Warner,
> These instances of overflow come from remainders of division
> operations overflowing. They all can be derived from a single base
> number (say number of seconds since 1970, MJD, etc). However, when
> you are deriving that single base number, it can be much harder.
Yeah, I also prefer to use words like remainder,
modulus, or rollover rather than overflow (which
sounds like something unforeseen or a mistake).
> Could you tell me what year it was if I told you it was Monday,
> October 15th? No, you couldn't. You could tell me that it might be
> 2001, but it could also be 2007 or 1990. You need more information to
> resolve the ambiguity. If I told you that it was Monday, October 15th
> and that TAI-UTC=32, you'd know it was 2001. If I told you
> TAI-UTC=100, you might guess that it is 2063, or maybe even 2068 or
> 2057 or maybe other years earlier or later depending on your leap
> second model, utc-ut1 tolerance parameters, and other factors
> unknowable today.
I understand the problem but think, in this case, it
is grossly overstated. Not only do can you know the
leap second number, and the modulus GPS week
number, but also the date of manufacture and the
date of last signal acquisition. We also know about
the useful and market lifetime of electronic gadgets.
In all real-life situations this is sufficient to resolve
the 20 year cycle.
The counter-example I used in years prior to the
August 1999 WNRO event was -- the only way a
GPS receiver could come up with the wrong date
was if you turned it on in the 90's, turned it off for
at least 19.5 years, and then turned it on again.
In that case, it would still provide correct navigation
but, yes, it would come up with the wrong date.
And that's assuming the manufacturer didn't apply
a leap second heuristic (which wasn't published
at the time).
See also:
GPS Week Number Rollover (WNRO)
http://www.leapsecond.com/notes/gpswnro.htm
256-Week Leap Second Bug
http://www.leapsecond.com/notes/leapsec256.htm
> The GPS 1024 week overflow is easier to deal with, since it is a 20
> year ambiguity, not a 5 year one. You can make a better guess than in
> my example, I'll not argue. The better the guess you make based on
> today's understanding, the more external factors that might cause you
> to be wrong. Eg, leap second rules changes, lifetime of GPS signals,
> etc.
>
> I guess I agree with you that these things are doable. Working out
> the details, however, makes them non-trivial.
>
> Warner
The other point I was trying to make is that there are
web pages that still claim that "GPS WILL FAIL" on
such and such a date because of the 8-bit leap second
field. This sort of hyperbole is uncalled for. I don't see
this any more or less of an engineering detail than a
PC booting up and not knowing for sure if it's 1905,
2005, or 2105.
/tvb
Received on Mon Sep 26 2005 - 11:34:13 PDT