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