Under conditions of constant sampling rate and constant sampling errors, after a sufficiently long tracking time, all terms of the covariance matrix converge to their corresponding asymptotic magnitudes. After convergence, all variables of the Riccati equation remain unchanged. In such conditions the only unknown in this equation is the steady-state covariance matrix. An analytic solution of the resulting steady-state Riccati equation for "short" sampling times is derived. After solution all terms of the resulting covariance matrix are then expressed as functions of a particularly defined "time constant". The application of the time constant produces several practical advantages: it greatly facilitates the determination of the model-noise parameter (q), provides a fair assessment of the tracking accuracies, and determines the steady-state transfer function of the filter.
Steady-State Time Constant of the Kalman Filter
Itzhack Y. Bar-Itzhack Memorial Symposium on Estimation, Navigation, and Spacecraft Control ; 2012 ; Haifa, Israel October 14, 2012 - October 17, 2017
Advances in Estimation, Navigation, and Spacecraft Control ; Chapter : 1 ; 3-19
2015-01-01
17 pages
Article/Chapter (Book)
Electronic Resource
English