Poisson point processes: Imaging, tracking, and sensing

Poisson Point Processes: Imaging, Tracking, and Sensing

Volumn , Issue , 2010, Pages 1-273

  Streit, Roy L ^a  

^a METRON INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84889863964     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4419-6923-1     Document Type: Book

References (143)

1. D. A. Abraham and A. P. Lyons. Novel physical interpretations of K-distributed reverberation. IEEE Journal of Oceanic Engineering, JOE-27(4):800-813, 2002.
2. A. Baddeley. Stochastic geometry: An introduction and reading-list. International Statistical Review, 50(2):179-193, 1982.
3. A. Baddeley and E. B. V. Jensen. Stereology for Statisticians. Chapman & Hall/CRC, Boca Raton, FL, 2004.
4. Y. Bar-Shalom and T. E. Fortmann. Tracking and Data Association. Academic, Boston, MA, 1988.
5. E. W. Barankin. Locally best unbiased estimates. Annals of Mathematical Statistics, 20:477-501, 1949.
6. M. S. Bartlett. Smoothing periodograms from time series with continuous spectra. Nature, 161:686-687, May 1948.
7. M. S. Bartlett. The spectral analysis of two-dimensional point processes. Biometrica, 51:299-311, 1964.
8. M. S. Bartlett. The Statistical Analysis of Spatial Pattern. Chapman and Hall, New York, 1975.
9. R. E. Bellman. Adaptive Controls Processes: A Guided Tour. Princeton University Press, Princeton, NJ, 1961.
10. B. Bollobás. Random Graphs. Cambridge University Press, New York, 2001.
11. N. R. Campbell. The study of discontinuous phenomena. Proceedings of the Cambridge Philosophical Society, 15:117-136, 1909.
12. M. Á. Carreira-Perpiñán. Gaussian mean shift is an EM algorithm. IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-29(5):767-776, May 2007.
13. V. Cevher and L. Kaplan. Pareto frontiers of sensor networks for localization. In Proceedings of the 2008 International Conference on Information Processing in Sensor Networks, pages 27-38, St. Louis, Missouri, 2008.
14. D. G. Chapman and H. Robbins. Minimum variance estimation without regularity assumptions. Annals of Mathematical Statistics, 22(4):581-586, 1951.
15. E. Çinlar. On the superposition of m-dimensional point processes. Journal of Applied Probability, 5:169-176, 1968.
16. N. A. C. Cressie. Statistics for Spatial Data. Wiley, New York, Revised edition, 1993.
17. D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, volume I: Elementary Theory and Methods. Springer, New York, Second edition, 2003.
18. W. B. Davenport, Jr., and W. L. Root. An Introduction to the Theory of Random Signals and Noise. McGraw-Hill, New York, 1958.
19. J. de Leeuw. Applications of convex analysis to multidimensional scaling. In J. R. Barra, F. Brodeau, G. Romier, and B. van Cutsem, editors, Recent Developments in Statistics, pages 133-145. North-Holland, Amsterdam, 1977.
20. J. de Leeuw and W. J. Heiser. Convergence of correction matrix algorithms for multidimensional scaling. In J. C. Lingoes, editor, Geometric Representations of Relational Data, pages 735-752. Mathesis Press, Ann Arbor, MI, 1977.
21. J. de Leeuw and W. J. Heiser. Multidimensional scaling with restrictions on the configuration. In P. R. Krishnaiah, editor, Multivariate Analysis, volume 5, pages 501-522. North-Holland, Amsterdam, 1980.
22. A. H. Delaney and Y. Bresler. A fast and accurate iterative reconstruction algorithm for parallel-beam tomography. IEEE Transactions on Image Processing, IP-5(5):740-753, 1996.
23. A. P. Dempster, N. M. Laird, and D. B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, B, 39:1-39, 1977.
24. P. Diaconis. The Markov chain Monte Carlo revolution. Bulletin (New Series) of the American Mathematical Society, 46:179-205, 2009.
