[FOSS-GPS] Question of reference satellite selection
Tomoji Takasu
ttaka at yk.rim.or.jp
Mon Mar 22 06:45:03 EDT 2010
Dear Shaocheng
> Michael's solution is quite good, I think that's how Trimble Office
> software
> "planning" do for the prediction of the available satellites, but I think
> it
> will influence the compute efficiency in real time algorithm.
The static reference satellite strategy can be applied only
to static survey. If an obstacle blocks the visibility of the
reference satellite, you can not get solutions in kinematic
mode.
So usually you had better to "shift" the reference satellite
suggested by John. Other implementations are possible
but mathmatically same as "shift" way.
> And also, John told me the method to shift one
> reference satellite to another, and I will
> try to use single difference observation to create
> equations like Ax=b, and try fix double difference
> ambiguities when I need the fixed solution.
SD (single-difference) does not cancel the receiver clock
bias so you have to estimate an addtional parameter. For
simplicity, you had beter to use DD equations instead SD
even if you estimate SD ambiguities.
regards,
********
Tomoji TAKASU
WWW: http://gpspp.sakura.ne.jp
----- Original Message -----
From: "Shaocheng Zhang" <gnss.zhangsc at gmail.com>
To: "Open Source GPS-related discussion and support"
<foss-gps at lists.osgeo.org>
Sent: Sunday, March 21, 2010 9:39 PM
Subject: Re: [FOSS-GPS] Question of reference satellite selection
> Thank you Michael and John,
>
> Michael's solution is quite good, I think that's how Trimble Office
> software
> "planning" do for the prediction of the available satellites, but I think
> it
> will influence the compute efficiency in real time algorithm. And also,
> John
> told me the method to shift one reference satellite to another, and I will
> try to use single difference observation to create equations like Ax=b,
> and
> try fix double difference ambiguities when I need the fixed solution.
>
> Regards and Thank you again.
>
> Shaocheng Zhang
> School of Geodesy and Geomatics, Wuhan University, P.R.China
> Email: gnss.zhangsc at gmail.com
>
>
> On Tue, Mar 16, 2010 at 2:01 AM, John Morris <john at coyotebush.net> wrote:
>
>> For long measurements, you will want to shift from one reference
>> satellite
>> to another.
>>
>> As an analogy, double differencing is similar to a surveyor comparing
>> altitudes between a set of hills. You don't know the absolute altitudes,
>> but you can figure out how high each hill is relative to the others. To
>> get
>> the job done, you pick one hill as your benchmark and define the
>> variables
>> Hill(1)-Hill(benchmark) = x1
>> Hill(2)-Hill(benchmark) = x2
>> ...
>> Hill(benchmark)-Hill(benchmark) = xbenchmark = 0
>> Based on your survey measurements you create a set of equations: Ax =
>> b
>> which solves for the relative altitudes. (Since xbenchmark is zero, you
>> don't include xbenchmark in the equations.)
>>
>> Now, you decide you want to use a different hill as your benchmark. You
>> need to redefine your variables and find an equivalent set of equations
>> based on the new benchmark. It takes some figuring out, but you end up
>> with
>> a fairly simple procedure based on the following:
>> xi' = Hill(i) - Hill(newbenchmark)
>> = [ Hill(i) - Hill(oldbenchmark) ] - [ Hill(new) -
>> Hill(oldbenchmark) ]
>> = xi - xnew
>>
>> If you are more mathematically inclined than I am, you would see the new
>> set
>> of equations as a linear transform of the old ones, and you would express
>> it
>> as matrix multiplication.
>>
>> A second problem you will encounter with long measurements is the
>> repeated
>> gain and loss of satellites. One solution is to assign a separate
>> ambiguity
>> variable to each period of time you track a satellite, but over time you
>> will create an unlimited number of variables. To prevent unlimited
>> growth,
>> you will need to "eliminate" lost satellites from the equations.
>>
>>
>> - John
>>
>>
>>
>> -----Original Message-----
>> From: foss-gps-bounces at lists.osgeo.org
>> [mailto:foss-gps-bounces at lists.osgeo.org] On Behalf Of Michael Tandy
>> Sent: Monday, March 15, 2010 4:06 AM
>> To: Open Source GPS-related discussion and support
>> Subject: Re: [FOSS-GPS] Question of reference satellite selection
>>
>> Well, you have the almanac and ephemeris for all the satellites you can
>> see,
>> so you can calculate each satellite's future elevations, right? So you
>> could
>> do something along these lines:
>>
>> for x = each satellite visible
>> for time = now to (now+6 hours)
>> calculate satellite x's elevation at time
>> if elevation < 10 degrees
>> print "Satellite x visible until time"
>> break
>> end if
>> end for
>> end for
>>
>> Let's say you started your survey today, at midnight UTC time, that you
>> were
>> at my location, and that you apply an elevation mask of 10 degrees.
>>
>> You would see the following satellites, at that time:
>> SV 2, elevation 28.76
>> SV 4, elevation 13.53
>> SV 12, elevation 49.46
>> SV 14, elevation 36.90
>> SV 29, elevation 51.25
>> SV 30, elevation 84.05
>> SV 31, elevation 38.94
>>
>> Those satellites would be above the 10 degree elevation cutoff for:
>> SV 2: 1 hour 57 mins
>> SV 4: 16 mins
>> SV 12: 1 hour 40 mins
>> SV 14: 1 hour 7 mins
>> SV 29: 4 hours 11 mins
>> SV 30: 2 hours 52 mins
>> SV 31: 3 hours 53 mins
>>
>> Hence, if you simply chose the highest elevation satellite (SV 30) it
>> would
>> be visible for over two and a half hours, but if you select the right
>> satellite it can be visible for longer.
>>
>> I use the highest elevation satellite because my initializations never
>> take
>> anything like two and a half hours!
>>
>> Hope this helps!
>>
>>
>> On 15 March 2010 09:26, Shaocheng Zhang <gnss.zhangsc at gmail.com> wrote:
>> > Dear GPS Developers
>> > I am a Ph.D student working on real-time GPS algorithms. Currently I
>> > have a problem about the reference satellite selection.
>> > As we know, most of the RTK algorithm choose the highest elevation
>> > satellite as reference satellite, but when the baseline is quite
>> > long(eg.
>> > network-rtk), it may take quite long time (may be more than half
>> > hours) to get the ambiguity initialized, and during the initialization
>> > we don't want the reference satellite changes, otherwise we may need
>> > to restart the initialization.
>> > So if at the very beginning, we could find the longest session
>> > satellite as the reference satellite, it will help us to guarantee the
>> > reference satellite will not change before the initialization
>> > finished. I read GPStk's source code of "vecsol", it give a solution
>> > of project the satellite's velocity "V" to the U direction of the
>> > local NEU coordinate "Vu", and take the biggest "Vu" satellite as the
>> > reference satellite. I check this method and find it indeed give us a
>> > longer session satellite, however, when I check this method for all
>> > the available satellite at that epoch, It doesn't conclude that "the
>> > bigger the Vu, the longer the following observed session".
>> > I am very interested in this method because It's easy to implement and
>> > can be use in real-time algorithm. So I am wondering if someone can
>> > explain this method in a mathematical way, or give a better solution.
>> > Thanks in advance.
>> > Regards.
>> > Shaocheng Zhang
>> > School of Geodesy and Geomatics, Wuhan University, P.R.China
>> > Email: gnss.zhangsc at gmail.com
>> > _______________________________________________
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