Abstract
This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on genetic algorithm to find and track the best estimation. In the proposed filter, each individual is set based on stochastic selection and multiple mutations to find the best estimation at every time step. The population searches the state space dynamically in a similar scheme to the optimization algorithm. This approach is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters. The results indicate an improved performance of heuristic filters relatives to classic versions. Comparison of the results to those of extend Kalman filter, unscented Kalman filter, particle filter and heuristic filters indicated that the proposed heuristic filter called genetic filter fulfills the essential requirements of fast and accuracy for nonlinear state estimation.
Similar content being viewed by others
References
Alspach DL, Sorenson HW (1972) Nonlinear Bayesian estimation using Gaussian sum approximations. Autom Control IEEE Trans 17:439–448
Andrew HJ (1970) Stochastic processes and filtering theory. In: Mathematics in science and engineering, vol 64. Academic Press, Inc London
Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. Signal Process IEEE Trans 50:174–188
Bucy RS (1969) Bayes theorem and digital realizations for non-linear filters. J Astronaut Sci 17:80
Carpenter J, Clifford P, Fearnhead P (1999) Improved particle filter for nonlinear problems. In: IEE proceedings radar, sonar and navigation. IET, pp 2–7
Clapp TC (2001) Statistical methods for the processing of communications data. Doctoral dissertation, University of Cambridge
Gordon NJ, Salmond DJ, Smith AFM (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In: IEE proceedings F radar and signal processing. IET, pp 107–113
Hao Z, Zhang X, Yu P, Li H (2010) Video object tracing based on particle filter with ant colony optimization. In: 2010 2nd international conference on advanced computer control (ICACC). IEEE, pp 232–236
Heris SMK, Khaloozadeh H (2014) Ant colony estimator: an intelligent particle filter based on ACOR. Eng Appl Artif Intell 28:78–85
Higuchi T (1997) Monte Carlo filter using the genetic algorithm operators. J Stat Comput Sim 59:1–23
Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U Michigan Press, Ann Arbor
Jarvis RM, Goodacre R (2005) Genetic algorithm optimization for pre-processing and variable selection of spectroscopic data. Bioinformatics 21:860–868
Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. In: AeroSense’97. International Society for Optics and Photonics, pp 182–193
Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45
Kiani M, Pourtakdoust SH (2015) State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization. Appl Soft Comput 34:1–17
Kim Y-S, Hong K-S (2004) An IMM algorithm for tracking maneuvering vehicles in an adaptive cruise control environment. Int J Control Autom Syst 2:310–318
Kitagawa G (1987) Non-Gaussian state–space modeling of nonstationary time series. J Am Stat Assoc 82:1032–1041
Kramer SC, Sorenson HW (1988) Recursive Bayesian estimation using piece-wise constant approximations. Automatica 24:789–801
Li B, Zhao J, Pang F (2017) Adaptive genetic MM-CPHD filter for multitarget tracking. Soft Comput 21:4755–4767
Liu JS, Chen R (1998) Sequential Monte Carlo methods for dynamic systems. J Am Stat Assoc 93:1032–1044
Nobahari H, Sharifi A (2012) A novel heuristic filter based on ant colony optimization for non-linear systems state estimation. In: Computational intelligence and intelligent systems. Springer, pp 20–29
Nobahari H, Zandavi SM, Mohammadkarimi H (2016) Simplex filter: a novel heuristic filter for nonlinear systems state estimation. Appl Soft Comput J. https://doi.org/10.1016/j.asoc.2016.08.008
Park S, Hwang JP, Kim E, Kang H-J (2009) A new evolutionary particle filter for the prevention of sample impoverishment. Evol Comput IEEE Trans 13:801–809
Pitt MK, Shephard N (1999) Filtering via simulation: auxiliary particle filters. J Am Stat Assoc 94:590–599
Pole A, West M (1988) Efficient numerical integration in dynamic models. Department of Statistics, University of Warwick, Coventry
Pourtakdoust SH, Nobahari H (2004) An extension of ant colony system to continuous optimization problems. In: International workshop on ant colony optimization and swarm intelligence. Springer, Berlin, pp 294–301
Siouris GM (1996) An engineering approach to optimal control and estimation theory. Wiley, New York
Smith A, Doucet A, de Freitas N, Gordon N (2013) Sequential Monte Carlo methods in practice. Springer, Berlin
Socha K, Dorigo M (2008) Ant colony optimization for continuous domains. Eur J Oper Res 185:1155–1173
Sorenson HW (1988) Recursive estimation for nonlinear dynamic systems. Bayesian Anal Time Ser Dyn Model 94:127–165
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Tong G, Fang Z, Xu X (2006) A particle swarm optimized particle filter for nonlinear system state estimation. In: IEEE congress on evolutionary computation, 2006. CEC 2006. IEEE, pp 438–442
Uosaki K, Kimura Y, Hatanaka T (2003) Nonlinear state estimation by evolution strategies based particle filters. In: The 2003 congress on evolutionary computation, 2003. CEC’03. IEEE, pp 2102–2109
Wu Y, Liu G, Guo X et al (2017) A self-adaptive chaos and Kalman filter-based particle swarm optimization for economic dispatch problem. Soft Comput 21:3353–3365
Yu Y, Zheng X (2011) Particle filter with ant colony optimization for frequency offset estimation in OFDM systems with unknown noise distribution. Sig Process 91:1339–1342
Zandavi SM, Sha F, Chung V, Lu Z, Zhi W (2017) A novel ant colony detection using multi-region histogram for object tracking. In: International conference on neural information processing. Springer, Cham, pp 25–33
Zhong J, Fung Y, Dai M (2010) A biologically inspired improvement strategy for particle filter: ant colony optimization assisted particle filter. Int J Control Autom Syst 8:519–526
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflict of interest.
Ethnical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zandavi, S.M., Chung, V. State estimation of nonlinear dynamic system using novel heuristic filter based on genetic algorithm. Soft Comput 23, 5559–5570 (2019). https://doi.org/10.1007/s00500-018-3213-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3213-y