Attila,
On 04/06/2015 11:14 AM, Attila Kinali wrote:
Moin,
On Fri, 03 Apr 2015 22:51:34 -0500
Robert Watzlavick <roc...@watzlavick.com> wrote:
On 04/03/2015 10:12 PM, Robert Watzlavick wrote:
I have an amateur radio license (mostly CW/HF and some VHF/UHF
experience) and I've written some driver software for an IQ
demodulation board but I have to admit, I would have no idea how to
begin setting up that system as initially described by Attila and
expanded by you and others. I have a rudimentary understanding of the
modulation schemes involved but I don't fully understand how the
various codes mentioned fit in. I've poked around a bit at some
articles on PN codes and I can see how data would be transmitted but I
think I'm missing something key that allows you to extract positions,
velocities, etc. out of the various links. I think I have some more
reading to do :)
The basic system is that of an DSSS modulator/demodulator.
The best text on spread spectrum systems I have found sofar
is [1]. I explains modulation and demodulation in a hands on
fashion. But, due to the age of the book, it does not contain
any of the advanced stuff done today. But I think you don't need
anything more fancy than an early-prompt-late correlator architecture
for tracking.
For the way how GPS works and how correlation and everything is
done, I would suggest [2,3,4]. [2] is a good overview of how
GPS is done and contains 99% of everything you need to know
(special thanks to Magnus for mentioning it). It lacks some
details on how to actually implement the system though.
I think that the Kaplan GPS book is better than the Misra&Enge [2] in
many regards. It is better at explaining the workings of a GPS receiver.
[3] helps to cover some of the weaknesses of the Kaplan book. However,
the Misra&Enge is better at some of the more advanced topics and more
thorough on details than Kaplan. So, Kaplan is better at teach how to
build a normal GPS receiver, and the Misra&Enge is better at teaching
how to build one with advanced features. The combination kills.
The Bore et. al helps to cover some details about getting that initial
guess. Implementing FFT based cross-correlation phase-guessing was
trivial after reading that and another book.
There [3] helps a lot, as it's a book specifically on building a
GPS/Galileo receiver. I only skimmed trough a digital copy of [4]
yet, so I cannot say too much about it, but that it's probably the
most complete book on radio and inertial navigation I have seen
sofar. The level of detail seems to vary from topic to topic
quite a bit, but it is a treasure trove of references for everything
the book covers (which is a damn lot!)
If you are tight on time I would probably recommend to start with [3]
and have a look at [1] and [2] when things don't make sense.
I would recommend going with Kaplan first, to get the first overview.
Then, as the refreshment coarse do the Misra&Enge.
To head off a bunch of replies - I think I stumbled upon what is being
suggested. To extract the pseudorange, you have to figure out the
offset of the locally generated PN code against the one that is
received. In this reverse GPS case, I assume each ground station would
have to start their local PN codes at the same time? Then you would be
able to get the pseudoranges at each ground station and use those values
for the multilateration equations. You still would have an uncertainty
of one clock cycle since the phases of the local clocks at the stations
wouldn't be aligned but several folks have suggested ways around that.
There are multiple things here:
* PRN generation: The locally generated PRN has to be time synchronous
with the one received from the rocket transmitter. If you are more than
one clock period off, you will only get noise out of the demodulator.
What you measure is the time difference of the locally generated PRN to
your ground station system time.
You might want to consider the more advanced variants of loop filters as
shown in Kaplan. Works great with simple dimensioning formulas to aid
the setup.
* Uncertainty: The autocorrelation function of a PRN sequence has a quite
steep peak at \tau=0 with width of the clock period. Yes, this does mean
that you get a one clock period uncertainty, if you do a hit/miss
correlation. But as the correlation function is actually triangle shaped,
you can get quite a bit better than that. The limit is afaik around
your sampling clock period for naive approaches, which you can further
improve with some statistics (you have multiple edges to work with, ie
can average over those).
* Synchronisation of ground stations: There are easy and diffuclt ways to
do that. Probably the easiest is to use to use an additional transmitter
at the launch point on the same frequency, but with a different PRN than
the rocket. This way you can do a difference of the two PRN codes in
your receiver, which gets away with a lot of nasty effects that you
would need to account for otherwise.
This is what I propose. I even go further and propose that each base
location has one, so that you can track and evaluate the distances
between the stations.
Another approach would be to use a GPSDO on each ground station and
run all the receivers already synchronized. This also enables you to
get the position of all stations very accurately, especially if you
let the GPSDO average its position for some time. But for ultimate
accuracy, you'd need to calibrate the GPSDO's (including antennas)
against each other, to know what the systematic offsets are
(ie set them up all together at the same location and measure the
time difference of the PPS).
You can do that, but then you have two systems to care about.
Not depending on GPS, but use it as a guide makes it more self-contained.
Of course, it's possible to use a combination of multiple approaches.
Eg a nice one would be to GPSDO's to provide position and a precise
frequency reference, but then use a central transmitter for the
synchronization.
Indeed.
Cheers,
Magnus
HTH
Attila Kinali
[1] "Spread Spectrum Systems with Commercial Applications", 3rd edition,
by Robert C. Dixon, 1994
[2] "Global positioning system signals, measurements, and performance",
2nd edition, by Partap Misra and Per Enge, 2012.
[3] "A Software-Defined GPS and Galileo Receiver",
by Bore, Akos, Bertelsen, Rinder, Jensen, 2007
[4] "Principles of GNSS, Inertial, and Multisensor
Integrated Navigation Systems", 2nd edition, by Paul D. Groves, 2013
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