Orthogonal Projection and Discrete Optimal Linear Smoothing

The smoothing filter and smoothing error covariance matrix equations are developed for discrete linear systems using the method of orthogonal projection. Two equivalent formulations are presented and found to agree with those of previous authors who had used other methods. The present results in conjunction with the earlier work of Kalman on prediction and filtering give a complete treatment of the discrete linear estimation problem from the viewpoint of orthogonal projection.