If any at all requires a "delta-T" (lapsed time between) then a true delta-T is needed, not some correction to an earth based notion of noon.
The correct way (with multiple instruments) is with calibration runs to establish parameters and frequent (at the very least at start and end of aquisition runs) syncronisation signals or events, and for each isolated cluster of instruments to have an epoch counting clock (a sufficiently fine resolution incremental counter of time units lapsed since X (for varying X)).
"Raw GPS Sat time" - the super raw satellite frame uses a monotonically increasing count of lapsed seconds of satellite time that resets on a weekly basis.
Satellite time being a moving frame in a reduced gravity locale .. so a time frame in which atomic clocks do not run as they do at ground level and at nominal 1G.
This, of course, varies for each satellite and is reconciled by a ground station which transmits a correction frame for position and time back to each satellite to pass on to handheld recievers.