Hello,
I have a question regarding the choice of parameter estimation approach. I have a nonlinear 3rd order dynamic model which is linear in the parameter. I need to figure out a parameter estimation technique for it. I tried simple Least Square (LS), and Moving Horizon Estimation (MHE), but both gives me almost similar results. I have in mind also LS-SVM.
My question is , Is there an advantage of LS-SVM or MHE over simple LS for parameters estimation of systems which are linear in the parameter?
Note: I assume full state measurement.
Thanks in advance
LS-SVM allow us to ignore over-fitting effect, which is regular effect for simple LS method.
@Sergey Porotsky
Thank you very your answer.
If the model is predetermined by physical modelling and the objective is just to estimate the parameters, will i face also the problem of overfitting??
My understanding of the term "overfitting" is using more parameters than there are degrees of freedom. In effect, we approximate experimental noise rather than the phenomenon under investigation. This simply cannot happen when there is exactly one unknown parameter and at least 3 measurements. The other question is sensitivity to outliers of this or that procedure. LS are known to be prone to such kind of perturbations. From practical point of view: when two approaches generate similar results then the one producing smaller uncertainties should be preferred. The presence of outliers always leads to overestimated uncertainties of estimated parameters.
The recursive least squares algorithm (RLS) is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations and a set of dependent (observed) variables.
Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS algorithm with forgetting factor (RLS-FF) to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
This software uses an improved iterative least squares method:
www.lerenisplezant.be/fitting.htm
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