I do not think having the same Q and R matrices for both techniques will be a fair strategy. It is possible to compare the mean square error of the estimation techniques, and the time required to run the algorithms using the same micro-controller/computer. Consequently, you will be able to conclude which algorithm (UKF or EKF) should be implemented based on accuracy and the effect on the control loop running speed.

Check this paper, I found UKF is better than EKF in power systems application

Conference Paper Advantage of Unscented Kalman Filter Over Extended Kalman Fi...

For nonlinear estimation, both the EKF and the UKF are approximate strategies. The propagation of the error covariance matrix P is simplified by the use of Jacobian in the EKF and the choice of sigma points in the UKF.

Though Q and R matrices generally refer to the process noise covariance and measurement noise covariance respectively, they can also compensate for the errors in the approximation of the propagation of the error covariance P. That is, in the EKF Q can be tuned such that it compensates for the loss of higher order information that result from linearization. The same holds for the UKF too.

To sum up, Q and R can be tuned to represent a little more than process noise and measurement noise for nonlinear Kalman-based estimation schemes. This gives rise to difficulty in tuning for some applications. Since you work with simulated data, you can easily verify if your tuning is reasonably correct by checking if the actual error covariance is approximately close to the one obtained by the filter. This implies that the estimation scheme works reasonably well. In the absence of the true state value as happens in real-world situations, the innovations can be compared.

Coming to the specific case, if you want to do the fair comparison tune both the estimation schemes separately to obtain the best results. Then compare them as pointed out early.

Thank you for the answers!

Best regards,

Maximilian

Hi Maximilian,

Actually, a huge problem with KFs is the adequate selection of these matrices. Also, you cannot compare EKF and UKF with the same covariance matrices, since the underlying approximations modify in a different way the dynamic system. My recommendation (and what I actually do when using KFs) is to select the covariance matrices according to the KF's marginal likelihood. You can see the form of the marginal likelihood of the linear KF in Shumway and Stoffer's book "Time series analysis and its applications", Sec. 6.3. Also, an Expectation Maximization method for optimization of the covariance matrices is explained in the book. To simplify the optimization, you may assume a diagonal structure in the covariance matrices.

Once you obtain optimal values for the covariances, you can make a fair performance comparison.

I hope this helps.

Best,

David