This works the other way - you get to prove your assertion that inertial navigation could work with cheap miniaturized sensors. Anyone can cast a doubt without proof.

If your acceleration sensor is off by 1 part per million, 9.8 m/s^2 (i.e. gravity) will turn into a positioning error of ~73km in one day.

Cruise missiles combine (using Tomahawk as an example) GPS, visual terrain-matching, radar terrain-matching, and INS. Because they know INS needs those constant corrections.

> Most weapons are INS guided despite the long fly times of cruise missiles etc.

And because of a long fly time or imprecise initial reference point (a submarine is floating) some do corrections. One of the coolest one for ICBMs is to use celestial navigation to correct errors. They'd have a window with a camera and would "look" for a few stars.

Drift is over a given time, not distance. Missiles generally have an very short fly time, even if they're going really far.

Cruise missiles are very different from (quasi-)ballistic or anti-aircraft missiles - they fly at subsonic speeds at low altitudes (usually using a turbojet) to avoid interception. For example, the classic Tomahawk flies at ~900km/h, with the long-range variants having a range of 2500km, giving a maximum flight time on the order of hours, and so a pure INS drift on the order of low hundreds of meters.

sensor fusion combines multiple sensors with different characteristics such as:

- GPS; widespread, low accuracy

- INS; always available, high short-term accuracy, terrible long-term accuracy

- terrain-matching: large-scale corrections.

The different characteristics allow one sensor to correct another to a degree to produce an overall stable position.