Calculation of Hyperparameter for the process noise (Qx)

I have measurement data, by using that i am taking measurement noise covariance R= rms(measurement)^2. but I want to use the optimized value of Q. Can anyone suggest some documents or something which can help me out in this. I have attatched the images for the better understanding.

Thanks in advance.

[Md Armanul Hoda]

And I am just curious about the trend, why do this come into estimation, What should we keep in mind to remove this. I am attaching the trandy estimated value of input. If I will use Dc block high pass filte, then it will remove the trend. I want to get answer from filter itself.

please help me out in this and thank you very much.

Answer 1

[Raghava S N]

Hi Md Armanul Hoda,

From the description, it seems you are discussing the use of a Kalman filter or a similar estimation algorithm where the measurement noise covariance (“R”) and the process noise covariance (“Q”) are critical parameters.

When you say you have the "trendy estimated value of input," I assume you mean that your measurements or estimations exhibit a trend over time that you believe does not reflect the true behaviour of the underlying process.

The following example explains the workflow involved in setting up and tuning a Kalman filter. It details the importance of “Q” and “R” on filter setup as well. There is also an additional section that describes automated tuning and optimization of “Q” and “R”. Please refer to the workflow in this link - https://www.mathworks.com/help/fusion/ug/tuning-kalman-filter-to-improve-state-estimation.html#:~:text=the%20test%20trajectories.-,Automated%20Tuning,-Sometimes%20measurement%20parameters

The output of the Kalman filter is an estimate of the state. Hence, you do not need any other filters to obtain the output required.

You can find out more about Kalman filters here - https://www.mathworks.com/help/control/ug/kalman-filtering.html, and about adaptive filters here - https://www.mathworks.com/help/dsp/adaptive-filters.html.