×

Joint state and parameter robust estimation of stochastic nonlinear systems. (English) Zbl 1346.93367

Summary: Successful implementation of many control strategies is mainly based on accurate knowledge of the system and its parameters. Besides the stochastic nature of the systems, nonlinearity is one more feature that may be found in almost all physical systems. The application of extended Kalman filter for the joint state and parameter estimation of stochastic nonlinear systems is well known and widely spread. It is a known fact that in measurements, there are inconsistent observations with the largest part of population of observations (outliers). The presence of outliers can significantly reduce the efficiency of linear estimation algorithms derived on the assumptions that observations have Gaussian distributions. Hence, synthesis of robust algorithms is very important. Because of increased practical value in robust filtering as well as the rate of convergence, the modified extended Masreliez-Martin filter presents the natural frame for realization of the joint state and parameter estimator of nonlinear stochastic systems. The strong consistency is proved using the methodology of an associated ODE system. The behaviour of the new approach to joint estimation of states and unknown parameters of nonlinear systems in the case when measurements have non-Gaussian distributions is illustrated by intensive simulations.

MSC:

93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory
93C10 Nonlinear systems in control theory
93E11 Filtering in stochastic control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mei, Practical development of the second-order extended Kalman filter for very long range radar tracking, Signal Processing 91 (3) pp 1240– (2011) · Zbl 1219.94043
[2] Cui, Real-time Kalman filtering based on distributed measurements, International Journal of Robust and Nonlinear Control 23 (14) pp 1597– (2013) · Zbl 1286.93175
[3] Stojanovic, Adaptive input design for identification of output error model with constrained output, circuits, Systems and Signal Processing 33 (1) pp 97– (2014)
[4] Tong, Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems, IEEE Transactions on Systems, Man and Cybernetics, Part B 41 (4) pp 1693– (2011)
[5] Tong, A combined backstepping and stochastic small-gain approach to robust adaptive fuzzy output feedback control, IEEE Transactions on Fuzzy Systems 21 (2) pp 314– (2013)
[6] Mourikis, Vision-aided inertial navigation for spacecraft entry, descent, and landing, IEEE Transactions on Robotics 25 (2) pp 264– (2009)
[7] Lefferts, Kalman filtering for spacecraft attitude estimation, Journal of Guidance, Control and Dynamics 5 pp 417– (1982)
[8] Wu, A novel on-line observer/Kalman filter identification method and its application to input-constrained active fault-tolerant tracker design for unknown stochastic systems, Journal of the Franklin Institute 352 (1) pp 1119– (2015) · Zbl 1307.93432
[9] Zerouali, Extended Kalman filter for uninterruptible power supplies applied to nonlinear loads, International Journal of Applied Electromagnetics and Mechanics 25 pp 565– (2007)
[10] Utz, Extended Kalman filter and adaptive backstepping for mean temperature control of a three-way catalytic converter, International Journal of Robust and Nonlinear Control 24 (15) pp 3437– (2014) · Zbl 1302.93218
[11] Lightcap, An extended Kalman filter for real-time estimation and control of a rigid-link flexible-joint manipulator, IEEE Transactions on Control Systems Technology 18 (1) pp 91– (2010)
[12] Ray, Nonlinear tire force estimation and road friction identification: simulation and experiments, Automatica 33 (8) pp 1819– (1997) · Zbl 0900.93213
[13] Filipovic, Robust identification of pneumatic servo actuators in the real situations, Forschung im Ingenieurwesen - Engineering Research 75 (2) pp 183– (2011)
[14] Cox, On the estimation of state variables and parameters for noisy dynamic systems, IEEE Transactions on Automatic Control 9 (1) pp 5– (1964)
[15] Ljung, Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems, IEEE Transactions on Automatic Control 24 (1) pp 36– (1979) · Zbl 0399.93054
[16] Wang, An extended Kalman filtering approach to modelling nonlinear dynamic gene regulatory networks via short gene expression time series, IEEE/ACM Transactions on Computational Biology and Bioinformatics 6 (1) pp 410– (2009)
[17] Aksoy S Muhurcu A Kizmaz H State and parameter estimation in induction motor using the extended Kalman filtering algorithm Wroclaw 2010 1 5
[18] Plett, Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation, Journal of Power Sources 134 (2) pp 277– (2004)
[19] Carrassi, State and parameter estimation with the extended Kalman filter: an alternative formulation of the model error dynamics, Quarterly Journal of the Royal Meteorological Society 137 (655) pp 435– (2011)
[20] Barnet, Outliers in Statistical Data (1994)
[21] Huber, Robust Statistics (2009) · Zbl 1276.62022
[22] Masreliez, Robust Bayesian estimation for the linear model and robustifying the Kalman filter, IEEE Transactions on Automatic Control 22 (1) pp 361– (1977) · Zbl 0354.93054
[23] Stojanovic, Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non-Gaussian noise, International Journal of Robust and Nonlinear Control · Zbl 1332.93353
[24] Ljung, Theory and Practice of Recursive Identification (1983) · Zbl 0548.93075
[25] Ljung, Analysis of recursive stochastic algorithms, IEEE Transactions on Automatic Control 22 (2) pp 551– (1977) · Zbl 0362.93031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.