The mistake is to treat a satellite fix as ground truth and everything else as backup. In a clear sky the fix is trustworthy; in an urban canyon it can be present, confident and metres wrong, because the signal reached the receiver by bouncing off a building rather than travelling straight down. A fusion system that believes that reflected fix is worse than one that ignored it. So the real work is not adding an inertial sensor as a fallback — it is deciding, moment to moment, how much each source deserves to be believed.
Between fixes, the system dead-reckons: it propagates the last known position forward using how the platform has moved — acceleration, rotation, wheel distance. That coasts cleanly through a tunnel, but inertial estimates drift, because small errors accumulate. Dead reckoning therefore holds an accurate position for the length of a real gap — an underpass, a short indoor stretch — not indefinitely, and the fusion has to know and bound that drift rather than pretend it away.
When the satellites return, the estimate has to snap back to truth without a visible jump, and it has to reject the first few reflected fixes that often arrive at the mouth of a tunnel or between tall buildings. Getting that transition right — correcting smoothly, weighting the returning fixes by their real quality — is what separates a position that feels solid from one that lurches every time conditions change.