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A Gaussian approximation recursive filter for nonlinear systems with correlated noises. (English) Zbl 1257.93102
Summary: This paper proposes a Gaussian Approximation Recursive Filter (GASF) for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other. Through presenting the Gaussian approximations about the two-step state posterior predictive Probability Density Function (PDF) and the one-step measurement posterior predictive PDF, a general GASF framework in the Minimum Mean Square Error (MMSE) sense is derived. Based on the framework, the GASF implementation is transformed into computing the multi-dimensional integrals, which is solved by developing a new Divided Difference Filter (DDF) with correlated noises. Simulation results demonstrate the superior performance of the proposed DDF as compared to the standard DDF, the existing UKF and EKF with correlated noises.

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
Full Text: DOI
[1] Anderson, B.D.O.; Moore, J.B., Optimal filtering, (1979), Prentice-Hall New York · Zbl 0758.93070
[2] Arasaratnam, I.; Haykin, S., Cubature Kalman filter, IEEE transactions on automatic control, 54, 8, 1254-1269, (2009) · Zbl 1367.93637
[3] Arasaratnam, I.; Haykin, S., Cubature Kalman filtering for continuous-discrete systems: theory and simulations, IEEE transactions on signal processing, 58, 10, 1254-1269, (2010) · Zbl 1367.93637
[4] Astrom, K.J., Introduction to stochastic control theory, (1970), Academic Press New York · Zbl 0387.93001
[5] Boutayeb, M.; Aubry, D., A strong tracking extended Kalman observer for nonlinear discrete-time systems, IEEE transactions on automatic control, 44, 8, 1550-1556, (1999) · Zbl 0957.93086
[6] Chen, R.R.; Liu, B.; Cheng, X.L., Pricing the term structure of inflation risk premia: theory and evidence from TIPS, Journal of empirical finance, 17, 4, 702-721, (2010)
[7] Cho, S.Y.; Kim, B.D., Adaptive IIR/FIR fusion filter and its application to the INS/GPS integrated system, Automatica, 44, 8, 2040-2047, (2008) · Zbl 1283.93276
[8] Doucet, A.; Godsill, S.; Andrieu, C., On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and computing, 10, 3, 197-208, (2000)
[9] Gobbo, D.D.; Napolitano, M.; Famouri, P.; Innocenti, M., Experimental application of extended Kalman filtering for sensor validation, IEEE transactions on control systems technology, 9, 2, 376-380, (2001)
[10] Hermoso-Carazo, A.; Linares-Pérez, J., Unscented filtering from delayed observations with correlated noises, Mathematical problems in engineering, 2009, 593-681, (2009) · Zbl 1179.93160
[11] Ho, Y.C.; Lee, R.C.K., A Bayesian approach to problems in stochastic estimation and control, IEEE transactions on automatic control, 9, 333-339, (1964)
[12] Ito, K.; Xiong, K., Gaussian filters for nonlinear filtering problems, IEEE transactions on automatic control, 45, 5, 910-927, (2000) · Zbl 0976.93079
[13] Julier, S.J.; Uhlmann, J.K.; Durrant-Whyte, H.F., A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE transactions on automatic control, 45, 3, 477-482, (2000) · Zbl 0973.93053
[14] Kotecha, J.H.; Djuric, P.A., Gaussian particle filtering, IEEE transactions on signal processing, 51, 10, 2592-2601, (2003) · Zbl 1369.94195
[15] Leven, W.E.; Lanterman, A.D., Unscented Kalman filters for multiple target tracking with symmetric measurement equations, IEEE transactions on automatic control, 54, 2, 370-375, (2009) · Zbl 1367.93650
[16] Nørgaard, M.; Poulsen, N.K.; Ravn, O., New developments in state estimation for nonlinear systems, Automatica, 36, 11, 1627-1638, (2000) · Zbl 0973.93050
[17] Nørgaard, M., Poulsen, N. K., & Ravn, O. (2000b). Advances in derivative-free state estimation for nonlinear systems. Technical report IMM-REP-1998-15 (revised edition). Department of Mathematical Modelling. Technical University of Denmark. · Zbl 0973.93050
[18] Šimandl, M.; Duník, J., Derivative-free estimation methods: new results and performance analysis, Automatica, 45, 7, 1749-1757, (2009) · Zbl 1184.93109
[19] Subrahmanya, N.; Shin, Y.C., Adaptive divided difference filtering for simultaneous state and parameter estimation, Automatica, 45, 7, 1686-1693, (2009) · Zbl 1184.93110
[20] van der Merwe, R. (2004). Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. http://www.cslu.ogi.edu/.
[21] van der Merwe, R., Wan, E. A., Julier, S. J., Bogdanov, A., Harvey, G., & Hunt, J. (2004). Sigma-point Kalman filters for nonlinear estimation and sensor fusion: applications to integrated navigation. In Proceedings of the AIAA guidance navigation and control conference. Providence, RI, USA (pp. 1735-1764).
[22] Wu, Y.X.; Hu, D.W.; Hu, X.P., Comments on performance evaluation of UKF-based nonlinear filtering, Automatica, 43, 3, 567-568, (2007) · Zbl 1137.93417
[23] Wu, Y.X.; Hu, D.W.; Wu, M.P.; Hu, X.P., A numerical-integration perspective on Gaussian filters, IEEE transactions on signal processing, 54, 8, 2910-2921, (2006) · Zbl 1388.65025
[24] Xiong, K.; Zhang, H.Y.; Chan, C.W., Performance evaluation of UKF-based nonlinear filtering, Automatica, 42, 2, 261-270, (2006) · Zbl 1103.93045
[25] Xiong, K.; Zhang, H.Y.; Chan, C.W., Author’s reply to “comments on ‘performance evaluation of UKF-based nonlinear filtering”’, Automatica, 43, 3, 569-570, (2007) · Zbl 1137.93418
[26] Xu, J. H., Dimirovski, G. M., Jing, Y. W., & Shen, C. (2007). UKF design and stability for nonlinear stochastic systems with correlated noises. In Proceedings of the 46th IEEE conference on decision and control. New Orleans, USA (pp. 6626-6631).
[27] Zhan, R.H.; Wan, J.W., Neural network-aided adaptive unscented Kalman filter for nonlinear state estimation, IEEE signal processing letters, 13, 7, 445-448, (2006)
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