Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices. (11th December 2013)

• Record Type: Journal Article
• Authors: Assimakis, Nicholas; Adam, Maria
• Other Names: Corti D. S. Academic Editor.; Lima F. W. S. Academic Editor.; Ruskin H. J. Academic Editor.
• Is Part Of: ISRN computational mathematics. Volume 2013(2013)
• Publication Date: 2013-12-11
• Subjects: Numerical analysis -- Periodicals; Mathematics -- Data processing -- Periodicals; Mathematics -- Data processing; Numerical analysis; Electronic journals; Periodicals; 510
• DOI: 10.1155/2013/249594
• Languages: English
• ISSNs: 2090-7842

Abstract

Abstract : The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.