Re: Longitude or Right ascension

Hi Cedric

I was drawing your explanation in a paper and I realized that you have
condisered the motion of the ascending node only due tk for correction.
However, I think we must consider it also since from the begining,
because the orbit moves not only between toe and currentGPSTime but also
from week start (0) to toe.

This would give

Omegak = Omega0 + (RAANRate - OmegaDot_E)*tk - OmegaDot_E*toe + RAANRate*toe

Note the extra term RAANRate*toe in the equation...

I deduced this using the definition of Omega0 as
the longitude of orbit plane wrt ECEF at the week start
(both at week start), which makes sense.

However, if you add  Omega0' = Omega0 + RAANRate*toe you have the
longitude of the orbit plane at the reference time but wrt to ECEF of
start of week (something crazy), but you would then reach the ICD equation:

Omegak = Omega0' + (RAANRate - OmegaDot_E)*tk - OmegaDot_E*toe

What do you think?
Is that the definition for Omega0 in the ICD?

Regards,


Msc. Eng. Gustavo Baldo Carvalho
ZARM - Uni-Bremen - Room 1210
Am Fallturm, 28359 Bremen
www.zarm.uni-bremen.de
Tel:(0049)-(0)421-218-4796
Fax:(0049)-(0)421-218-2521

Cedric wrote:
> Hi Gustavo,
> 
> The term Omega0 is the longitude of ascending node at the weekly epoch,
> which means the angle between the orbital plane and the ECEF x-axis at the
> beginning of the GPS week (GPS seconds = 0). It is expressed in ECEF, not
> inertial, coordinates.
> 
> Maybe an easy way to look at this is the following:
> - consider that Omega0 is the longitude of the ascending node at GPS Second
> = 0
> 
> - then Omega' = Omega0 - OmegaDot_E * toe is the longitude of ascending node
> at the time of ephemeris toe (simple rotation by toe seconds)
> 
> - then Omega'' = Omega' - OmegaDot_E * tk = Omega' - OmegaDot_E *
> (currentGPSTime - toe) is the longitude of ascending node at the current GPS
> time (here we just did an additional rotation by tk seconds)
> 
> - in an unperturbed orbit, the term OmegaDot (RAAN rate) would be zero, and
> Omega'' would be equal to the Omegak given in the ICD. However, because the
> RAAN rate is not quite zero, we have to further correct the longitude at
> currentGPSTime: Omegak = Omega'' + RAANRate * (currentGPSTime - toe)
> 
> I hope this helps,
> 
> Cedric
> 
> 
> 
> 
> 
> 
> 
> 
> 
> ______________________________________________
> Dr. Cedric Seynat
> Satellite Navigation Systems Engineer
> GPSat System Australia Pty. Ltd.
> Suite1, 22 Aberdeen Road
> MacLeod, Victoria
> Australia 3085
> Ph.: +61(0)3 9455 0041
> Fax: +61(0)3 9455 0042
> www.gpsatsys.com.au
> 
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Gustavo
> Sent: Tuesday, 12 September 2006 5:32 AM
> To: [email protected]
> Subject: [OpenSource_GPS] Longitude or Right ascension
> 
> Dears,
> 
> I have a very basic but important question.
> 
> In GPS-ICD the definition for the term Omega0
> is: Longitude of ascending node
> 
> Well, from that definition I understand that
> Omega0 is then the angle in equator from X-ECEF
> to ascending node at ref time t0 (definition of Longitude).
> 
> However, when wee look at the equation for the corrected longitude:
> 
> Omega = Omega0 + (Omegadot - Omegadot_E)*tk - Omegadot_E*t0
> 
> we see a term Omegadot_E*t0 which only makes sense if Omega0 is
> a right ascension (angle in the equator between X-ECI and ascending
> node) instead of longitude.
> 
> See that Long0 = RA0 - Omegadot_E*t0
> 
> Using proper names...
> Long = RA0 + (Omegadot - Omegadot_E)*tk - Omegadot_E*t0
>      = (RA0 - Omegadot_E*t0) + (Omegadot - Omegadot_E)*tk
>      = Long0 + (Omegadot - Omegadot_E)*tk
> 
> See that if we got from GPS message is Long0 (instead of RA0), the
> equation is quite different...
> By the way, in Hofmann's book (GPS Theory and practice pg 38), he uses
> the term Right ascension instead of Longitude...
> 
> Can anyone clarify that?
> 
> Msc. Eng. Gustavo Baldo Carvalho
> ZARM - Uni-Bremen - Room 1210
> Am Fallturm, 28359 Bremen
> www.zarm.uni-bremen.de
> Tel:(0049)-(0)421-218-4796
> Fax:(0049)-(0)421-218-2521
> 
> [email protected] wrote:
> 
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>>Today's Topics:
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>>   1. Building a GPS Receiver (Redefined Horizons)
