if the aircraft maintains a constant heading in level flight for some minimum time
Actually, and counterintuitively, exactly the opposite is true. The below is from the Challenger 605 FCOM. Note 1 is interesting.
In-Flight Alignment
If a power interruption or a transient system fault occurs in-flight and a GPS signal is valid, the IRS
system will have the capability for re-alignment. During in-flight re-alignment the IRS ALIGNING
message appears on the PFDs.
The FMS will prompt the crew with a yellow SET IRS HOG message on the FMS CDU scratchpad
(required for FMS navigation - IRS will align without this action). If the crew enters a heading, the
IRS will work as a DG until it transitions to the ATT mode at which point it starts calculating its own
HOG.
Typically, the time required for a full alignment in navigation mode is between 10 to 20 minutes.
However the time may be reduced to less than 10 minutes, because the initial aircraft attitude and
true heading are known with greater accuracy than under normal power-up conditions (ground).
The alignment time may exceed 20 minutes if any of the following condftions are present:
• No change in heading during alignment
• No changes in acceleration during alignment
• An east to west flight trajectory such that the IRUs' sensed rotational rates in inertial space
is nearly equal to zero.
1. Aircraft maneuvers involving changes in heading reduces the
alignment time.
2. The alignment time increases as a function of latitude with the
minimum time occurring at the equator and the maximum time
occurring at the poles.