Linearly Constrained Wiener Filter Estimates For Linear Discrete State-Space Models

For linear discrete state-space (LDSS) models, under certain conditions, the Wiener filter (WF) has a convenient recursive predictor/corrector format, aka the Kalman filter (KF). As a contribution to Wiener filtering and Kalman filtering in the context of LDSS models, the paper derives the family of linear constraints for which the linearly constrained WF (LCWF) can be computed recursively in the form of a KF, leading to a linearly constrained KF (LCKF). Among other things, as exemplified by an array processing example, the LCKF may provide alternative solutions to H∞ filter and unbiased finite impulse response filter to robustify the KF, which performance are sensible to misspecified noise or uncertainties in the system matrices.