[time-nuts] GPS receiver clock bias

jmfranke at cox.net jmfranke at cox.net
Fri Nov 18 10:18:00 EST 2005

Let me take a stab at this question and either provide some help or embarrass myself.

In order to calculate the range to each satellite, you need to know the instant in time the satellites transmitted the reference timing mark or sync pulse train.  Of course, all of the satellites are synchronized within a small error.  The problem is that your receiver clock is not synchronized to the satellite clocks.  Your receiver clock needs to be operating at the same rate as atomic time and needs to be adjusted to be in sync or phase with the satellite clocks.  The absolute time, GPS time frame, is not as critically important for ranging.  The absolute time is determined from the navigation message, using the seconds counter, etc.  So, your receiver clock can be set to the nearest second by reading the navigation message, but the phasing and rate adjustment is done using the signals from several satellites.  In the simplist model, the receiver assumes the receiver clock is correct and then measures the time delays for the sync signals from all of the satellites to compute a navigation solution.  The degree to which the solution lines of position for each satellite do not cross at a single point indicates the error between your receiver clock and the satellite clocks.  Your receiver adjusts the internal clock to reduce the error. At that point, your receiver clock is now in sync with GPS time, which is tied to atomic time with a known offset from UTC.

The adjustment is normally done with multiple satellites, but if your three-dimensional position and velocity is known, only one satellite is needed.  Afterall, in the general case, you have four unknowns; latitude, longitude, altitude, and time.  So, in the worst case you need four independent measurements, which would require four satellites.  Knowing any of the unknowns reduces the number of satellites required.

I hope this helps,

> From: TwoSpades <michelangelo.albertazzi at gmail.com>
> Date: 2005/11/18 Fri AM 09:51:32 EST
> To: time-nuts at febo.com
> Subject: [time-nuts] GPS receiver clock bias
> Hi everybody,
> I have got a interesting question to ask you!
> Most of us have read a GPS overview, and some of us consider oneself a
> GPS expert. Well, I've got the basic question about GPS timing.
> In short, you know that we need a fourth satellite in order to solve
> for position and clock bias (first page of every GPS overview).
> Who knows what really is that deltaT (?T) named receiver clock bias?
> Every book tells that it is the time bias between the receiver local
> clock and the
> GPS system time (GPST).
> But, delta T (?T) = t1-t2.
> What are precisely t1 and t2?
> When I use epochs like t1 and t2, I must refer to a time scale, what's
> the time scale in this case?
> I don't think this is a banal question, on the contrary.
> Hope to read some interesting replies.
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