Conditionally Suboptimal Filtering in Nonlinear Stochastic Differential System

ABSTRACT

This paper presents a novel conditionally suboptimal filtering algorithm on estimation problems that arise in discrete nonlinear time-varying stochastic difference systems. The suboptimal state estimate is formed by summing of conditionally nonlinear filtering estimates that their weights depend only on time instants, in contrast to conditionally optimal filtering, the proposed conditionally suboptimal filtering allows parallel processing of information and reduce online computational requirements in some nonlinear stochastic difference system. High accuracy and efficiency of the conditionally suboptimal nonlinear filtering are demonstrated on a numerical example.

This paper presents a novel conditionally suboptimal filtering algorithm on estimation problems that arise in discrete nonlinear time-varying stochastic difference systems. The suboptimal state estimate is formed by summing of conditionally nonlinear filtering estimates that their weights depend only on time instants, in contrast to conditionally optimal filtering, the proposed conditionally suboptimal filtering allows parallel processing of information and reduce online computational requirements in some nonlinear stochastic difference system. High accuracy and efficiency of the conditionally suboptimal nonlinear filtering are demonstrated on a numerical example.

Cite this paper

nullT. He and Z. Shi, "Conditionally Suboptimal Filtering in Nonlinear Stochastic Differential System,"*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 757-763. doi: 10.4236/am.2011.26101.

nullT. He and Z. Shi, "Conditionally Suboptimal Filtering in Nonlinear Stochastic Differential System,"

References

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[2] C. Chui and G. Chen, “Kalman Filtering with Real-Time and Applications,” Springer-Verlag, Berlin, 2009.

[3] V. I. Shin, “Pugachev’s Filters for Complex Information Processing,” Automation and Remote Control, Vol. 11, No. 59, 1999, pp. 1661-1669.

[4] F. Lewis, “Optimal Estimation with an Introduction to Stochastic Control Theory,” John Wiley and Sons, New York, 1986.

[5] M. Oh, V. I. Shin, Y. Lee and U. J. Choi, “Suboptimal Discrete Filters for Stochastic Systems with Different Types of Observations,” Computers & Mathematics with Applications, Vol. 35, No. 4, 1998, pp. 17-27. doi:10.1016/S0898-1221(97)00275-7

[6] V. S. Pugachev and I. N. Sinitsyn, “Stochastic Systems: Theory and Applications,” World Scientific, Singapore, 2002.

[7] I. N. Sinitsyn, “Conditionally Optimal Filtering and Recognition of Signals in Stochastic Differential System,” Automation and Remote Control, Vol. 58, No. 2, 1997, pp. 124-130.

[8] Y. Cho, V. I. Shin, M. Oh and Y. Lee, “Suboptimal Continuous Filtering Based on the Decomposition of Observation Vector,” Computers & Mathematics with Applications, Vol. 32, No. 4, 1996, pp. 23-31. doi:10.1016/0898-1221(96)00121-6

[9] Y. Bar-Shalon and L. Campo, “The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 22, No. 6, 1986, pp. 803-805.doi:10.1109/TAES.1986.310815

[10] I. N. Sinitsyn, N. K. Moshchuk and V. I. Shin, “Conditionally Optimal Filtering of Processes in Stochastic Differential Systems by Bayesian Criteria,” Doklady Mathematics, Vol. 47, No. 3, 1993, pp. 528-533.

[11] R. C. Luo and M. G. Kay, “Multisensor Integration and Fusion in Intelligent Systems,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 19, No. 5, 1989, pp. 901-931. doi:10.1109/21.44007

[1] B. ?ksendal, “Stochastic Differential Equations,” 6th Edition, Springer-Verlag, Berlin, 2003.

[2] C. Chui and G. Chen, “Kalman Filtering with Real-Time and Applications,” Springer-Verlag, Berlin, 2009.

[3] V. I. Shin, “Pugachev’s Filters for Complex Information Processing,” Automation and Remote Control, Vol. 11, No. 59, 1999, pp. 1661-1669.

[4] F. Lewis, “Optimal Estimation with an Introduction to Stochastic Control Theory,” John Wiley and Sons, New York, 1986.

[5] M. Oh, V. I. Shin, Y. Lee and U. J. Choi, “Suboptimal Discrete Filters for Stochastic Systems with Different Types of Observations,” Computers & Mathematics with Applications, Vol. 35, No. 4, 1998, pp. 17-27. doi:10.1016/S0898-1221(97)00275-7

[6] V. S. Pugachev and I. N. Sinitsyn, “Stochastic Systems: Theory and Applications,” World Scientific, Singapore, 2002.

[7] I. N. Sinitsyn, “Conditionally Optimal Filtering and Recognition of Signals in Stochastic Differential System,” Automation and Remote Control, Vol. 58, No. 2, 1997, pp. 124-130.

[8] Y. Cho, V. I. Shin, M. Oh and Y. Lee, “Suboptimal Continuous Filtering Based on the Decomposition of Observation Vector,” Computers & Mathematics with Applications, Vol. 32, No. 4, 1996, pp. 23-31. doi:10.1016/0898-1221(96)00121-6

[9] Y. Bar-Shalon and L. Campo, “The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 22, No. 6, 1986, pp. 803-805.doi:10.1109/TAES.1986.310815

[10] I. N. Sinitsyn, N. K. Moshchuk and V. I. Shin, “Conditionally Optimal Filtering of Processes in Stochastic Differential Systems by Bayesian Criteria,” Doklady Mathematics, Vol. 47, No. 3, 1993, pp. 528-533.

[11] R. C. Luo and M. G. Kay, “Multisensor Integration and Fusion in Intelligent Systems,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 19, No. 5, 1989, pp. 901-931. doi:10.1109/21.44007