# IMU Model: how to specify the bias correlation time?

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Thomas on 13 Sep 2023
Commented: Thomas on 14 Sep 2023
Hi,
I'm tryng to set up the simulation of a gyroscope, and I'm interested in the stochastic errors only. To do so, I identified on the Allan variance curve the following parameters that I can then set in the the gyroparams for simulation:
• NoiseDensity (Angle Random Walk), generally noted N in the litterature
• BiasDensity (Bias instability), generally noted B
• RandomWalk (Rate Random Walk), generally noted K
There parameters are sufficient to launch a simulation of the stochastic errors with a gyro sensor model in Matlab.
However, following the reference [1], there is also the parameter Bias correlation time noted T that can be measured on the Allan variance curve, but I can't find how to specify it in the gyroparams.
I have therefore two questions:
1. Does the fact that we can't specify this bias correlation time comes from the fact that Bias is modelled differently in Matlab (instead of a first-order Gauss-Markov model)?
2. Is there a way to incorporate this parameter to the simulation still?
Thank you.
[1] J. A. Farrell, F. O. Silva, F. Rahman, and J. Wendel, “Inertial Measurement Unit Error Modeling Tutorial: Inertial Navigation System State Estimation with Real-Time Sensor Calibration,” IEEE Control Syst., vol. 42, no. 6, pp. 40–66, Dec. 2022, doi: 10.1109/MCS.2022.3209059.

Ryan Salvo on 14 Sep 2023
Hi Thomas,
Unfortunately, the Bias correlation time, T, cannot be directly specified on the gyroparams object. However, starting in R2023b, the BiasInstabilityCoefficients can be specified to incorporate this parameter into simulation.
Thanks,
Ryan
Thomas on 14 Sep 2023
Hi Ryan,
Thank you very much for the update. Look forward to it. I'll develop my own model for now.
Thomas

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