25. S. W. Dufour. Intersections of Random Convex Regions. PhD thesis, Department of Statistics, Stanford University, Stanford, CA, 1972.
26. B. Efron and D. V. Hinkley. Assessing the accuracy of the maximum likelihood estimator: Observed versus expected fisher information (with discussion). Biometrika, 65(3):457-487, 1978.
27. A. Einstein. On the method of theoretical physics. Philosophy of Science, 1(2):163-169, 1934.
28. C. L. Epstein. Introduction to the Mathematics of Medical Imaging. SIAM Press, Philadelphia, PA, second edition, 2007.
29. A. Erdélyi, editor. Higher Transcendental Functions, volume 2. Bateman Manuscript Project, New York, 1953.
30. O. Erdinc, P. Willett, and Y. Bar-Shalom. A physical space approach for the probability hypothesis density and cardinalized probability hypothesis density filters. In Proceedings of the SPIE Conference on Signal Processing of Small Targets, Orlando, FL, volume 6236, April 2006.
31. O. Erdinc, P. Willett, and Y. Bar-Shalom. The bin-occupancy filter and its connection to the PHD filters. IEEE Transactions on Signal Processing, 57:4232-4246, 2009.
32. K. J. Falconer. Applications of a result on spherical integration to the theory of convex sets. The American Mathematical Monthly, 90(10):690-693, 1983.
33. P. Faure. Theoretical model of reverberation noise. Journal of the Acoustical Society of America, 36(2):259-266, 1964.
34. J. A. Fessler. Statistical image reconstruction methods for transmission tomography. In M. Sonka and J. M. Fitzpatrick, editors, Handbook of Medical Imaging, SPIE, Bellingham, Washington, volume 2, pages 1-70, 2000.
35. J. A. Fessler and A. O. Hero. Space-alternating generalized expectation-maximization algorithm. IEEE Transactions on Signal Processing, SP-42(10):2664-2677, 1994.
36. P. M. Fishman and D. L. Snyder. The statistical analysis of space-time point processes. IEEE Transactions on Information Theory, IT-22:257-274, 1976.
37. D. Fränken, M. Schmidt, and M. Ulmke. "Spooky action at a distance" in the cardinalized probability hypothesis density filter. IEEE Transactions on Aerospace and Electronic Systems, AES-45(4):1657-1664, October 2009.
38. K. Fukunaga and L. D. Hostetler. The estimation of the gradient of a density function, with application in pattern recognition. IEEE Transactions on Information Theory, IT-21(1):32-40, January 1975.
39. I. I. Gikhman and A. V. Skorokhod. Introduction to the Theory of Random Processes. Dover, Mineola, NY, Unabridged republication of 1969 edition, 1994.
40. J. R. Goldman. Stochastic point processes: Limit theorems. The Annals of Mathematical Statistics, 38(3):771-779, 1967.
41. I. R. Goodman, R. P. S. Mahler, and H. T. Nguyen. Mathematics of Data Fusion. Kluwer, Dordrecht, 1997.
42. G. R. Grimmett and D. D. Stirzaker. Probability and Random Processes. Oxford University Press, Oxford, Third edition, 2001.
43. M. Haenggi. On distances in uniformly random networks. IEEE Transactions on Information Theory, IT-51:3584-3586, 2005.
44. P. Hall. Introduction to the Theory of Coverage Processes. Wiley, New York, 1988.
45. J. M. Hammersley. On estimating restricted parameters. Journal of the Royal Statistical Society, Series B, 12(2):192-240, 1950.
46. W. Härdle and L. Simar. Applied Multivariate Statistical Analysis. Springer, Berlin, 2003.
47. S. I. Hernandez. State Estimation and Smoothing for the Probability Hypothesis Density Filter. Tech. Report ECSTR10-13, Victoria University of Wellington, School of Engineering and Computer Science, April 14, 2010. (Available from http://ecs.victoria.ac.nz/Main/TechnicalReportSeries) (Also submitted as a PhD thesis, Victoria University of Wellington, New Zealand, 2010.)
