Least-squares parameter estimation for state-space models with state equality constraints

If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in constrained discrete-time state-space estimation, equality constraint defined for parameter matrix not as commonly found regression problems. To address this problem, firstly, we show how to rewrite matrices be estimated. Then, vectorise matricial least squares problem systems such that any method from equality-constrained framework may employed. Both time-invariant time-varying cases considered well case where exactly known.