For the purpose of state estimation of induction motor how to find noise covariance matrix Q and measurement noise covariance matrix R?
Dear Satish, the answer cannot be given immediately, since noise analysis is typically a matter of special investigations, often expensive. To specify Q, you need to know the motor model and connect it to possible physical disturbances. Then approximate the noise sources with white Gaussian distribution. Matrix R is much easy to ascertain, because the measurement equipment often has some error characteristics. Otherwise, you also need to analyze possible sources of disturbances and assume them to be white Gaussian in order to use Kalman filtering. If you know nothing about Q and R, you may fit them intuitively. But note that the Kalman filter is sensitive to errors in Q and R and its output can be unacceptable if errors are large. In this case, you better use the iterative unbiased FIR filter that has the Kalman filter structure but ignores both Q and R.
I would like to add that one can also use the results from model-fitting / parameter estimation to quantify the model uncertainty and choose a suitable Q matrix. This procedure and some additional insights into Kalman filter tuning are described in the attached paper.
Moreover, it is often not known that systematic mathematical methods to identify Q and R exist. In fact, a recent one is called the Autocovariance least-squares method, and its development started in the group of Prof. Rawlings. While there are more recent developments, a good start into this topic may be their original publication, which can be found using the link below.
http://jbrwww.che.wisc.edu/tech-reports/twmcc-2003-04.pdf
Article How To NOT Make the Extended Kalman Filter Fail
Please see the reports arXiv:1503.04313v1.pdf, arXiv:1505.07201v1.pdf and arXiv:1505.07208v1.pdf. and the papers in SADHANA December 2016 issues.
Please see the reports arXiv:1503.04313v1.pdf, arXiv:1505.07201v1.pdf and arXiv:1505.07208v1.pdf.
and the two papers in SADHANA December 2016 issue.
Please see the latest intech open book Kalman Filters - Theory for Advanced Applications
Edited by Ginalber Luiz de Oliveira Serra,
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