48. A. O. Hero. Poisson models and mean-squared error for correlator estimators of time delay. IEEE Transactions on Information Theory, IT-34:843-858, 1988.
49. A. O. Hero. Lower bounds on estimator performance for energy-invariant parameters of multidimensional Poisson processes. IEEE Transactions on Information Theory, IT-35:287-303, 1989.
50. A. O. Hero and J. A. Fessler. A fast recursive algorithm for computing CR-type bounds for image reconstruction problems. In Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference, Orlando, FL, pages 1188-1190, 1992.
51. A. O. Hero and J. A. Fessler. A recursive algorithm for computing Cramér-rao-type bounds on estimator variance. IEEE Transactions on Information Theory, IT-40:843-848, 1994.
52. P. G. Hoel, S. C. Port, and C. J. Stone. Introduction to Probability Theory. Houghton Mifflin, Boston, MA, Fourth edition, 1971.
53. E. Jakeman and R. J. A. Tough. Non-Gaussian models for the statistics of scattered waves. Advances in Physics, 37(5):471-529, 1988.
54. A. Jazwinski. Stochastic Processes and Filtering Theory. Dover, Mineola, NY, Unabridged republication of 1970 edition, 2007.
55. T. Jebara. Machine Learning: Discriminative and Generative. Kluwer, Boston, MA, 2004.
56. M. E. Johnson. Multivariate Statistical Simulation. Wiley, New York, 1987.
57. A. F. Karr. Point Processes and Their Statistical Inference. Marcel Dekker, New York, Second edition, 1991.
58. K. Kastella. A maximum likelihood estimator for report-to-track association. In Proceedings of the SPIE, Signal and Data Processing or Small Targets, Orlando, Florida, volume 1954, 386-393, 1993.
59. K. Kastella. Event averaged maximum likelihood estimation and mean-field theory in multitarget tracking. IEEE Transactions on Automatic Control, 50:1070-1073, 1995.
60. K. Kastella. Discrimination Gain for Sensor Management in Multitarget Detection and Tracking. IMACS Conference on Computational Engineering in Systems Applications, Symposium on Control, Optimization and supervision, volume 1, Lille, France, 9-12 July pages 167-172, 1996.
61. M. G. Kendall and P. A. P. Moran. Geometrical Probability. Griffin, London, 1963.
62. A. I. Khinchine. Mathematical Methods in the Theory of Queueing. Griffon, London, 1955. Translated from Russian, 1960.
63. J. F. C. Kingman. Poisson Processes. Clarendon Press, Oxford, 1993.
64. G. E. Kopec. Formant tracking using hidden Markov models and vector quantization. IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34:709-729, 1986.
65. K. Lange and R. Carson. EM reconstruction algorithms for emission and transmission tomography. Journal of Computer Assisted Tomography, 8(2):306-316, 1984.
66. J. Langner. Development of a parallel computing optimized head movement correction method in positron emission tomography. Master's thesis, University of Applied Sciences Dresden and Research Center, Dresden-Rossendorf, 2003. http://www.jens-langner.de/ftp/MScThesis.pdf.
67. L. Lazos and R. Poovendran. Stochastic coverage in heterogeneous sensor networks. ACM Transactions on Sensor Networks, 2(3):325-358, 2006.
68. K. Lewin. The research center for group dynamics at Massachusetts Institute of Technology. Sociometry, 8:126-136, 1945.
69. T. A. Lewis. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 44(2):226-233, 1982.
70. R. M. Lewitt and S. Matej. Overview of methods for image reconstruction from projections in emission computed tomography. Proceedings of the IEEE, 91(10):1588-1611, 2003.
71. M. J. Lighthill. Introduction to Fourier Analysis and Generalized Functions. Cambridge University Press, London, 1958.
72. L. B. Lucy. An iterative technique for the rectification of observed distributions. The Astronomical Journal, 79:745-754, 1974.
