  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
