Hi, Mellah
The Kalman Filter is a filter that works as a least square error optimizer, and, for this to work, it is necessary that the system that you consider inside the filter is linear.
In order to make state estimation on nonlinear systems, or parameter estimation, using the Kalman filter, one of the possible approaches is to linearize the system under investigation around its current state and force the filter to use this linearized version of your system as a model. This is the Extended Kalman Filter, or EKF.
However, the EKF is not very stable and many times, when it does converge to the "right" solution, it does it very slowly. In order to improve this filter, instead of using linearization to predict the behavior of the system under investigation, some authors started using the Unscented Transformation. Hence, the Kalman Filter with the Unscented transformation is called Unscented Kalman Filter, or UKF.
This filter has some advantages when compared to the EKF, because the Unscented transformation somehow describes the nonlinear system better than the linearization, hence this filter converges to the right solution more rapdly. However, as the EKF, this filter may become unstable and results may be biased.
I hope I could help a little bit.
Best regards,
Vinícius
Hi, Mellah
The Kalman Filter is a filter that works as a least square error optimizer, and, for this to work, it is necessary that the system that you consider inside the filter is linear.
In order to make state estimation on nonlinear systems, or parameter estimation, using the Kalman filter, one of the possible approaches is to linearize the system under investigation around its current state and force the filter to use this linearized version of your system as a model. This is the Extended Kalman Filter, or EKF.
However, the EKF is not very stable and many times, when it does converge to the "right" solution, it does it very slowly. In order to improve this filter, instead of using linearization to predict the behavior of the system under investigation, some authors started using the Unscented Transformation. Hence, the Kalman Filter with the Unscented transformation is called Unscented Kalman Filter, or UKF.
This filter has some advantages when compared to the EKF, because the Unscented transformation somehow describes the nonlinear system better than the linearization, hence this filter converges to the right solution more rapdly. However, as the EKF, this filter may become unstable and results may be biased.
I hope I could help a little bit.
Best regards,
Vinícius
Dear Mellah, I think Wikipedia gives quite complete answers. In brief, the KF is an optimal estimator for linear discrete-time state-space models. If the model is nonlinear, then the EKF serves as the first-order or second-order approximating estimator. If the system is highly nonlinear, the EKF may diverge and the UKF produces typically better results. The UKF uses the unscented transform to form the output trough the moments.
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