  Long horizon lengths in Moving Horizon Estimation are desirable to reach the
performance limits of the full information estimator. However, the conventional
MHE technique suffers from a number of deficiencies in this respect. First, the
problem complexity scales at least linearly with the horizon length selected,
which restrains from selecting long horizons if computational limitations are
present. Second, there is no monitoring of constraint activity/inactivity which
results in conducting redundant constrained minimizations even when no
constraints are active. In this study we develop a Multiple-Window Moving
Horizon Estimation strategy (MW-MHE) that exploits constraint inactivity to
reduce the problem size in long horizon estimation problems. The arrival cost
is approximated using the unconstrained full information estimator arrival cost
to guarantee stability of the technique. A new horizon length selection
criteria is developed based on maximum sensitivity between remote states in
time. The development will be in terms of general causal descriptor systems,
which includes the standard state space representation as a special case. The
potential of the new estimation algorithm will be demonstrated with an example
showing a significant reduction in both computation time and numerical errors
compared to conventional MHE.
