A state space model is frequently used for a description of real systems. Usually, some state variables are hidden and cannot be measured directly and some model parameters are unknown. Then, the need for learning, i.e., the state filtering and parameter estimation, arises. Probabilistic models provide a suitable description of the always uncertain reality and call for such approaches as Bayesian learning. Uncertainties are standardly modelled by the Gaussian distribution. This leads to Kalman-filter-based algorithms.
However, the modelled quantities are often physically constrained. Then, methods based on the Gaussian distribution with unbounded support do not work properly and they have to be adapted. The alternative sophisticated algorithms based on “unknown-but-bounded errors” principle address the same problem but they are poorly harmonised
with the subsequent dynamic decision making (like control, prediction of hidden quantities or future measurements) to which any learning serves.
This research operates in probabilistic framework while coping with bounded uncer-tainties and physically constrained quantities. Here, learning algorithms for models with constraints are constructed that (i) are based on the Bayesian principle, (ii) are recursive and (iii) have relatively simple setting and maintenance, (iv) are at disposal to subsequent
dynamic decision making.