Re: Longitude or Right ascension - picture

Hi Cedric,

to clarify what I was thinking I made a picture.
See That we have 3 longitudes:
L0 - Longitude at week start
Lt0 - Longitude at reference time
Lk - longitude at transmission time
Omegak - Right ascension at transmission time
alphaEk - sideral time angle of ECEF at transmission time

By analysing the figure you can deduce:

Lk = L0 + (Omegadot - Omegadot_E)*tk - Omegadot_E*t0 + Omegadot*t0
Omegak = Lk + alphaEk

Unless the Omega0 transmitted in the Nav message is

Omega0 = L0 + Omegadot*t0

we can not reach the ICD equation:

Lk = Omega0 + (Omegadot - Omegadot_E)*tk - Omegadot_E*t0

Regards,

Kelley, would you please give your position about that?
Thanks

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:
> 
>>Send opensource_gps mailing list submissions to
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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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>

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