Re: GPS timing - amazing that it actually works

peter <prathman@xxxxxxxxxxx> writes:

It also helps to realized that most hardware and software only needs to
measure and preserve nanosecond-scale *differences* in timing in order
to calculate position accurately. A hardware design that adds delay to
the GPS signals, but affects the signals from all satellites equally,
has no effect on the final position calculated.

So let's say I have a hardware design that adds a one-second delay to
all signals.

As you note, this is a ridiculous example. In a system with nanosecond
differential resolution, added delays common to all satellites are
likely to be in the microsecond range or smaller. But let's continue
anyway.

The receiver then uses the broadcast ephemeris data to
determine the exact satellite positions where they were one second ago
rather than where they are now. The position calculation is done
using the time differences observed between the different satellites
together with the information about the absolute satellite positions
at the current time. If those satellite positions are off because of
an overall timing delay then I'd expect the calculated position to be
off by about the same order of magnitude (and the satellites move a
few miles in a single second).

The receiver has no idea of absolute time; it only sees the time-related
signals transmitted by the satellites. To calculate its position, it
only has the difference in delay experienced by satellites in different
positions. There is no "current time" source independent of the
satellite signals (except a time of day clock used during acquisition,
and it is reset once the receiver begins navigating).

To calculate its position, a GPS receiver has to essentially assume
that it is located on the surface of a sphere at some distance from
each satellite, based on the time of light delay of the signal. It
knows the time the signal was sent (timing being embedded in the signal
structure), but it doesn't know the time of reception precisely, so
there's some error in the radius of the sphere. With multiple signals
from multiple satellites, the receiver can calculate multiple spheres -
and all of them share the same error in radius due to any local clock
error. With enough signals from well-spaced satellites (at least 4),
the spheres in general *do not* intersect in a common point when there
is a clock error. So the receiver can (effectively) solve for the value
of the local clock error by varying it and finding the value for which
the N spheres come closest to intersecting in a single point. When
that's done, the intersection point is the receiver's location (actually
the antenna location), while the calculated clock error allows correcting
the local receiver clock for any error common to all signals.
Essentially, the GPS receiver knows what time each signal was sent, and
can calculate the current local time assuming time-of-flight delays are
the only delays.

Adding delay uniformly to this system looks exactly like a local clock
error, and it's automatically removed by the navigation solution. It
affects the calculated time, but not the position. Since the receiver
has no independent way of determining time, it's not even aware of the
extra delay, so the time output will be wrong by the amount of the
delay.

You could record GPS signals at a particular location with a sensitive
receiver, delay them for one second, one hour, or one day - any amount
really. When played back into a GPS receiver, it will tell you the
position and time *that the signal was originally acquired*, no matter
how long the signal was delayed since then. (Well, let's assume that
the delay is less than 1024 weeks, since the GPS time repeats after
that amount of delay).

Of course signal delays will generally be much smaller than a second.

Of course, but it doesn't matter whether the delay is 10 ns or 10
days. A GPS receiver calculates position and time entirely by
measurements of the satellite signals, with no independent outside
reference. (This applies to standalone GPS receivers, but probably not
to the assisted GPS used by cellphones).

Dave
.

Relevant Pages

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  • Re: iPhone location
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