Estimation of linearly constrained parameters via the Kalman filter

The estimation of a least-squares parameter (or state) vector in a standard model is extended to the least-squares estimation of a linearly constrained vector. It is shown that the required pseudoinverses can be computed recursively, and, with suitable initialisation, a standard Kalman filter will provide the same estimates. The resulting recursion is a powerful starting point in the design of adaptive communications filters and antennas.