  We propose a moving horizon estimation scheme for joint state and parameter
estimation for nonlinear uncertain discrete-time systems. We establish robust
exponential convergence of the combined estimation error subject to process
disturbances and measurement noise. We employ a joint incremental
input/output-to-state stability ($\delta$-IOSS) Lyapunov function to
characterize nonlinear detectability for the states and (constant) parameters
of the system. Sufficient conditions for the construction of a joint
$\delta$-IOSS Lyapunov function are provided for a special class of nonlinear
systems using a persistence of excitation condition. The theoretical results
are illustrated by a numerical example.
