  Moving horizon estimation (MHE) offers benefits relative to other estimation
approaches by its ability to explicitly handle constraints, but suffers
increased computation cost. To help enable MHE on platforms with limited
computation power, we propose to solve the optimization problem underlying MHE
sub-optimally for a fixed number of optimization iterations per time step. The
stability of the closed-loop system is analyzed using the small-gain theorem by
considering the closed-loop controlled system, the optimization algorithm
dynamics, and the estimation error dynamics as three interconnected subsystems.
By assuming incremental input/output-to-state stability ({\delta}- IOSS) of the
system and imposing standard ISS conditions on the controller, we derive
conditions on the iteration number such that the interconnected system is
input-to-state stable (ISS) w.r.t. the external disturbances. A simulation
using an MHE- MPC estimator-controller pair is used to validate the results.
