  A computationally efficient method for online joint state inference and
dynamical model learning is presented. The dynamical model combines an a priori
known state-space model with a radial basis function expansion representing
unknown system dynamics. Thus, the model is inherently adaptive and can learn
unknown and changing system dynamics on-the-fly. Still, by including prior
knowledge in the model description, a minimum of estimation performance can be
guaranteed already from the start, which is of utmost importance in, e.g.,
safety-critical applications. The method uses an extended Kalman filter
approach to jointly estimate the state of the system and learn the system
properties, via the parameters of the basis function expansion. By using
compact radial basis functions and an approximate Kalman gain, the
computational complexity is considerably reduced compared to similar
approaches. The approximation works well when the system dynamics exhibit
limited correlation between points well separated in the state-space domain.
The method is exemplified via two intelligent vehicle applications where it is
shown to: (i) have essentially identical system dynamics estimation performance
compared to similar non-real-time algorithms, and (ii) be real-time applicable
to large-scale problems.
