Kalman filtering from POP-based diagonalization of ARH(1)

The autoregressive Hilbertian model of order one (ARH(1)) is considered to represent the dynamics of a sequence of spatial functional data. Spatiotemporal interaction is defined in terms of the autocorrelation operator. A diagonalization of ARH(1) models is derived based on the functional principal oscillation pattern (POP) decomposition of such an operator. The results are applied to implement the Kalman filter for spatiotemporal prediction from the information provided by the observation of a finite sequence of spatial functional data.