Reduced-order estimation via a two point boundary value problem and comparison with other techniques

A uniform derivation of reduced-order estimation (filtering and smoothing) algorithms by application of Pontryagin´s minimum principle and a two-point boundary value problem is presented. An appropriate performance index for a general class of reduced-order estimation problems is formulated to account for the entire time interval of estimation. The results provide quantitative criteria for measuring the performance of certain classes of heuristically designed suboptimal reduced-order estimators as well as explicit guidance with respect to the suboptimal estimator design process. A third-order system is used as an example to illustrate the result