73. T. E. Luginbuhl. Estimation of General, Discrete-Time FM Signals. PhD thesis, Department of Electrical Engineering, University of Connecticut, Storrs, CT, 1999.
74. R. P. S. Mahler. Multitarget Bayes filtering via first-order multitarget moments. IEEE Transactions on Aerospace and Electronic Systems, AES-39:1152-1178, 2003.
75. R. P. S. Mahler. PHD filters of higher order in target number. IEEE Transactions on Aerospace and Electronic Systems, AES-43:1523-1543, 2007.
76. R. P. S. Mahler. Statistical Multisource-Multitarget Information Fusion. Artech House, Boston, MA, 2007.
77. B. Matérn. Spatial variation. Meddelanden fran Statens Skogsforskningsinstitut (Communications of the State Forest Research Institute), 49(5):163-169, 1960.
78. B. Matérn. Spatial Variation. Number 36 in Lecture Notes in Statistics. Springer, New York, second edition, 1986.
79. G. Matheron. Random Sets and Integral Geometry. John Wiley & Sons, New York, 1975.
80. G. J. McLachlan and T. Krishnan. The EM Algorithm and Extensions. Wiley, New York, 1997.
81. G. J. McLachlan and D. Peel. Finite Mixture Models. Wiley, New York, 2000.
82. M. I. Miller, D. L. Snyder, and T. R. Miller. Maximum-likelihood reconstruction for single-photon emission computed-tomography. IEEE Transactions on Nuclear Science, NS-32(1):769-778, 1985.
83. P. Mitra. Spectral analysis: Point processes, August 16, 2006. http://wiki.neufo.org/neufo/jsp/Wiki?ParthaMitra.
84. J. Møller and R. P. Waagepetersen. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, Boca Raton, FL, 2004.
85. M. R. Morelande, C. M. Kreucher, and K. Kastella. A bayesian approach to multiple target detection and tracking. IEEE Transactions on Signal Processing, SP-55:1589-1604, 2007.
86. N. Nandakumaran, T. Kirubarajan, T. Lang, and M. McDonald. Gaussian mixture probability hypothesis density smoothing with multiple sensors. IEEE Transactions on Aerospace and Electronic Systems. Accepted for publication, 2010.
87. N. Nandakumaran, T. Kirubarajan, T. Lang, M. McDonald, and K. Punithakumar. Multitarget tracking using probability hypothesis density smoothing. IEEE Transactions on Aerospace and Electronic Systems. submitted, March 2008.
88. J. K. Nelson, E. G. Rowe, and G. C. Carter. Detection capabilities of randomly-deployed sensor fields. International Journal of Distributed Sensor Networks, 5(6):708-728, 2009.
89. R. Niu, P. Willett, and Y. Bar-Shalom. Matrix CRLB scaling due to measurements of uncertain origin. IEEE Transactions on Signal Processing, SP-49:1325-1335, 2001.
90. B. Øksendal. Stochastic Differential Equations, An Introduction with Applications. Springer, Berlin, Fourth edition, 1995.
91. J. A. O'Sullivan and J. Benac. Alternating minimization algorithms for transmission tomography. IEEE Transactions on Medical Imaging, MI-26:283-297, 2007.
92. C. Palm. Intensitätsschwankungen im fernsprechverkehr. Ericsson Techniks, 44:1-189, 1943.
93. A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York, 1965.
94. M. D. Penrose. On k-connectivity for a geometric random graph. Random Structures and Algorithms, 15(2):145-164, 1999.
95. A. Popescu. Markov-Modulated Poisson Processes. http://www.itm.bth.se/ ~adrian/courses/modern-techniques-networking/assignments/Tools.html.
96. J. G. Propp and D. B. Wilson. Exact sampling with coupled markov chains and applications to statistical mechanics. Random Structures and Algorithms, 9(1/2):223-252, 1996.
97. S. L. Rathbun and N. Cressie. Asymptotic properties of estimators for the parameters of a spatial inhomogeneous poisson point process. Advances in Applied Probability, 26:122-154, 1994.
