Fusion Filters Weighted by Scalars and Matrices for Linear Systems
An optimal mean-square fusion formulas with scalar
and matrix weights are presented. The relationship between them is
established. The fusion formulas are compared on the continuous-time
filtering problem. The basic differential equation for cross-covariance
of the local errors being the key quantity for distributed fusion is
derived. It is shown that the fusion filters are effective for multi-sensor
systems containing different types of sensors. An example
demonstrating the reasonable good accuracy of the proposed filters is
given.
[1] D. L. Hall, Mathematical Techniques in Multisensor Data Fusion, Artech
House, London, 1992.
[2] Y.Bar-Shalom (Ed.), Multitarget-Multisensor Tracking: Advanced
Applications, Artech House, Norwood, MA, 1990.
[3] Y.Bar-Shalom and X. Rong Li, Multitarget-Multisensor Tracking:
Principles and Techniques, YBS Publishing, 1995.
[4] J.Manyika and H.Durrant-Whyte, Data Fusion and Sensor Management:
A Decentralized Information-Theoretic Approach, Ellis Horwood, New
York, 1994.
[5] Y.Bar-Shalom and L. Campo, "The effect of the common process noise
on the two-sensor fused-track covariance", IEEE Trans. Aerospace and
Electronic Systems, 22(11), pp. 803-805, 1986.
[6] Li, X.R., Zhu, Y.M., Wang, J., Han, C.Z., 2004. Optimal linear estimation
fusion - Part I: Unified fusion rules, IEEE Trans. Inf. Theory, vol. 49, no.
9, pp. 2192-2208.
[7] V.I. Shin, Y. Lee and T. Choi, Suboptimal Linear Filtering and
Generalized Millman-s Formula, Proc. IASTED Inter. Conf. Signal and
Image Process, Honolulu, Hawaii, USA, pp. 369-374, 2004.
[8] V.Shin, Y.Lee, and T.-S.Choi, Generalized Millman's formula and its
applications for estimation problems, Signal Processing, vol.86, No.2,
pp. 257-266, 2006.
[9] J. Zhou, Y. Zhu, Z. You and E. Song, An efficient algorithm for optimal
linear estimation fusion in distributed multisensor systems, IEEE Trans.
Syst., Man, Cybern., vol.36, no.5, pp. 1000-1009, 2006.
[10] V.Shin "Optimal Linear Fusion of Local Estimates", Proc. IEEE Intern.
Conf. Control and Applic., Toronto, Canada, pp. 1435-1440, 2005.
[11] V. Shin, G. Shevlyakov, K. Kim, "A New Fusion Formula and Its
Application to Continuous-Time Linear Systems with Multisensor
Environment", Computational Statistics & Data Analysis, 2007 (in
Press).
[12] S.L.Sun, Z.L.Deng, Multi-Sensor Information Fusion Kalman Filter
Weighted by Scalars for Systems with Colored Measurement Noises,
Journ. Dynam. Syst, Measurem., Contr., vol. 127, no.12, pp.663-667,
2005.
[13] F.L. Lewis, Optimal Estimation with an Introduction to Stochastic
Control Theory, John Wiley & Sons, New York.
[1] D. L. Hall, Mathematical Techniques in Multisensor Data Fusion, Artech
House, London, 1992.
[2] Y.Bar-Shalom (Ed.), Multitarget-Multisensor Tracking: Advanced
Applications, Artech House, Norwood, MA, 1990.
[3] Y.Bar-Shalom and X. Rong Li, Multitarget-Multisensor Tracking:
Principles and Techniques, YBS Publishing, 1995.
[4] J.Manyika and H.Durrant-Whyte, Data Fusion and Sensor Management:
A Decentralized Information-Theoretic Approach, Ellis Horwood, New
York, 1994.
[5] Y.Bar-Shalom and L. Campo, "The effect of the common process noise
on the two-sensor fused-track covariance", IEEE Trans. Aerospace and
Electronic Systems, 22(11), pp. 803-805, 1986.
[6] Li, X.R., Zhu, Y.M., Wang, J., Han, C.Z., 2004. Optimal linear estimation
fusion - Part I: Unified fusion rules, IEEE Trans. Inf. Theory, vol. 49, no.
9, pp. 2192-2208.
[7] V.I. Shin, Y. Lee and T. Choi, Suboptimal Linear Filtering and
Generalized Millman-s Formula, Proc. IASTED Inter. Conf. Signal and
Image Process, Honolulu, Hawaii, USA, pp. 369-374, 2004.
[8] V.Shin, Y.Lee, and T.-S.Choi, Generalized Millman's formula and its
applications for estimation problems, Signal Processing, vol.86, No.2,
pp. 257-266, 2006.
[9] J. Zhou, Y. Zhu, Z. You and E. Song, An efficient algorithm for optimal
linear estimation fusion in distributed multisensor systems, IEEE Trans.
Syst., Man, Cybern., vol.36, no.5, pp. 1000-1009, 2006.
[10] V.Shin "Optimal Linear Fusion of Local Estimates", Proc. IEEE Intern.
Conf. Control and Applic., Toronto, Canada, pp. 1435-1440, 2005.
[11] V. Shin, G. Shevlyakov, K. Kim, "A New Fusion Formula and Its
Application to Continuous-Time Linear Systems with Multisensor
Environment", Computational Statistics & Data Analysis, 2007 (in
Press).
[12] S.L.Sun, Z.L.Deng, Multi-Sensor Information Fusion Kalman Filter
Weighted by Scalars for Systems with Colored Measurement Noises,
Journ. Dynam. Syst, Measurem., Contr., vol. 127, no.12, pp.663-667,
2005.
[13] F.L. Lewis, Optimal Estimation with an Introduction to Stochastic
Control Theory, John Wiley & Sons, New York.
@article{"International Journal of Information, Control and Computer Sciences:61754", author = "Seok Hyoung Lee and Vladimir Shin", title = "Fusion Filters Weighted by Scalars and Matrices for Linear Systems", abstract = "An optimal mean-square fusion formulas with scalar
and matrix weights are presented. The relationship between them is
established. The fusion formulas are compared on the continuous-time
filtering problem. The basic differential equation for cross-covariance
of the local errors being the key quantity for distributed fusion is
derived. It is shown that the fusion filters are effective for multi-sensor
systems containing different types of sensors. An example
demonstrating the reasonable good accuracy of the proposed filters is
given.", keywords = "Kalman filtering, fusion formula, multi-sensor,mean-square error.", volume = "1", number = "10", pages = "3231-6", }
