[LEAPSECS] the big artillery

[Zefram]

David Malone wrote:
>if you transmit a second boundary at what you later identify to be
>the wrong time, you can correct for that in your paper estimate of
>TAI(X) so that it does may not align with UTC(X).

That's not what I mean by TAI(k).  You're describing having two distinct
time scale realisation efforts from one authority, but my situation
involves applying a single realisation effort to both time scales.
I define

    TAI(k) = TAI + (UTC(k)-UTC) = UTC(k) + (TAI-UTC)

It follows that

    TAI(k) - UTC(k) = TAI - UTC
    TAI(k) - TAI = UTC(k) - UTC

(Around leap seconds, "TAI-UTC" in the above expressions must be
understood to refer to the difference that is appropriate for the UTC(k)
value in question.)

>                                                  This corrected
>estimate of TAI(X) would then, presumably, be what as an input to
>the calculation of TAI, and subsequently UTC.

The steering of TAI is based on the comparisons made between the clocks of
the national labs.  Those comparisons are no longer made via the public
time signals broadcast by the individual labs, so conceptually there is
room for a distinction between the TAI/UTC realisation embodied in MSF and
the TAI/UTC realisation that constitutes NPL's contribution to TAI(BIPM).
I'm somewhat curious as to how this distinction plays out in practice.
But it's irrelevant to my argument here, which is why I ignored it,
just like I ignored the issue of the time signal receiver imperfectly
realising UTC(NPL) from the signal.

-zefram