  We propose a moving horizon estimation scheme for estimating the states and
time-varying parameters of nonlinear systems. We consider the case where
observability of the parameters depends on the excitation of the system and may
be absent during operation, with the parameter dynamics fulfilling a weak
incremental bounded-energy bounded-state property to ensure boundedness of the
estimation error (with respect to the disturbance energy). The proposed
estimation scheme involves a standard quadratic cost function with an adaptive
regularization term depending on the current parameter observability. We
develop robustness guarantees for the overall estimation error that are valid
for all times, and that improve the more often the parameters are detected to
be observable during operation. The theoretical results are illustrated by a
simulation example.
