On the efficient low cost procedure for estimation of high-dimensional prediction error covariance matrices

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

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Conservative Quantization of Covariance Matrices with Applications to Decentralized Information Fusion

Sensors ◽

10.3390/s21093059 ◽

2021 ◽

Vol 21 (9) ◽

pp. 3059

Author(s):

Christopher Funk ◽

Benjamin Noack ◽

Uwe D. Hanebeck

Keyword(s):

Information Fusion ◽

Data Transmission ◽

Covariance Matrices ◽

Networked Systems ◽

High Dimensional ◽

Available Bandwidth ◽

Error Covariance ◽

Covariance Intersection ◽

Fusion Methods ◽

Optimal Fusion

Information fusion in networked systems poses challenges with respect to both theory and implementation. Limited available bandwidth can become a bottleneck when high-dimensional estimates and associated error covariance matrices need to be transmitted. Compression of estimates and covariance matrices can endanger desirable properties like unbiasedness and may lead to unreliable fusion results. In this work, quantization methods for estimates and covariance matrices are presented and their usage with the optimal fusion formulas and covariance intersection is demonstrated. The proposed quantization methods significantly reduce the bandwidth required for data transmission while retaining unbiasedness and conservativeness of the considered fusion methods. Their performance is evaluated using simulations, showing their effectiveness even in the case of substantial data reduction.

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Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

ISRN Computational Mathematics ◽

10.1155/2013/249594 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 6

Author(s):

Nicholas Assimakis ◽

Maria Adam

Keyword(s):

Kalman Filter ◽

Riccati Equation ◽

Discrete Time ◽

Prediction Error ◽

Estimation Error ◽

Riccati Equations ◽

Covariance Matrices ◽

Linear Estimation ◽

Solution Algorithms ◽

Error Covariance

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.

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