E Partial Observation with the Kalman Filter

Abstract

This appendix contains the proofs of Lemmas 7.1 and 7.2. These lemmas state that, for static systems, (i) a Kalman Filter can be run on only the observable state variables; and (ii) the full state estimate and covariance matrix (i.e., including the unobservable state variables) can be calculated at any time based on the full initial state estimate and covariance matrix and the new state estimate and covariance matrix of the observed part of the state.