Alex,
I located the following on Naval-Technology.com and the Trident 2 takes their CN sights after the final third stage of the missile is separated. This is late 1980's technology. The Trident 1 may have operated differently.
"Trident II is a three-stage solid propellant missile with supersonic speed. Weight is 59,000kg. The US Navy gives the range of the D5 as 'greater than 7,360km' but this could be up to 12,000km, depending on the payload mix.
The accuracy of strike on the target is given by the Circle of Equal Probability (CEP) value, which is the radius of the circle within which half the strikes will impact. The Mark 6 guidance system on Trident II is a star-sight aided inertial guidance system, which gives a CEP of 120m. The missile is ejected from the submarine by high-pressure gas. When it reaches the surface the first rocket stage fires automatically. The missile's inertial
guidance system calculates flight behaviour and guidance.
After the third rocket motor has separated, the warhead carrier takes a star-sighting to confirm position and manoeuvres to the point at which the warheads can be released to freefall onto the target."
Greg Rudzinski
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