Stochastic stability of the continuous-time extended Kalman filter

2000 ◽  
Vol 147 (1) ◽  
pp. 45-52 ◽  
Author(s):  
K. Reif ◽  
R. Unbehauen ◽  
E. Yaz ◽  
S. Günther
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Stochastic Stability ◽  
Continuous Time

H∞-Property of the Continuous-Time Extended Kalman Filter

2016 ◽  
Author(s):  
Jennifer L. Bonniwell ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Continuous Time ◽  
Estimation Error ◽  
Finite Energy ◽  
Minimum Variance ◽  
Nonlinear Observer ◽  
Minimum Variance Estimator ◽  
Error Energy ◽  
Special Case

This work elucidates another theoretical property of the ubiquitous extended Kalman filter by analyzing the energy gain of the continuous-time extended Kalman filter used as a nonlinear observer in the presence of finite-energy disturbances. The analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that the extended Kalman filter inherently has the H∞-property along with being the locally optimal minimum variance estimator. A special case of this result is also shown to be the H2-property of the extended Kalman filter.

scholarly journals Surface-constrained continuous-time extended Kalman filter: optimal estimation of a state of a constrained dynamic system-ball-rover rolling on a known surface

2021 ◽  
Author(s):  
Maksims Demjanenko
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Continuous Time ◽  
Contact Point ◽  
Optimal Estimation ◽  
State Estimate ◽  
Rolling Ball ◽  
Novel Approach ◽  
Variable Wind ◽  
Better Than

The Surface-constrained Continuous-time Extended Kalman Filter (SCEKF), derived in thesis, contains a novel approach for handling surface or equality constraints, in which the surface-constrained CEKF is the projection of the unconstrained CEKF onto the set of state estimate rates that satisfy the constraints. The filter is used for optimal estimation of a state of a ball rolling on a known surface with uneven elevation. The state consists of surface contact point and geometrical center positions, attitude and angular velocity of the ball. The dynamics of the ball is affected by "unknown" to the filter disturbances, due to off-center point mass and variable wind. Thesis includes derivations of the SCEKF and the constraint dynamics of a rolling ball. The numerical computation results show that the surface-constrained filter can produce an accurate state estimate of the rolling ball and demonstrate that the estimate is significantly better than that produced by unconstrained filter.

Stochastic stability of the discrete-time extended Kalman filter

1999 ◽  
Vol 44 (4) ◽  
pp. 714-728 ◽  
Author(s):  
K. Reif ◽  
S. Gunther ◽  
E. Yaz ◽  
R. Unbehauen
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Discrete Time ◽  
Stochastic Stability

Stochastic Stability Condition for the Extended Kalman Filter With Intermittent Observations

2017 ◽  
Vol 64 (3) ◽  
pp. 334-338 ◽  
Author(s):  
Xiangdong Liu ◽  
Luyu Li ◽  
Zhen Li ◽  
Tyrone Fernando ◽  
Herbert H. C. Iu
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Stability Condition ◽  
Stochastic Stability
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