[time-nuts] 1PPS accuracy of commercial GPS receivers

Magnus Danielson magnus at rubidium.dyndns.org
Thu May 14 11:37:30 UTC 2009


Poul-Henning Kamp skrev:
> In message <E660D55B75514E29A5735AF7DCB484B2 at athlon>, "Ulrich Bangert" writes:
> 
>> The receiver can use this redundant information in two ways:
>> a) to improve the solutions for the position
>> or 
>> b) to improve the solutions for the time
>>
>> but not both at the same time. 
> 
> That's just bogus.
> 
> First of all, you need four sats for a complete solution: X+Y+Z+T, second
> the more sats you add after that, provided they do contribute gainfully,
> will improve both the position and time solutions, for the very simple
> reasons that they are one and the same solution.
> 
> Once you go to position-hold mode, all the sats contribute to is the
> time solution, and in principle one sat is enough to get a solution,
> because, as the name implies, you stop treating X+Y+Z as variables.
> 

I totally agree. This is well covered in the books that go into the deep 
details of GPS navigation.

3D positioning requires at least 4 sats for resolving X, Y, Z and T 
coordinates, which translates to Lat, Long, heigth and T.

2D positioning requires at least 3 sats for resolving Lat, Long, T 
(really X, Y, Z and T which a fixed relationship between X, Y and Z so 
given two the third will be given, as the heigth is assumed).

T positioning requires at least 1 sat for resolving T.

Also, you can use the redundant information to identify false-tickers 
and remove them before final position is calculated, this is done by 
making a preliminary calculation and then compare the calculated time 
with the pseudo-range value for each and let those being significantly 
off be removed.

The pseudo-range system make the time of the receiver a critical 
variable to establish. The stability of the receives time will therefore 
also be a critical parameter in order to establish good quality 
positional values. High short-term stability oscillators is being 
deployed even in simple L1 receivers to reduce LO phase noise and its 
effect on code and carrier pseudo-range measures. All pseudo-ranges will 
depend on the actual distatance, but also on the time of the sat and the 
receiver. The sat time is being corrected into propper GPS time by 
additional correction values, such that remaining timing errors is to be 
found in the receiver. Phase offsets of the signal from the sats center 
of mass is also given, since it is the center of mass which the 
positional values of the sat indicate.

The receiver uses the previous time estimates to correct its own clock 
and advanced receivers use Kalman filtering for optimum clock 
estimation. Each positional solution also feeds the clock algorithm so 
that the clock is steered towards a zero offest. The pseudo-ranges is 
samples with a sample clock, which has known deviation from the local clock.

In the end, I can't see how this type of receiver would fit the claim 
that one has to optimize for position or time. It does not make sense to 
me, as I know the system. What is true is that not all receivers has the 
algorithms to provide optimum time solutions in the fixed geografical 
position (it's not fixed in time position). The same receivers where one 
has the time option performs the same on normal positioning. In fixed 
position the solution part of the receiver must know that the position 
is fixed in order to resolve all pseudo-ranges into time-offset only.

So, 3D positioning does not give the same time-stability as a fixed 
position does, that is true, but it is not the same as being claimed.

Cheers,
Magnus



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