[time-nuts] GPS receiver vs local oscillator

Hal Murray hmurray at megapathdsl.net
Thu Feb 2 21:07:36 UTC 2012

>> I thought the 4th satellite was needed to determine the time.  Wouldn't
>> it take a 5th satellite to also determine the frequency of the local clock?

> Not really. There are two ways to get the postion and time derivatives. One
> is to either use two fixes which give you each a (x,y,z,t) tuple, while you
> know what your expected delta-t is, you can calculate the "real" delta-t and
> get from that your frequency offset. 

That's the sort of thing I'm looking for, but I don't quite get it yet.

I have 4 satellites. If I know f, I can solve for x, y, z, and t.  If I don't 
know f, I'm short an equation.

If I get two samples, I have 8 equations and I need to solve for:
  x0, y0, z0, t0, and f0
  x1, y1, z1, t1, and f1
That's 10 unknowns with 8 equations.  I get a 9th equation by setting t1 = t0 
+ 1.  I'm still short one equation.

Can I do something like assume f0 = f1?  That would make sense if the change 
in frequency is small relative to the noise/error in all the other 

> The other way is to use the doppler shifts of the satelites. You know what
> position and speed relative to you the satelites have and can from this
> calculate what your speed, respektive frequency is. 

There is a chicken-and-egg problem in there.  If I need the local clock 
frequency to solve for position, I can't use position to solve for frequency.

Consider the time-nut case of 1 satellite, known position, and trying to find 
time.  If I know the rough time I can calculate the Doppler.  That tells me 
which FFT bucket to look in.  Is the local clock close enough for that even 
if it's off by a few/10s of PPM?

These are my opinions, not necessarily my employer's.  I hate spam.

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