I'm interested in wind forecasting, which I have analyzed over some time by means of ARMA methods. Now I've being reading about Kalman filtering. Kalman filter is optimal when Gaussian assumption can be hold. However, wind distributions are far from normal (with Weibull the most popular). My question is, Is it correct to transform a wind speed time series by means of Box-Cox transformation before estimating the parameters of Kalman filter, so that the normality assumption holds? If it were so, why then using particle filters?
Box-Cox transformation is most often used to address non-constant variance. It doesn't convert non-Gaussian noise to Gaussian generally.
Kalman filter's a very convenient and fast method of estimation of state-space models (SSM) when the errors are Gaussian, and the models are linear. There are other ways of estimating SSM though. If you wish to venture beyond ARMA, then I would suggest reading about SSM in general, not just Kalman filters. The good book on SMM is Shumway and Stoffer, it has its own R package with code and examples. The non-gaussian estimation is in section 6.10 of 2nd edition. I didn't read the 3rd edition yet.
They have a follow up book on nonlinear modeling.