The time remaining is predetermined – a pre-set time function that is carried out. You can actually keep aligning for longer (more on that later), but as far as the required accuracy is concerned, you'd be wasting time unless the plane is at a high latitude.
[The ALIGN] mode requires 10 seconds of initialization during which the initial BITE is completed and ten minutes of alignment characterized by a Kalman filter. The filter gains are predetermined functions of align time developed for an optimum final alignment error that considers the sensor noise characteristics and the aircraft disturbances that may occur during alignment, such as wind gusts, refueling and passenger-loading. [...]
The fine alignment: implementation uses a seven-state Kalman filter with a pre-set gain schedule to perform the alignment function.
— DTIC ADA143244: Advances in Strapdown Inertial Systems. Lecture Series Held in Athens, Greece on 14-15 May 1984, in Rome, Italy on 17-18 May 1984 and in Copenhagen, Denmark on 21-22 May 1984 https://apps.dtic.mil/sti/citations/ADA143244
Boeing example
Before the 777 and 787, the INS mode selections were OFF
, ALIGN
, NAV
, and ATT
.
- Going from
OFF
to ALIGN
(momentarily) then NAV
is the ~7-minute alignment
- Going from
NAV
to ALIGN
(and reentering present position) then back to NAV
is a fast alignment (~30 seconds) between flights
- Going from
OFF
to ALIGN
(and staying there) is used at high latitudes (for the Boeing 747-400 that's between 70°12.0' and 78°15.0'), and takes a minimum of 17 minutes (after which NAV
is selected).
Now, where did this 17 come from?
That last bullet point is where it gets more interesting, and then more clear by going back in time:
Since by the 747-400's time the technology was well-known and not new anymore, the flight manuals started to skip what exactly happens in the alignment process, unlike the Carousel IV's manual – the first INS to be installed as default equipment.
The Carousel IV's manual explains the INS alignment sub-modes 8
to 0
, which were counted down—with that in mind, see this excerpt:
As you can see, the C-IV can be left to go through another five (5) predetermined steps of 3.4 minutes each (3.4 times 5 is 17) to further improve the alignment; this more clearly shows how alignment is based on time-based steps.
In the newer 777 and 787 with only OFF
and ON
selections, the unit decides for itself if it's high latitude or not, and based on that it will show the predetermined time remaining.