98. H. E. Rauch, F. Tung, and C. T. Striebel. Maximum likelihood estimates of linear dynamic systems. AIAA Journal, 3:1445-1450, 1965.
99. R. A. Redner and Homer F. Walker. Mixture densities, maximum likelihood, and the EM algorithm. SIAM Review, 26(2):195-239, 1984.
100. S. Resnick. Adventures in Stochastic Processes, with Illustrations. Birkhäuser, Boston, MA, 1992.
101. S. O. Rice. Mathematical analysis of random noise. Bell System Technical Journal, 23-24:1-162, 1944.
102. W. H. Richardson. Bayesian-based iterative method of image restoration. Journal of the Optical Society of America, 62:55-59, 1972.
103. B. D. Ripley. Spatial Statistics. John Wiley & Sons, New York, 1981.
104. B. Ristic, S. Arulampalam, and N. Gordon. Beyond the Kalman Filter. Artech House, Boston, 2004.
105. H. E. Robbins. On the measure of a random set. The Annals of Mathematical Statistics, 15:70-74, 1944.
106. H. E. Robbins. On the measure of a random set. II. The Annals of Mathematical Statistics, 16:342-347, 1945.
107. E. G. Rowe and T. A. Wettergren. Coverage and reliability of randomly distributed sensor systems with heterogeneous detection range. International Journal of Distributed Sensor Networks, 5(4):303-320, 2009.
108. L. A. Santaló. Integral Geometry and Geometric Probability. Cambridge University Press, Cambridge, Second edition, 2004.
109. R. T. Seeley. Spherical harmonics. The American Mathematical Monthly, 73:115-121, 1966. Slaught Memorial Supplement.
110. L. A. Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Transactions on Medical Imaging, MI-1(2):113-122, 1982.
111. H. Sidenbladh. Multi-target particle filtering for probability hypothesis density. In Proceedings of the International Conference on Information Fusion, Cairns, Australia, pages 800-806. ISIF, 2003.
112. M. Šimandl, J. Královec, and P. Tichavský. Filtering, predictive and smoothing Cramér-Rao bounds for discrete-time nonlinear dynamic systems. Automatica, 37:1703-1716, 2001.
113. I. M. Slivnyak. Some properties of stationary flows of homogeneous random events. Theory of Probability and Its Applications, 7:336-341, 1962.
114. Russian original in Teoriya Veroyatnostei i ee Primeneniya, 347-352, 1962.
115. B. J. Slocumb and D. L. Snyder. Maximum likelihood estimation applied to quantum-limited optical position keeping. In Proceedings of the SPIE Technical Symposium on Optical Engineering and Photonics in Aerospace Sensing Orlando, FL, pages 165-176, 1990.
116. B. J. Slocumb. Position-sensing algorithms for optical communications. Master's thesis, Department of Electrical Engineering, Washington University, St. Louis, MO, 1988.
117. W. B. Smith and R. R. Hocking. A simple method for obtaining the information matrix for a multivariate normal distribution. The American Statistician, 22:18-20, 1968.
118. D. L. Snyder and P. M. Fishman. How to track a swarm of fireflies by observing their flashes. IEEE Transactions on Information Theory, IT-21:692-695, 1975.
119. D. L. Snyder. Random Point Processes. Wiley, New York, 1975.
120. D. L. Snyder and M. I. Miller. Random Point Processes in Time and Space. Springer, New York, Second edition, 1991.
121. H. Solomon. Geometric Probability. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1978.
122. M. C. Stein and C. L. Winter. An additive theory of probabilistic evidence accrual, 1993. Report LA-UR-93-3336, Los Alamos National Laboratories.
123. L. D. Stone, T. L. Corwin, and C. A. Barlow. Bayesian Multiple Target Tracking. Artech House, Inc., Norwood, MA, 1999.
124. D. Stoyan, W. S. Kendall, and Joseph Mecke. Stochastic Geometry and its Applications. Wiley, Chichester, second edition, 1995.
