# IMU and GNSS fusion

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Silvia Ceccato on 7 May 2019
Answered: Brian Fanous on 14 Jun 2019
I would like to use the matlab implementation of an extended kalman filter for pose estimation with GPS and IMU measurements that I found here: https://it.mathworks.com/help/fusion/examples/imu-and-gps-fusion-for-inertial-navigation.html?searchHighlight=imu%20gps%20fusion%20example&s_tid=doc_srchtitle
However I was wondering if any reference exists for the EKF implementation contained there, as a paper or a book where the model is written down. One of the doubts I have about this implementation regards the sensor measurement model (even though if I understand correctly, IMU measurements are used as a control input to the filter). The code makes a distinction between additive and multiplicative noise and both are used during the prediction phase to update the P matrix. From what I understand, multiplicative noise regards the bias estimation for the accelerometer and the gyroscope. Is it correct to say that bias here is considered as a gauss-markov process? So the bias equation is , where is the bias at time k and is gaussian noise? Then the IMU measures an acceleration .
Am I misinterpreting the multiplicative noise?
But most importantly, is a reference of this implementation available anywhere?
The following is a reference for MARGGPSFuser, but I am looking for something a bit more in depth

Brian Fanous on 14 Jun 2019
Hi Silvia
Sorry for the late reply on this. The various insfilters are based on a few sources. At least some of the MARGGPSFuser is based on the InertialNav library:
The other flavors of insfilter draw on that but other sources as well.
You are correct that the bias for the gyroscope and accelerometer are modeled as a Gauss Markov processes in the MARGGPSFuser. However, the gyro and accel inputs are integrated (trapezoidal) to produce a delta angle and delta velocity. These are used as control inputs to the predict phase of the EKF. So the internal EKF tracks the bias in the delta angle and delta velocity.

R2019a

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