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Error analysis for numerical formulation of particle filter
1. | 221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 |
2. | Institute of Natural sciences, Department of Mathematics, MOE Key Lab of Scientic and Engineering Computing, Shanghai JiaoTong University, 800 Dongchuan Rd, Minhang 200240, Shanghai, China |
3. | Department of Mathematics, Scientific Computing and Imagining Institute, The University of Utah, Salt Lake City, UT 84112, United States |
References:
[1] |
S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking, IEEE Tran. Signal Process., 50 (2002), 174-188. |
[2] |
O. Cappé, S. J. Godsill and E. Moulines, An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo, Proc. IEEE 95, May 2007. |
[3] |
S. Chib, F. Nardari and N. Shephard, Markov chain Monte Carlo methods for stochastic volatility models, J. Econometr., 108 (2002), 281-316.
doi: 10.1016/S0304-4076(01)00137-3. |
[4] |
S. E. Cohn, An introduction to estimation theory, J. Meteor. Soc. Jpn., 75 (1997), 257-288. |
[5] |
D. Crisan and A. Doucet, A survey of convergence results on particle filtering for practitioners, IEEE Trans. Signal Process., 50 (2002), 736-746.
doi: 10.1109/78.984773. |
[6] |
A. Doucet, N. Defreitas and N. Gordon, Sequential Monte Carlo Methods in Practice, Springer, 2001.
doi: 10.1007/978-1-4757-3437-9. |
[7] |
A Doucet, S Godsill and C Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Stat. & Comput., 10 (2000), 197-208. |
[8] |
Y. Ho and R. Lee, A Bayesian approach to problems in stochastic estimation and control, IEEE Tran. Auto. Control, 9 (1964), 333-339. |
[9] |
X. Hu, T. B. Schön and L. Ljung, A basic convergence result for particle filtering, IEEE Tran. Signal Process., 56 (2008), 1337-1348.
doi: 10.1109/TSP.2007.911295. |
[10] |
A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970. |
[11] |
L. Kuznetsov, K. Ide and C. K. R. T. Jones, A method for assimilation of Lagrangian data, Mon. Wea. Rev., 131 (2003), 2247-2260.
doi: 10.1175/1520-0493(2003)131<2247:AMFAOL>2.0.CO;2. |
[12] |
C. Lemieux, D. Ormoneit and D. J. Fleet, Lattice Particle Filters, Proc. 17th Ann. Conf. UAI, 2002. |
[13] |
J. Li and D. Xiu, On numerical properties of the ensemble kalman filter for data assimilation, Comput. Methods Appl. Mech. Engrg., 197 (2008), 3574-3583.
doi: 10.1016/j.cma.2008.03.022. |
[14] |
J. Liu and R. Chen, Sequential Monte Carlo methods for dynamic systems, J. Am. Stat. Assoc., 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[15] |
A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, Springer-Verlag, New York, 2000. |
[16] |
H. Salman, L. Kuznetsov, C. K. R. T. Jones and K. Ide, A method for assimilating Lagrangian data into a shallow-water equation ocean model, Mon. Wea. Rev., 134 (2006), 1081-1101.
doi: 10.1175/MWR3104.1. |
[17] |
E. T. Spiller, A. Budhirajab, K. Ide and C. K. R. T. Jones, Modified particle filter methods for assimilating Lagrangian data into a point-vortex model, Phys. D, 237 (2008), 1498-1506.
doi: 10.1016/j.physd.2008.03.023. |
[18] |
S. Thrun, Particle Filters in Robotics, Proc. 17th Ann. Conf. UAI, 2002. |
[19] |
P. Van Leeuwen, Particle filtering in geophysical systems, Mon. Wea. Rev., 137 (2009), 4089-4114. |
[20] |
G. Welch and G. Bishop, An introduction to the Kalman filter, Tech. Rep. TR95-041. |
show all references
References:
[1] |
S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, A tutorial on particle filters for on-line non-linear/non-Gaussian Bayesian tracking, IEEE Tran. Signal Process., 50 (2002), 174-188. |
[2] |
O. Cappé, S. J. Godsill and E. Moulines, An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo, Proc. IEEE 95, May 2007. |
[3] |
S. Chib, F. Nardari and N. Shephard, Markov chain Monte Carlo methods for stochastic volatility models, J. Econometr., 108 (2002), 281-316.
doi: 10.1016/S0304-4076(01)00137-3. |
[4] |
S. E. Cohn, An introduction to estimation theory, J. Meteor. Soc. Jpn., 75 (1997), 257-288. |
[5] |
D. Crisan and A. Doucet, A survey of convergence results on particle filtering for practitioners, IEEE Trans. Signal Process., 50 (2002), 736-746.
doi: 10.1109/78.984773. |
[6] |
A. Doucet, N. Defreitas and N. Gordon, Sequential Monte Carlo Methods in Practice, Springer, 2001.
doi: 10.1007/978-1-4757-3437-9. |
[7] |
A Doucet, S Godsill and C Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Stat. & Comput., 10 (2000), 197-208. |
[8] |
Y. Ho and R. Lee, A Bayesian approach to problems in stochastic estimation and control, IEEE Tran. Auto. Control, 9 (1964), 333-339. |
[9] |
X. Hu, T. B. Schön and L. Ljung, A basic convergence result for particle filtering, IEEE Tran. Signal Process., 56 (2008), 1337-1348.
doi: 10.1109/TSP.2007.911295. |
[10] |
A. H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, 1970. |
[11] |
L. Kuznetsov, K. Ide and C. K. R. T. Jones, A method for assimilation of Lagrangian data, Mon. Wea. Rev., 131 (2003), 2247-2260.
doi: 10.1175/1520-0493(2003)131<2247:AMFAOL>2.0.CO;2. |
[12] |
C. Lemieux, D. Ormoneit and D. J. Fleet, Lattice Particle Filters, Proc. 17th Ann. Conf. UAI, 2002. |
[13] |
J. Li and D. Xiu, On numerical properties of the ensemble kalman filter for data assimilation, Comput. Methods Appl. Mech. Engrg., 197 (2008), 3574-3583.
doi: 10.1016/j.cma.2008.03.022. |
[14] |
J. Liu and R. Chen, Sequential Monte Carlo methods for dynamic systems, J. Am. Stat. Assoc., 93 (1998), 1032-1044.
doi: 10.1080/01621459.1998.10473765. |
[15] |
A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, Springer-Verlag, New York, 2000. |
[16] |
H. Salman, L. Kuznetsov, C. K. R. T. Jones and K. Ide, A method for assimilating Lagrangian data into a shallow-water equation ocean model, Mon. Wea. Rev., 134 (2006), 1081-1101.
doi: 10.1175/MWR3104.1. |
[17] |
E. T. Spiller, A. Budhirajab, K. Ide and C. K. R. T. Jones, Modified particle filter methods for assimilating Lagrangian data into a point-vortex model, Phys. D, 237 (2008), 1498-1506.
doi: 10.1016/j.physd.2008.03.023. |
[18] |
S. Thrun, Particle Filters in Robotics, Proc. 17th Ann. Conf. UAI, 2002. |
[19] |
P. Van Leeuwen, Particle filtering in geophysical systems, Mon. Wea. Rev., 137 (2009), 4089-4114. |
[20] |
G. Welch and G. Bishop, An introduction to the Kalman filter, Tech. Rep. TR95-041. |
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