Pure inertial navigation gets worse over time, even a $20,000 gyroscope wouldn't get the job done.

This is because gyroscopes measure rotational velocity, velocity is the first derivative of position, so you need to integrate velocity in order to get rotational position. The integral of velocity is (velocity x time), so your error gets bigger over time.

I'd imagine an inertial solution plus optical flow could result in some pretty good results.

You want even better than optical flow. You need a SLAM system that can do loop closures (i.e. remember stuff that it has seen before). The propagated error from accelerometers and gyroscopes (that are not controlled by arms treaties is huge) blow up really quickly. Fun fact, gyroscopes and accelerometers actually do measure a change in angle and a change in velocity over a time interval (as opposed to an instantaneous angular rate and acceleration). For high precision applications you even need to worry about if the delta is relative to the frame of the inertial navigation system at the beginning or end of the time interval (shuddering at the memories).

I was always under the impression that integrating unknown biases in gyroscope and accelerometer measurments is the main issue with dead reckoning.

Today I am convinced that attitude errors are the far bigger issue, since they will make you misinterpret gravity as genuine acceleration.

Even with a 1° error in your pitch estimate, you will start integrating 9.81ms^-2*cos(1°) = 0.17ms^-2 as a forward acceleration. Within one minute, you are 308m off already. This is the real issue with dead reckoning IMO.

It's complicated. It depends on the sensor and the motion of the object. Because the gravity vector doesn't change spatially very quickly if you are doing loops you can use the accelerometers to calibrate the gyro biases in the sensor fusion loop (via the gravity vector). You can also use the magnitude of the vector to calibrate the accelerometers (roughly). Nothing helps pin all that stuff down like a global position measurement though. Some sensors are just less prone to bias drift as well.

I've had this project in the back of my mind for a long time. Use some kind of discreet inertial navigation while riding subways, then render the paths over views looking down from above-ground. Kind of like an over (under) lay to see where the trains actually go. You can hear the subways rumble in many shops along the lines, but I'm always curious where exactly they are -- imagining the ground was transparent and I could just see those people sitting while zipping by underfoot.

Like, as in dead reckoning? It's always a sketchy approximation, without a good caliberation, to zero the frame of reference, dead reckoning is guess work, until you hit the next benchmark.

By definition, it's like dunking underwater, and swimming in the dark with your eyes closed. You don't know how accurate your frame of reference is until you reach out to grab a landmark and open your eyes, to recaliberate.

For larger environments you tend to need a full-blown SLAM system that can close loops to avoid drift that accumulates inevitably.

SLAM?

https://en.m.wikipedia.org/wiki/Simultaneous_localization_an...

Yes, this is what he means. It uses visual/laser information (sometimes combined with the IMU like the phones you talk about) to map and track movement.

They also want to create dynamic meshes on the fly for use in OTS game engines which is quite a challenge.

I'm not sure why everyone in that domain is obsessed with meshes and won't work with a voxel rendering system which seems more flexible for most types of current geometry capture techniques. I get that they want to reuse existing simulators using existing gaming technologies but sometimes its fitting a square car through a round garden hose.

too much drift, they are very noisy. double integration is hard.

Just to expand on what my parent poster said: double integration is hard, not in the "hard to get the implementation right" sense, but in the "even with perfect implementation the small errors add up fast, and the uncertainty grows out of all practical bounds". I'm just saying this because even very smart people can fail into the trap of "we just need a better kalman filter".