  Bayesian filtering is a general framework for recursively estimating the
state of a dynamical system. Classical solutions such that Kalman filter and
Particle filter are introduced in this report. Gaussian processes have been
introduced as a non-parametric technique for system estimation from supervision
learning. For the thesis project, we intend to propose a new, general
methodology for inference and learning in non-linear state-space models
probabilistically incorporating with the Gaussian process model estimation.
