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Comment by mparr4 | Hacker News Reader

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.

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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.

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