Long horizon lengths in Moving Horizon Estimation (MHE) 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 program 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 sensitivity between remote states in time. The development was 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 was demonstrated with an example
in filtering with measurement outliers.
Reference paper: Multiple Window Moving Horizon Estimation; http://arxiv.org/abs/1402.3317