Can I add that as artjomh points out with the short flight time... a modern ring laser gyro uses a very very long fibre optic cable with a laser beam flowing through it to measure movement. Modern examples are so sensitive they can measure the effect of the earths rotation while sitting still on a table.
the inertial guidance system, which will include a ring laser gyro, will be set with the precise launch position and with the known coordinates of the target will be able to adjust the control surfaces and direction of rocket thrust to get within a few kilometres of the target.
the problem with inertial navigation is that it will have an error rate that will increase over time, so a very long range cruise missile can't rely on inertial navigation (IN) alone because it becomes less and less accurate over time, so after flying 3,000km at subsonic speeds it might be 20km out.
Different options are currently available including astro navigation and satellite navigation... for ballistic missiles the stars will be visible as they travel through space so the IN system still guides the missile and its payload but regular fixes from star positions means that the missiles precise location can be recalculated so instead of landing 30 minutes later 10,000km away from the launch area with an accuracy of say 2km, with constant updates from star positions accuracy can be less than 200m.
Satellite navigation can also greatly improve accuracy by allowing updates, but with a cruise missile the physical shape of the terrain and a few known fixed points on the way to the target can also be used to greatly improve accuracy.
For instance a cruise missile launched at the US might travel past an area with a mountain peak that is 1,200m tall... the terrain avoidance radar the missile uses could detect that peak and its precise position in relation to the missile... based on that a more accurate position for the missile could be calculated... or it might be a major highway intersection that could be used.