For estimation problem, measurements with different updating frequency might be used. For example, the updating frequency for measurement y1 is 10 Hz, and that for y2 is 1 Hz. In the paper "Fast auto generated ACADO integrators and application to MHE with
multi-rate measurements", it mentioned this problem but didn't go into detail on how to implement this in ACADO toolkit. My questions are as follows:
Is this supported in the toolkit? How to do that?
If continuous output functionality is used to obtain those pesudo measurements based on the lastest estimation, there might be a big error on those measurements since there are not true measurements. How to deal with this? Just give them bigger measurement noise? Will the estimation actually benefit from dealing with multi-rate measurements this way? After all, the true measurements are limited.
Thank you.
Best regards,
Francis
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There might be a misunderstanding of the concept of using continuous output for implementing multi-rate Moving Horizon Estimation, if I understood your question. The idea is namely not to create pseudo measurements, but instead to use all the real measurements (but only real measurements with a particular accuracy) and minimize the misfit between these measurements and simulation based predictions. So continuous output is only a numerical tool to efficiently provide such simulation based predictions on a time grid which can be different from the control grid.
In your example, where you have a frequency of 10 Hz for y1 and 1 Hz for y2, then you could line up the discretization of the control horizon with the 1 Hz measurements and use continous output to obtain model based simulation results for the intermediate measurements of the output function in y1, for the purpose of numerical efficiency (of course, this only makes sense for some applications not for all).
Sadly, this feature is not directly supported in the ACADO Toolkit. Instead, you could export the code for a continuous output based integrator, using the SIMexport module, and provide the problem linearization results to an embedded QP solver similar to what was done in the publication that you refer to.
I hope this more or less answers your question.
Best,
Rien
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi all,
For estimation problem, measurements with different updating frequency might be used. For example, the updating frequency for measurement y1 is 10 Hz, and that for y2 is 1 Hz. In the paper "Fast auto generated ACADO integrators and application to MHE with
multi-rate measurements", it mentioned this problem but didn't go into detail on how to implement this in ACADO toolkit. My questions are as follows:
Thank you.
Best regards,
Francis
Hi Francis,
There might be a misunderstanding of the concept of using continuous output for implementing multi-rate Moving Horizon Estimation, if I understood your question. The idea is namely not to create pseudo measurements, but instead to use all the real measurements (but only real measurements with a particular accuracy) and minimize the misfit between these measurements and simulation based predictions. So continuous output is only a numerical tool to efficiently provide such simulation based predictions on a time grid which can be different from the control grid.
In your example, where you have a frequency of 10 Hz for y1 and 1 Hz for y2, then you could line up the discretization of the control horizon with the 1 Hz measurements and use continous output to obtain model based simulation results for the intermediate measurements of the output function in y1, for the purpose of numerical efficiency (of course, this only makes sense for some applications not for all).
Sadly, this feature is not directly supported in the ACADO Toolkit. Instead, you could export the code for a continuous output based integrator, using the SIMexport module, and provide the problem linearization results to an embedded QP solver similar to what was done in the publication that you refer to.
I hope this more or less answers your question.
Best,
Rien
Hi Rien,
Thanks for your explanation. I'll try that.
Best regards,
Francis