Linearly Constrained Kalman Filter For Linear Discrete State-Space Models

For linear discrete state-space (LDSS) models, under certain conditions, the linear least mean squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter (KF). The aim of the paper is to introduce the general form of the linearly constrained KF (LCKF) for LDSS models, which encompasses the linearly constrained minimum variance estimator (LCMVE). Thus the LCKF opens access to the abundant litterature on LCMVE in the deterministic framework which can be transposed to the stochastic framework. Therefore, among other things, the LCKF may provide alternative solutions to $H_{\infty }$ filter and unbiased finite impulse response filter to robustify the KF, which performance are sensible to misspecified noise or uncertainties in the system matrices