  A major challenge in state estimation with model-based observers are
low-quality models that lack of relevant dynamics. We address this issue by
simultaneously estimating the system's states and its model uncertainties by a
square root UKF. Concretely, we extend the state by the parameter vector of a
linear combination containing suitable functions that approximate the lacking
dynamics. Presuming that only a few dynamical terms are relevant, the parameter
vector is claimed to be sparse. In Bayesian setting, properties like sparsity
are expressed by a prior distribution. One common choice for sparsity is a
Laplace distribution. However, due to some disadvantages of a Laplacian prior,
the regularized horseshoe distribution, a Gaussian that approximately features
sparsity, is applied. Results exhibit small estimation errors with model
improvements detected by an automated model reduction technique.