125. R. L. Streit. Multisensor multitarget intensity filter. In Proceedings of the International Conference on Information Fusion, Cologne, Germany. ISIF, pp 1694-1701 30 June-3 July 2008.
126. R. L. Streit. PHD intensity filtering is one step of a MAP estimation algorithm for positron emission tomography. In Proceedings of the International Conference on Information Fusion, Seattle. ISIF, pp 308-315 6 July - 9 July 2009.
127. R. L. Streit and T. E. Luginbuhl. Maximum likelihood method for probabilistic multihypothesis tracking. In Proceedings of the SPIE Conference on Signal and Data Processing of Small Targets, volume 2235, pages 394-405, Orlando, FL, 1991.
128. R. L. Streit and T. E. Luginbuhl. A probabilistic multi-hypothesis tracking algorithm without enumeration and pruning. In Proceedings of the Sixth Joint Service Data Fusion Symposium, pages 1015-1024, Laurel, Maryland, 1993.
129. R. L. Streit and T. E. Luginbuhl. Probabilistic multi-hypothesis tracking, 1995. Technical Report 10, 428, Naval Undersea Warfare Center, Newport, RI.
130. R. L. Streit and Tod E. Luginbuhl. Estimation of Gaussian mixtures with rotationally invariant covariance matrices. Communications in Statistics: Theory and Methods, 26:2927-2944, 1997.
131. R. L. Streit and L. D. Stone. Bayes derivation of multitarget intensity filters. In Proceedings of the International Conference on Information Fusion, Cologne, Germany. ISIF, pp. 1686-1693 30 June-3 July 2008.
132. M. Ter-Pogossian. The Physical Aspects of Diagnostic Radiology. Hoeber Medical Division, Harper and Rowe, New York, 1967.
133. H. R. Thompson. Distribution of distance to Nth neighbour in a population of randomly distributed individuals. Ecology, 37:391-394, 1956.
134. P. Tichavský, C. H. Muravchic, and A. Nehorai. Posterior Cramér-Rao bounds for discretetime nonlinear filtering. IEEE Transactions on Signal Processing, SP-46:1386-1396, 1998.
135. H. L. Van Trees. Detection, Estimation, and Modulation Theory-Part I. Wiley, New York, 1968.
136. H. L. Van Trees and Kristine L. Bell, editors. Bayesian Bounds for Parameter Estimation and Nonlinear Filtering and Tracking. Wiley, 2007.
137. M. N. M. van Lieshout. Markov Point Processes and Their Applications. Imperial College Press, London, 2000.
138. B.-N. Vo, S. Singh, and A. Doucet. Sequential Monte Carlo methods for multi-target filtering with random finite sets. IEEE Transactions on Aerospace and Electronic Systems, AES-41:1224-1245, 2005.
139. B.-T. Vo, B.-N. Vo, and A. Cantoni. The cardinalized probability hypothesis density filter for linear Gaussian multi-target models. In Proceedings of the 40th Annual Conference on Information Sciences and Systems, Princeton, NJ, pp. 681-686 March 22-24 2006.
140. B.-T. Vo, B.-N. Vo, and A. Cantoni. Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Transactions on Signal Processing, SP-55:3553-3567, 2007.
141. W. G. Warren. The center-satellite concept as a basis for ecological sampling (with discussion). In G. P. Patil, E. C. Pielou, and W. E. Waters, editors, Statistical Ecology, volume 2, pages 87-118. Pennsylvania State University Press, University Park, IL, 1971. (ISBN 0-271-00112-7).
142. Y. Watanabe. Derivation of linear attenuation coefficients from CT numbers for low-energy photons. Physics in Medicine Biology, 44:2201-2211, 1999.
143. T. A. Wettergren and M. J. Walsh. Localization accuracy of track-before-detect search strategies for distributed sensor networks. EURASIP Journal on Advances in Signal Processing, Article ID 264638:15, 2008.