Online functional prediction for spatio-temporal systems using time-varying radial basis function networks

In this paper, functional prediction is carried out for spatio-temporal systems in which the spatial data is irregularly sampled. We propose a novel method called Kalman Filter Radial Basis Function (KF-RBF) for such a purpose. It casts the problem into a Reproducing Kernel Hilbert Space (RKHS) defined by some continuous, symmetric and positive definite Radial Basis Function (RBF), thereby allowing for irregular sampling in the spatial domain. A Functional Auto-Regressive (FAR) model describing the system evolution in the temporal domain is further assumed. The FAR model is then formulated as a Vector Auto-Regressive (VAR) model embedded into a Kalman Filter (KF). This is achieved by projecting the unknown functions onto a time-invariant functional subspace. Subsequently, the weight vectors obtained become inputs into a Kalman Filter (KF). In this way, nonstationary functions can be forecasted by evolving these weight vectors.