It depends on the quality of the IMU but yes. All US military systems use ultra-high precision IMUs and will only accept GPS corrections within the (classified) error margins of their inertial measurements. US military-grade IMUs lose precision very slowly, it is an area where they have a huge technology lead over everyone else so (ironically) they are less dependent on GPS than anyone else that might use GPS. Access to state-of-the-art IMU technology is very strictly controlled by the US.
GPS was created in part to allow the US to measure the world precisely enough in peacetime that they have an accurate model to feed their IMUs in wartime. It was never designed to be a robust navigation system even though everyone commonly uses it that way.
You can make spoofing harder. Most of these spoofing attacks target off-the-self drone GSP, and don't work against adversary who plan against them.
If you want to spoof more expensive gear, like those used in commercial shipping, you do it gradually. You start by transmitting the correct coordinates and then gradually start to increase the difference between correct and false coordinates. When done gradually, IMU can't detect GPS spoofing.
Unfortunately many otherwise good navigation systems are not doing even the bare minimum to detect spoofing. It's not the cost. Spoofing protection has not been priority.
You can (should) throw more sensors with different characteristics at a Kalman filter for enhanced results in the presence of noise. The wiki page is actually excellent https://en.wikipedia.org/wiki/Kalman_filter
In the example presented some of the inputs could include direction finding to local broadcasters, a GLONASS receiver, a heading indicator and distance traveled odometer if we're talking a road vehicle, and many other things limited only by your imagination and resources at hand.
In another thread discussing BLE, you mentioned your profile contained your email addr. I checked your profile and couldn't find it -- maybe it's not made public? Would love to follow up. My email is in my profile.
The first acura nav systems were totally gps-free. They used gyros, compass, and speed data from the car, and managed to do pretty well. I imagine a similar system on top of gps and perhaps even cell/wifi/radio data to get near seamless coverage with civ tech.
It depends on what you are doing. ICBMs predate GPS, so for anything flying you can fall back to the old way of comparing terrain height to known maps. This is reliable and a widely-implemented technique (at least in weaponry).
If that's not an option you can use an IMU, but because of errors adding up over time IMUs aren't all that great if you can't calibrate from time to time. Satellites do it by looking at stars, if you're a car you might look at the streets and compare them to maps.
The only things that really have fundamental problems without GPS are ships and anything that flies over water. In any other application GPS is used because it's cheap to implement and reliable, not because it's the only way to do it.
Except that "store the last known location" logic breaks ferries, towing, and other movement of the car while it's off. You need an override, or some way of deciding that, yes, this new and different location is actually sane.
And in the case of a ferry, the user is expecting to have accurate location and nav instructions very quickly after key-on as they leave the port in the new place, so that mechanism needs to make its decision pretty fast.
GPS was created in part to allow the US to measure the world precisely enough in peacetime that they have an accurate model to feed their IMUs in wartime. It was never designed to be a robust navigation system even though everyone commonly uses it that way.