Unscented Kalman Filter - How to add noise to the system? - Simulink

Dear community,

I am trying to use the Unscented Kalman Filter block in my Simulink model. My state transition function and my measurement function have each noise (Equations are attached as a picture). I am not sure, how to include those noise to the Unscented Kalman Filter block. One can add the noise by typing those in to the Kalman filter block (first screenshot) or add those as the w[k] or v[k] variables to the state equation and to the measurement equation (secound screenshot). Unfortunately, the matlab documentation does not tell, wheter both options have the same functionality. Can someone please give me some advice and tell which option I should go for? Thank you!

[HF]

This is the answer form the support:

I am writing in reference to your Technical Support Case 04607739 regarding 'Questions regarding Unscented Kalman Filter - Simulink'. Thanks for providing more insight on your project. So far, I understand that you are concerned about where to add your state and measurement noise, w and v? Therefore I recommend you the last paragpah of the UKF doc page called "State Transition and Measurement Functions":

https://www.mathworks.com/help/control/ref/ukf_block.html

Based on that I provide you the following explanation. When dealing with Additive Noise Terms you do not have to add them to your State or Measurement Function because the block detects the additive noise setting and will add the noise automatically to the State or Measurement Function in the following way:

x[k+1] = f(x[k],us[k]) + w[k]

y[k] = h(x[k],um[k]) + v[k]

When dealing with Nonadditive Noise Terms you have to include them to the State or Measurement Function and define them by your own. This is done so to allow you to define more complex noise relation to the State or Measurment Functions.

So in short, choose if you have Additive Noise Terms or Nonadditive Noise Terms and based on that either do not add it or add it to your State and Measurement Function. I was having a quick look into the paper and I think you should be able to represent the noise as Additive Noise Terms. But I am not an expert and I do not have looked in depth into the paper. I highly recommend you to do your own research on this.

Answer 1

[Shubham Khatri]

Hello,

To my understanding, You have to do both the things. The function will be different based on the noise is additive or non additive and accordingly you have to give the noise value. Some more information would be helpful.