Further investigation into restricted Kalman filtering

In this paper I return to the issue of estimating linear state space models with constrained state vectors. My endeavor is towards the following tasks: (i) to give a new elementary derivation for restricted Kalman filtering under augmentation of the measurement equation, (ii) to prove the statistical efficiency due to the imposition of restrictions using a geometrical framework, and (iii) to propose an alternative approach for imposing time-invariant restrictions to the estimation of random walk state vectors.