>>   2. Re: Building a GPS Receiver (Andrew Greenberg)
>>   3. Re: Building a GPS Receiver (David Bengtson)
>>
>>
>>----------------------------------------------------------------------
>>
>>Message: 1
>>Date: Wed, 3 May 2006 14:36:59 -0700
>>From: "Redefined Horizons" <[email protected]>
>>Subject: [OpenSource_GPS] Building a GPS Receiver
>>To: [email protected]
>>Message-ID:
>>	<[email protected]>
>>Content-Type: text/plain; charset="iso-8859-1"
>>
>>I am a Land Surveyor and software developer that is very interested in
>>building a GPS receiver that uses an off-the-shelf commercial GPS receiver
>>and open source software.
>>
>>I had a couple questions for this mailing list. I'm hoping to determine if
>>this is a project that I can tackle.
>>
>>[1] Is there any active development on a "homegrown" GPS receiver? If so
>>which project? Would I be able to help with those development efforts?
>>
>>[2] I'm not very familiar with low-level programming and digital
>>electronics. I do know some basic prinicples of logic circuit design and
>>dabble in the C programming language. I do have a lot of experience with
>>high-level programming languages, and lots of time using survey-grade GPS.
> 
> I
> 
>>am a Linux user, but I'm no Unix pro. I am willing to learn new skills,
> 
> but
> 
>>am I getting in over my head if I try to build my own GPS receiver?
>>
>>Thanks,
>>
>>Scott Huey
>>
>>P.S. - If I can get this thing to work I will be developing GPS data
>>collection software for mobile devices. This would be released back to the
>>community under an open source license. (Probably GPL.)
>>-------------- next part --------------
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>>------------------------------
>>
>>Message: 2
>>Date: Wed, 03 May 2006 15:34:01 -0700
>>From: Andrew Greenberg <[email protected]>
>>Subject: Re: [OpenSource_GPS] Building a GPS Receiver
>>To: [email protected]
>>Message-ID: <[email protected]>
>>Content-Type: text/plain; charset=ISO-8859-1
>>
>>Hi Scott,
>>
>>
>>
>>>I am a Land Surveyor and software developer that is very interested in
>>>building a GPS receiver that uses an off-the-shelf commercial GPS
>>>receiver and open source software.
>>
>>
>>If you're talking about an OEM GPS receiver board, then it's called the
>>GPL-GPS project, and you can read about it on our website:
>>
>> http://gps.psas.pdx.edu/
>>
>>Feel free to join the GPL-GPS mailing list if this is what you're
>>interested in.
>>
>>
>>
>>>[1] Is there any active development on a "homegrown" GPS receiver? If so
>>>which project? Would I be able to help with those development efforts?
>>
>>
>>There's lots of "homegrown" GPS projects out there. Most require a PC to
>>operate. For example, see the OpenSource GPS project at:
>>
>> http://home.earthlink.net/~cwkelley/
>>
>>And here's a list of most of the open source projects:
>>
>> http://gps.psas.pdx.edu/OpenGnssProjects
>>
>>There's unfortunately no one working on a embedded open hardware GPS
>>receiver... it's a project we'd like to do with GPL-GPS, but it's a lot
>>of RF work and a pretty expensive endeavor as well.
>>
>>
>>
>>>[2] I'm not very familiar with low-level programming and digital
>>>electronics. I do know some basic prinicples of logic circuit design and
>>>dabble in the C programming language. I do have a lot of experience with
>>>high-level programming languages, and lots of time using survey-grade
>>>GPS. I am a Linux user, but I'm no Unix pro. I am willing to learn new
>>>skills, but am I getting in over my head if I try to build my own GPS
>>>receiver?
>>
>>
>>Getting involved in GPS is by its very nature an "over your head" kind
>>of thing because it involves everything from RF to DSP to software. But
>>it's fun! And as long as you have the time, it's possible to do. There
>>are tons of books and resources to help you out on your way. You can
>>focus on the things you want to, and let other people handle the details
>>you don't want to.
>>
>>In terms of GPL-GPS, all you need is a Linux box with a few serial ports
>>and you're on your way... everything is detailed on the website. We'll
>>soon have instructions for Windows development as well.
>>
>>I hope that helpes!
>>
>>Andrew
>>
>>
> 
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