As far as I know, the filter algorithm can be separated into two parts: prediction and update. How to optimally estimate the state relies on balancing the weight of prediction and update. On the other word, do we trust predicted state or the observations more? It is more important for the dynamic system with unknown model or measurements errors. Could any body can give some advice on what kinds of filters (Adaptive or Robust filters) are more practical for system with unknown model or measurements errors? Is H2/H infinity filter the only choice? Thank you very much!!
Dear Zheng,
I would like to suggest you to implement Extended Kalman Filter, if the system which you are working consists of near Gaussian distributions. I can also suggest you to try for Unscented Kalman Filter (Julier and Uhllman), if the state dimension of the system is not greater than 10, provided the system dynamics could result in sever non-Gaussian densities.
I hope that I have addressed your question.
Hello Zheng, it is a very complicated question to address. I worked on the topic few years ago and now I am coming back to it. As an overall response to your question I have to say that there is not a unique filter to overcome all the aforementioned issues. The use of one filter or another strongly depends on the specific problem you have. It also relies on the nature of the model, i.e., if the structure is linear or nonlinear. I have more experience with linear models and with uncertainties over the statistics of the unknown inputs. In this way, I have to say that H-infinity filters work quite good. I also studied the Moving Horizon Estimator and it showed a good trade-off between performance and robustness. The issue with the last filter is the formulation and solution of a min-max optimization problem at each sample time. Anyway, I hope this discussion keep going here. Best!!
Dear Krishna Kumar Kottakki,
Thank you very much for your answer! I agree with you about the simple implementation of EKF and UKF. However, I am dealing with a high nonlinear system with relatively low update rate. Therefore the performance of both EKF and UKF is not ideal. I'm moving on to find other possible solution. Thank you again!
Sincerely,
Zhengshi Yu
Dear Jose Garcia Tirado,
Thank you very much for your suggestion. It's true that the performance of filter is strongly depends on the specific problem. Now I am dealing with a high nonlinear system with relatively low update rate. Maybe H infinity filter is a good choice. I'll work on to this topic and contact with you in case of any progress.Thanks again for your helpful answer!
Sincerely yours,
Zhengshi Yu
Dear Zheng, that's a very encouraging topic. However, let me add an additional ingredient. If dealing with a highly nonlinear system as you mentioned, please be sure that the uncertainty is mainly on the parameters and/or the inputs to the system and not on the structure of the model. In this regard, I rather prefer to refine the structure of the model before implementing any estimation or control strategy. Best!
Hi Zheng-shi Yu
I like to keep things simple if I can. When very little is known about process and measurement models, simple linear regression, using a finite (FIR) or fading memory (IIR), can work well. Implemented recursively of course! Here you have only 3 parameters you need to tweak, to get the filter response you want, for a 1D problem - (polynomial) model order, memory length and delay.
This is all explained quite nicely in this book: N. Morrison, Introduction to Sequential Smoothing and Prediction, McGraw Hill, 1969.If you can't find that book, I also use this approach to design digital filters in a control paper I have submitted recently.
Hope this helps,
Hugh
Hello. I think it depends on what you mean by unknown. Even the simplest estimators/filters make implicit assumptions about the errors in the system and measurement models, with most techniques requiring independent (white) noise. If you are after robust estimators, then the H-infinity class may be a good choice. I understand that this filter may not always be realisable depending on its tuning. Another class of estimator that does not make many assumptions about the data is set theoretic. In this case, you only need to bound the noise.
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 issues.
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