[time-nuts] GPS receiver vs local oscillator
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?
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