Filters for spatial point processes

SIAM Journal on Control and Optimization

Volumn 48, Issue 4, 2009, Pages 2275-2295

  Singh, Sumeetpal S ^a   Vo, Ba Ngu ^b   Baddeley, Adrian ^c   Zuyev, Sergei ^d  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF MELBOURNE   (Australia)

^c CSIRO   (Australia)

^d CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Gauss Poisson point process; Hidden point process inference; Online filtering; Phd filter; Poisson point process prior; Target tracking

Indexed keywords

PHD FILTERS; POINT PROCESS; POISSON POINT PROCESS; SPATIAL POINT PROCESS;

TARGET TRACKING;

EID: 77955626970     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/070710457     Document Type: Article

References (23)

1. B. D. ANDERSON and J. B. MOORE, Optimal Filtering, Prentice-Hall, Englewood Cliffs, NJ, 1979.
2. D. R. BRILLINGER, A note on a representation for the Gauss-Poisson process, Stochastic Process. Appl., 6 (1978), pp. 135-137.
3. O. CAPPE, T. RYDEN, and E. MOULINES, Inference in Hidden Markov Models, Springer, New York, 2005.
4. D. J. DALEY and D. VERE-JONES, An Introduction to the Theory of Point Processes, Springer, New York, 1988.
5. A. DOUCET, N. DE FREITAS, and N. GORDON, eds., Sequential Monte Carlo Methods in Practise, Springer, New York, 2001.
6. K. GILHOLM and D. SALMOND, Spatial distribution model for tracking extended objects, IEEE Proc. Radar, Sonar and Navigation, 152 (2005), pp. 364-371.
7. R. M. I. GOODMAN and H. NGUYEN, Mathematics of Data Fusion, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
8. A. H. JAZWINSKI, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970.
9. J. F. C. KINGMAN, Poisson Processes, Clarendon Press, Oxford, UK, 1993.
10. G. KITAGAWA and W. GERSCH, Smoothness Priors Analysis of Time Series, Springer-Verlag, New York, 1996.
11. J. LUND and M. RUDEMO, Models for point processes observed with noise, Biometrika, 87 (2000), pp. 235-249.
12. J. LUND and E. THONNES, Perfect simulation and inference for point processes given noisy observations, Comput. Statist., 19 (2004), pp. 317-336.
13. R. MAHLER, Multi-target Bayes filtering via first-order multi-target moments, IEEE Trans. Aerospace and Electronic Systems, 39 (2003), pp. 1152-1178.
14. S. MORI, C. Y. CHONG, E. TSE, and R. WISHNER, Tracking and identifying multiple targets without a priori identifications, IEEE Trans. Automat. Control, 21 (1986), pp. 401-409.
15. J. E. MOYAL, The general theory of stochastic population processes, Acta Math., 108 (1962), pp. 1-31.
16. D. S. NEWMAN, A new family of point processes which are characterized by their second moment properties, J. Appl. Probab., 7 (1970), pp. 338-358.
17. N. PORTENKO, H. SALEHI, and A. SKOROKHOD, On optimal filtering of multitarget systems based on point process observations, Random Oper. Stochastic Equations, 5 (1997), pp. 1-34.
18. D. STOYAN, W. KENDALL, and J. MECKE, Stochastic Geometry and Its Applications, 2nd ed., Wiley, New York, 1995.
19. B.-N. VO and W.-K. MA, The Gaussian mixture probability hypothesis density filter, IEEE Trans. Signal Process., 54 (2005), pp. 4091-4104.
20. B.-N. VO, S. SINGH, and A. DOUCET, Sequential Monte Carlo implementation of the PHD filter for multi-target tracking, in Proceedings of the International Conference on Information Fusion, Cairns, Australia, IEEE Press, Piscataway, NJ, 2003, pp. 792-799.
21. B.-N. VO, S. SINGH, and A. DOUCET, Sequential Monte Carlo methods for multi-target filtering with random finite sets, IEEE Trans. Aerospace and Electronic Systems, 41 (2005), pp. 1224-1245.
22. R. WASHBURN, A random point process approach to multi-object tracking, in Proceedings of the American Control Conference, 1987, vol. 3, pp. 1846-1852.
23. M. WEST and J. HARRISON, Bayesian Forecasting and Dynamic Models, 2nd ed., Springer Ser. Statist., Springer-Verlag, New York, 1997.