# [time-nuts] Need advice for multilateration setup

Magnus Danielson magnus at rubidium.dyndns.org
Mon Apr 6 16:48:25 EDT 2015

Attila,

On 04/06/2015 11:14 AM, Attila Kinali wrote:
> Moin,
>
> On Fri, 03 Apr 2015 22:51:34 -0500
> Robert Watzlavick <rocket at 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
>
> 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
>