ON OPTIMAL LINEAR SMOOTHING THEORY
NORTHWESTERN UNIV EVANSTON IL INFORMATION-PROCESSING AND CONTROL SYSTEMS LAB
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The algorithm for generating the smoothed estimate xtt T of the state xt 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 xtt Txtt T is then derived. Computational aspects involved in mechanizing the algorithm are discussed in terms of the algorithms 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.
- Theoretical Mathematics