  In this paper, we propose a suboptimal moving horizon estimator for a general
class of nonlinear systems. For the stability analysis, we transfer the
"feasibility-implies-stability/robustness" paradigm from model predictive
control to the context of moving horizon estimation in the following sense:
Using a suitably defined, feasible candidate solution based on an auxiliary
observer, robust stability of the proposed suboptimal estimator is inherited
independently of the horizon length and even if no optimization is performed.
Moreover, the proposed design allows for the choice between two cost functions
different in structure: the former in the manner of a standard least squares
approach, which is typically used in practice, and the latter following a
time-discounted modification, resulting in better theoretical guarantees. We
apply the proposed suboptimal estimator to a nonlinear chemical reactor
process, verify the theoretical assumptions, and show that even a few
iterations of the optimizer are sufficient to significantly improve the
estimation results of the auxiliary observer. Furthermore, we illustrate the
flexibility of the proposed design by employing different solvers and compare
the performance with two state-of-the-art fast MHE schemes from the literature.
