  This paper considers the problem of Bayesian transfer learning-based
knowledge fusion between linear state-space processes driven by uniform state
and observation noise processes. The target task conditions on probabilistic
state predictor(s) supplied by the source filtering task(s) to improve its own
state estimate. A joint model of the target and source(s) is not required and
is not elicited. The resulting decision-making problem for choosing the optimal
conditional target filtering distribution under incomplete modelling is solved
via fully probabilistic design (FPD), i.e. via appropriate minimization of
Kullback-Leibler divergence (KLD). The resulting FPD-optimal target learner is
robust, in the sense that it can reject poor-quality source knowledge. In
addition, the fact that this Bayesian transfer learning (BTL) scheme does not
depend on a model of interaction between the source and target tasks ensures
robustness to the misspecification of such a model. The latter is a problem
that affects conventional transfer learning methods. The properties of the
proposed BTL scheme are demonstrated via extensive simulations, and in
comparison with two contemporary alternatives.
