Optimal design of symmetrical/asymmetrical sigma-point Kalman filter using genetic algorithms

Abstract

During the past decades, there have been a great amount of research activities in approximate problem solving to estimate the real amount of states of dynamical systems using measurement data corrupted with noise. One of the most famous approximate solving methods is Unscented Kalman Filter (UKF). In UKF, the estimation is based on a collection of symmetrical sigma points around an a priori-estimated state. In this paper, Genetic Algorithm (GA) is firstly used to optimally select the best coefficients of the symmetrical sigma points related to Scaled Unscented Transform in UKF (GA-UKF) to minimize the mean of squared error of estimations. Moreover, GA is also used to select a collection of asymmetrical sigma points (GA-ASKF) to minimize the mean of squared error of estimations together with same statistics of the mean and covariance matrix. The new idea of the asymmetric sigma points Kalman filter of this paper which are optimally found again by using GA evidently outperforms both conventional UKF and GA-UKF of this paper in estimating the states of dynamical systems.

Keywords

Genetic algorithms inverted pendulum optimization state estimation unscented Kalman filter

Get full access to this article

View all access options for this article.

References

Forbes

(2013) Adaptive approaches to nonlinear state estimation for mobile robot localization: an experimental comparison. Transactions of the Institute of Measurement and Control 35(8): 971–985.

Gelb

(1974) Applied optimal estimation. Cambridge, MA: MIT Press.

Hudas

Cheok

Overholt

(2007) Fuzzy variant of a statistical test point Kalman filter. International Journal of Approximate Reasoning 45: 455–469.

Jatoth

Rao

Kumar

(2010) Particle Swarm Optimization aided unscented Kalman filter for ballistic target tracking. Proceedings of the IEEE International Conference on Communication Control and Computing Technologies, pp. 455–460.

Julier

(2002) The scaled unscented transformation. Proceedings of the IEEE American Control Conference, pp. 4555–4559.

Julier

Uhlmann

Durrant-Whyte

(2000) A new method for the transformation of means and covariances in filters and estimators. IEEE Transaction on Automatic Control 45(3): 477–482.

Kalman

(1960) A new approach to linear filtering and prediction problems. Transactions of the ASME Journal of Basic Engineering 82: 35–45.

Kolas

Foss

Schei

(2009) Constrained nonlinear state estimation based on the UKF approach. Computers and Chemical Engineering 33: 1386–1401.

Nekoo

(2013) Nonlinear closed loop optimal control: A modified state-dependent Riccati equation. ISA Transactions 52: 285–290.

10.

Jian-Da

(2008) An Adaptive UKF Algorithm for the State and Parameter Estimation of a Mobile Robot. Acta Automatica Sinica 34: 72–79.

11.

Simon

(2006) Optimal State Estimation, Kalman, H_∞, and Nonlinear Approaches. New Jersey, USA: John Wiley & Sons.

12.

Van der Merwe

(2004) Sigma-point Kalman filters for probabilistic inference in dynamic state space models. PhD dissertation, OGI School of Science & Engineering at Oregon Health & Science University.

13.

Van der Merwe

Wan

(2001) The Square-Root Unscented Kalman Filter for State and Parameter-Estimation. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3461–3464.

14.

Wan

Van der Merwe

(2000) The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE Symposium 2000, Adaptive Systems for Signal Processing, Communication, and Control, Lake Louise, AB, October 1–4.

15.

Wan

Van der Merwe

Nelson

(2000) Dual estimation and the unscented transformation. Advances in Neural Information Processing Systems 12: 666–672.

16.

Yao

Jiang

. (2013) Identification of acceleration harmonic for an electro-hydraulic servo shaking table based on Kalman filter. Transactions of the Institute of Measurement and Control 35(8): 986–996.

17.

Zhu

(2013) Stability-based SDRE controller for spacecraft momentum management. Acta Astronautica 89: 71–82.