I want to implement an inertial navigation system that uses a basic IMU for indoor position tracking. From all the things I've read you need to assist the IMU with something like GPS or other means of position sensing since the error in position grows quadratically with time.
I looked into Kalman filtering and am confused why this doesn't fix the issue of quadratic position error. Since youre sensors only measure acceleration and gyro (and maybe magnetic field), you must get position from your estimated state, not from your estimated sensor reading. If this is the case then you update your position state with only the error on the accelerometer each time and not the double integration of the accelerometers past errors, right?
I may be just confused but I feel like Kalman should get rid of the quadratic error.
If this is not the case, then why? And what techniques do people use for reliable indoor position tracking with IMUs?
Best Answer
No amount fo filtering can correct a contant error that is inherit in your input data.
Assume you are in rest, but your accelerometer gives a reading of a very low constant value X (its error). No amount of filtering will change this.
Integrating this X over time gives your 'speed' t * X, which increases linearly.
Intergrating this speed over time gives your 'position' (1/2) * t^2 * X, which grows quadraticly.