correlation between
those distances and the measured velocities. Only then could the
velocity be taken as a measure of distance.
You
Lon <lon.s...@comcast.net> wrote:
Uhhh, No, Red Shift is Velocity... High School Physics.... Distance is
derived information from the velocity..... Red shift IS Doppler...
Lon
> On 1/08/10, Lon posted:
>> Fred McKenzie wrote:
>>> In article <0001HW.C76C88BB...@news.virginmedia.com>,
>>> Mike Lane <mike.lan...@ntlworld.co.uk> wrote:
>>>
>>>> The article pointed to here (among others) explains how Doppler
>>>> measurements are used to compute velocity:
>>>
>>> Mike-
>>>
>>> Use of Doppler for velocity measurements is well known. One example
>>> is use of color shift to determine velocity of stars.
>
>> Color [red] shift is not used to measure velocity, it is used to
>> measure distance.
>
> Incorrect.
>
> 1. Look into how most of the now known extrasolar planets have been found.
Quite familiar with the mission and the write ups. Might even know
exactly where the data is stored.
>
> 2. For generations, red (and blue) shifts have been used to measure
> stellar masses based on the orbital velocities of double stars.
You must be talking about mayfly generations.
>
> 3. Distances to far galaxies are measured by the correlation between
> velocity and distance (the Hubble constant). It is the velocity which is
> measured directly from the redshift, from which the distance is then
> derived. The distances originally were measured (for the closest
> galaxies) by other means, such as the brightness of known star types,
> and the researchers noticed serendipitously the correlation between
> those distances and the measured velocities. Only then could the
> velocity be taken as a measure of distance.
Ah, but not all redshift is velocity born.
Gene E. Bloch
Expect a reply from Lon :-)