Afshin,

I have worked previously with discrete-time joint UKF. We published a rather detailed application paper on this issue. You may want to take a look at it:

"Joint Unscented Kalman Filter for State and Parameter Estimation in Managed Pressure Drilling"

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6669753&queryText%3Dmahdianfar

The code/algorithm  that you write/use is obviously important. As far as I remember, if your system is continuous-time and you discretize it before applying UKF, the choice of your sampling rate would be critical to the performance of joint UKF. Furthermore, similar to other control/estimation problem the tuning of your filter is very important. I employed physical intuition of the system dynamics and some extra tuning for optimizing the performance. 

Let me know if I can be of any help.

Hessam.

Hi Afshin,

It seems to be difficult to give a fixed answer to your question based on your statement, but you may find a solution by exhausting a couple possibilities: 1) tuning the sampling rate; 2) whether the coupling between the states, parameters, or both; 3) the selection of initial conditions is too small or too big; 4) disturbances and uncertainties from the joints, since sometime they may cause steady-state error and deviate your estimation as your expected.

Please let me know whether it helps you or not..

Ming

Afshin,

two years ago during the course of estimation, I've tried to estimate some parameters of a reaction wheel (RW) using the extend Kalman Filter. I used the LuGrE model to represent the dynamics of the RW. However, I did not have successful to estimate the parameters. At that moment, I've realized that, despite of the system to be fully observable system, the "coupling" beetween the states (states and parameters) were not too strong. Then, the covariance of the parameters and some states did not converge to an acceptable levels.

One of the reasons that I think that could have happened is that, may I did not excited the system properly (input signal).

So my suggestions to your problem are: check your signal input to see if it is a good excitation signal and second check if your system is completely observable. Third, as Ming said, may your initials conditions are too far from the true values (for a non-linear system it could be a problem).

Adolfo

Hi Hessam,

Thanks for your answer, I read your conference paper paper on the joint estimation problem. I have used both joint and dual estimation approaches and failed to achieve satisfactory results in both. It seems to me that tuning the filter itself is very important as the parameters playing roles in the overall estimation problem are very critical. 

During my diagnosis process, I also figured that using adaptive filters also enhances the performance of the filter and its stability. However, it still did not fix my problem.

Noise level is another important factor in this area and playing with that parameter as well gives me different results none of which seem to be satisfactory for my case.

I am still investigating where else I could have gone wrong to finally get this right. Nevertheless I truly appreciate your willingness to help.

Regards,

Afshin

Hi Ming,

Thanks a lot for your response. I checked all the 4 possibilities you mentioned and somehow cannot understand which one could be causing it. In reality I have a model that is working and trying to replicate the work using literature but things don't seem to be working out. So I am wondering if I am doing something wrong or what I have from the literature is not consistent. Nevertheless I need to make the model and have it work as I need to enhance it.

Regards,

Afshin

Hi Adolfo,

Thanks for your response. My system is observable for the states and not parameters obviously and I am getting satisfactory results for the states. However as you mentioned the coupling could be the problem as my co-variance matrices seem to diverge drastically. I also added adaptive scheme to the UKF I had hoping that would fix the problem but it did not. 

So I will be looking into other systems to see if the problem is with the system or the UKF algorithm.

I will update you with the results if I get anywhere.

Regards,

Afshin

Hi Afshin,

as far I understand, when you have an unobservable system you cannot estimate the states (states/parameters) which are not observable. Does not matter which technique you are applying, it won't work. 

As you noted, your co-variance matrix diverges drastically, it may happen because your system is unobservable by the measurements of are you taking. 

Regards,

Adolfo

Afshin,

any news about the estimation? Did you solve your estimation problem?

Hi Adolfo,

Thanks for following up. I actually tried different approaches and different systems to see where the problem could be. I even tried coding the algorithm and systems instead of using Simulink.

All in all, I figured the solution is very much system specific. For simpler system I get satisfactory results while for the RW system I still get very random outputs for the parameters. So I am thinking of working on the RW model itself to examine why the algorithm works on other systems that I have tried and not the RW model.

If you have any references that could help with this problem I would appreciate it.

Regards,

Afshin

Great.  By the way what is the model are you using to represents the dynamics of a reaction wheel?

I've tried once the model called LuGre, you can find it on internet. However, I didn't have succeeded. 

Regards,

Adolfo

Hi Adolfo,

I am using the Bialke model from his paper back in the 1980s. It is very high fidelity model and that may be the reason.

~Afshin

Hi Asfhin,

Are there a special reason to you use this sophisticated (high fidelity) model instead of

J \dot{\omega} = T - B {\ omega} ?

where J is the moment of inertia and B is the viscous damping. 

Adolfo

Hi Adolfo,

The model is used due to its complexity and we were trying to see if it is feasible to use it.

~Afshin

Afshin Rahimi,

as you are studying the model of a reaction wheel I would like to make a question. I suppose that you as already do satellite pointing algorithm (attitude control) using a reaction wheel as actuator.

My question is, which is the best mode to operate a reaction wheel by the torque mode or speed mode? What are the tradeoff between the two strategies?

Thank you.

Hi Adolfo,

You are right about ACS but I should tell you that I am not working on the control development at this stage I am using a developed control from one of my colleagues. I am focusing more on the estimation and FDI aspect of the problem so I am not sure if I could be an asset to help you with your question.

-Afshin