Constraining Kalman Filter and Smoothing Estimates to Satisfy Time-Varying Restrictions

It sometimes happens that the unobservable state vector of a linear dynamic model expressed in the state space is subject to known restrictions. Incorporation of this information into the Kalman filter procedure will increase the efficiency of estimation. It is shown that a simple augmentation of the measurement equation constrains the estimated state vector to obey the restrictions. The method applies whether the restrictions are time-invariant, time-varying, linear, or nonlinear.