I want to use a EKF for parameter (p) and state (x) estimation.
I am currently not understanding the difference between (1) the formulation of the parameters as states:
x_new=[x,p] and using a normal EKF for estimating x_new
and (2) the formulation with a dual extended Kalman filter, where x and p are estimated individually.
Which of them provides more benefits?
I am very thankful for your tips.
Jan Bischof:
Kalman filter: Say, we have a physical system. It is driven by a set of ext. inputs/controls. The o/p is taken by sensors. Based on these available info. viz., control inputs and observations Kalman filter estimates the state of the system optimizing a certain criteria.
Extended Kalman filter (EKF): While the Kalman filter is designed for linear discrete-time dynamical system, EKF works for discrete-time nonlinear systems.
Dual EKF: The Dual EKF estimates both the states of the dynamical system and its
parameters simultaneously when only noisy observations are available.
Hi Jan,
currently I have a similar question (but no time so far to read deeper) and found this references that explain this topic in detail:
[book, see chapter 5 Dual Extended Kalman Filter Methods]
Haykin, S., ed. (2001), Kalman filtering and neural networks, Wiley Online Library.
[an application paper]:
Wenzel, T. A.; Burnham, K. J.; Blundell, M. V. & Williams, R. A. (2006), 'Dual extended Kalman filter for vehicle state and parameter estimation', Vehicle System Dynamics 44(2), 153--171.
If you find there somes answers, I would be happy to listen to it.
Best, Stephan
Hi Jan,
Discrete Kalman Filter is applicable only for linear system but in real world most of the system are non linear in this case linearization of the non linear system is required. After linearization of the system the state space model of the system is converted into Error state space model i.e. error in the state. In this case Linearized Kalman Filter is used for estimating error in the state. Extended Kalman Filter is used for non linear system but it estimates actual state not error in the system. You can get very good detail of Linearized Kalman Filter and Extended Kalman Filter in Chapter 9 of “Introduction to Random Signals And Applied Kalman Filtering” by Robert Grover Brown &Patrick Y.C. Hwang.
Regards
Brijesh
For Non-linear estimation in SLAM, what may be the best filer out of
1. KF
2.EKF
3. UKF
4. IEKF (Iterated EKF)
5. CEKF (Compressed EKF)
etc.
Jan Bischof:
Kalman filter: Say, we have a physical system. It is driven by a set of ext. inputs/controls. The o/p is taken by sensors. Based on these available info. viz., control inputs and observations Kalman filter estimates the state of the system optimizing a certain criteria.
Extended Kalman filter (EKF): While the Kalman filter is designed for linear discrete-time dynamical system, EKF works for discrete-time nonlinear systems.
Dual EKF: The Dual EKF estimates both the states of the dynamical system and its
parameters simultaneously when only noisy observations are available.
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