It's one thing to develop an ICBM with the payload and range required to hit targets on another continent. It's another thing to develop a guidance system accurate enough to hit the intended targets.
The missile guidance systems are perhaps the most closely guarded secret after the physics package itself (i.e. the fission/fusion device), and even though China may have given North Korea considerable help with missile technology, I doubt they'd willingly give them either one of the "crown jewels": the physics package or the guidance system.
ICBMs do not rely on external signals such as GPS, because it can always be jammed. The initial guidance of the missile and the reentry vehicles is done via inertial guidance.
The guidance system consists of an ultra sensitive gyroscope and the related electronics. You may have seen mechanical gyroscopes before.
A mechanical gyroscope is set of independently spinning wheels or discs. The axis of rotation for the whole assembly is free to assume any orientation by itself. Due to the conservation of angular momentum, the axis remains in a fixed position regardless of the motion of the assembly (e.g. rocket), the gyroscope can be used to record the acceleration of the missile in three dimensions. Once you know the acceleration, you can always calculate changes in the velocity and position.
That's the kind of a mechanical gyroscope that was used in the first missiles like the German V-2.
Modern missiles use very sophisticated gyroscopes called ring laser gyroscopes, or its ultra sensitive version called solid state ring laser gyroscope.
It has no moving parts and is based on the interference of two laser beams, instead.
According to a so called Sagnac effect, the speed of light changes slightly with rotation. When the assembly is rotated (e.g. the missile tilts one way), one of the laser beams slows down with respect to the other beam and this is detected as a phase shift leading to a change in the interference pattern (the beat waveform seen in the video above).
Note that the Sagnac effect does not contradict the theory of relativity, because it only states that the speed of light is invariable in vacuum
and non-accelerating frames of reference. In this case, we have a rotating frame of reference.
The gyroscope is just one component of the guidance system. How to make it work under the harsh conditions experienced by the payload, how to extract the output signal and process it into a reliable location and orientation reading, and how use it to steer the missile/reentry vehicle is an artform developed over years of experimentation.
After the burn of the final stage of the missile (post-boost phase), the warhead bus is separated from the stage and is oriented in space to align with a trajectory that will take the warhead to the target. Even the smallest of error here will grow in magnitude, because the trajectory cannot be corrected during the reentry. Remember. There is no GPS guidance or any other external signal to guide the warhead. That's why it is called a ballistic missile in the first place.
Hence, I seriously doubt the accuracy of the North Korean ICBMs. Are they accurate enough to hit and destroy a city in CONUS? Maybe, but that only makes them a weapon of terror like V-2 was. Are they accurate enough to hit and destroy a hardened, strategically relevant military target in CONUS? I don't think so.
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