ON OPTIMAL LINEAR SMOOTHING THEORY

Abstract
The algorithm for generating the smoothed estimate x(t/t + T) of the state x(t) of a continuous linear system, where t is continuous time, T is a positive real constant, and t + T is the time of the most recent measurement, is developed. A linear matrix differential equation whose solution gives the covariance matrix of the smoothing error x(t/t + T)=x(t/t + T) is then derived. Computational aspects involved in mechanizing the algorithm are discussed in terms of the algorithm's dependence on the solution of the prediction, filtering, and fixed-point smoothing problems. The results are then discussed in terms of the classical Wiener smoothing problem.