  Parameters of the mathematical model describing many practical dynamical
systems are prone to vary due to aging or renewal, wear and tear, as well as
changes in environmental or service conditions. These variabilities will
adversely affect the accuracy of state estimation. In this paper, we introduce
SSUE: Simultaneous State and Uncertainty Estimation for quantifying parameter
uncertainty while simultaneously estimating the internal state of a system. Our
approach involves the development of a Bayesian framework that recursively
updates the posterior joint density of the unknown state vector and parameter
uncertainty. To execute the framework for practical implementation, we develop
a computational algorithm based on maximum a posteriori estimation and the
numerical Newton's method. Observability analysis is conducted for linear
systems, and its relation with the consistency of the estimation of the
uncertainty's location is unveiled. Additional simulation results are provided
to demonstrate the effectiveness of the proposed SSUE approach.
