Kalman filter estimator for Gyro and accelerometer

On Friday, July 21, 2017 at 10:21:51 PM UTC-4, gyans...@gmail.com wrote:
> I am using a fairly standard approach to estimating angular pitch using a KF. It uses both accelerometer and Gyro angle data. Now it estimated the angle fine enough and I implement the steady-state KF. Never tried this before but then put a PID or lag-lead controller on this measurement. I find that the Kalman filter bandwidth is stuff all and severely reduces the bandwidth of my closed-loop system - which is using classical control methods. Since the bandwidth is obviously proportional is some way to the additive noise covariances I am thinking to lower their value in the algorithm so that the filter bandwidth increases.
> 
> Anyway, the KF, although useful does not appear to have any measure of its own bandwidth so we can at least get an idea of the limitations. Obviously the more filtering in a control loop the more phase lag and less stability.

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With a tactical grade IMU updated by GPS the EKF (extended Kalman filter) approach gave me very small residuals (less than 1 meter RMS from pseudoranges and 1 cm/sec from 1- sec carrier phase changes -- table near the bottom of http://jameslfarrell.com/wp-content/uploads/2012/03/GPSINS.pdf ),  while airborne under severe vibration.  The inertial instrument errors weren't anything like biases nor white noise; they could be modeled as "slowly-varying" (band-limited) for very short durations ONLY.  The reason is, as I noted once before in this discussion, they come from a diverse collection of sources, many of which are motion-dependent.  Those motions include vibrations as well as profile dynamics, generating error constituents proportional to rates and acceleration components, -- as well as their squares and
products, both translational and rotational, with in-phase and quadrature correlations across axes.
After a lifetime of dealing with those effects, including thousands of hours with in-flight data, I can assure you that a simple characterization for them is a very short-term phenomenon while they're in motion.  The errors change within less than a minute.

With a tactical grade IMU updated by GPS the EKF (extended Kalman filter) approach gave me very small residuals (less than 1 meter RMS from pseudoranges and 1 cm/sec from 1-sec carrier phase changes  (table near the bottom of http://jameslfarrell.com/wp-content/uploads/2012/03/GPSINS.pdf ), while airborne under severe vibration.  The inertial instrument errors weren't anything like biases nor white noise; they could be modeled as "slowly-varying" (band-limited) for very short durations ONLY.  The reason is, as I noted once before in this discussion, they come from a diverse collection of sources, many of them motion-dependent.  Those motions include vibrations as well as profile dynamics, generating error constituents proportional to rates and acceleration components -- and to their squares and products, both translational and rotational, with in-phase and quadrature correlations across axes.  After a lifetime of dealing with those effects, including thousands of hours with in-flight data, I can assure you that a simple characterization for them is a very short-term phenomenon while they're in motion.  The errors change within less than a minute.