Introduction
The subject of this chapter is sequential Bayesian inference in which we consider the Bayesian estimation of a dynamic system which is changing in time. Let θ k denote the state of the system, i. e. a vector which contains all relevant information required to describe the system, at some (discrete) time k. Then the goal of sequential Bayesian inference is to estimate the a posteriori probability density function (pdf) p(θ k |y 1:l , I), by fusing together a sequence of sensor measurements y1:l = (y1, y2, ... ,y l ). In this chapter we shall only consider the calculation of pdf p(θ k |y 1:l , I) for k = l which is known as (sequential) Bayesian filtering or filtering for short.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Sig. Process. 50, 174–188 (2002)
Bar-Shalom, Y., Campo, L.: The effect of the common process noise on the two sensor fused track covariance. IEEE Trans. Aero. Elect. Sys. 22, 803–805 (1986)
Bar-Shalom, Y., Li, X.: Multitarget-Multisensor Tracking: Principles and Techniques. YBS Publishing, Storrs (1995)
Blackman, S.S., Popoli, R.F.: Design and analysis of modern tracking Systems. Artech House (1999)
Brown, R.G., Hwang, P.Y.C.: Introduction to random signal analysis and Kalman filtering. John Wiley and Sons (1997)
Chen, Z.: Bayesian filtering: from Kalman filters to particle filters, and beyond. Adaptive Systems Laboratory, Communications Research Laboratory. McMaster University,Canada (2003)
Chang, K., Saha, R., Bar-Shalom, Y.: On optimal track-to-track fusion. IEEE Trans. Aero. Elect. Sys. 33, 1271–1276 (1997)
Cipra, T., Romera, R.: Kalman filter with outliers and missing observations. Test 6, 379–395 (1997)
Cox, I.J.: A review of statistical data association techniques for motion correspondence. Int. J. Comp. Vis. 10, 53–66 (1993)
Duncan, S., Singh, S.: Approaches to multisensor data fusion in target tracking: a survey. IEEE Trans. Know Data Engng. 18, 1696–1710 (2006)
Eshel, R., Moses, Y.: Tracking people in a crowded scene. Int. J. Comp. Vis. 88, 129–143 (2011)
Flament, M., Fleury, G., Davoust, M.-E.: Particle filter and Gaussian-mixture filter efficiency evaluation for terrain-aided navigation. In: 12th Euro. Sig. Proc. Conf. EUSIPCO 2004, Vienna, Austria (2004)
Galanis, G., Anadranistakis, M.: A one-dimensional Kalman filter vfor the correction of near surface temperature forecasts. Meteorological Appl. 9, 437–441 (2002)
Gao, J.B., Harris, C.J.: Some remarks on Kalman filters for the multisensor fusion. Inf. Fusion 3, 191–201 (2002)
Huber, P.J.: Robust Statistics. John Wiley and Sons (1981)
Julier, S., Uhlmann, J.: General decentralized data fusion with covariance intersection (CI). In: Hall, D., Llians, J. (eds.) Handbook of Multidimensional Data Fusion, ch. 12. CRC Press (2001)
Julier, S.J., Uhlmann, J.K., Nicholson, D.N.: A method for dealing with assignment ambiguity. In: Proc. 2004 Am. Control Conf., Boston, Mass (2004)
Li, X.R., Jilkov, V.P.: A survey of maneuvering target tracking. Part I: Dynamic models. IIEEE Trans. Aero. Elec. Syst. 39, 1333–1363 (2003)
Li, X., Zhi, X.: PSNR: a refined strongest neighbor filter for tracking in clutter. In: Proc. 35th IEEE Conf. Dec. Control. (1996)
Lian, G., Lai, J., Zheng, W.-S.: Spatial-temporal consistent labeling of tracked pedestrians across non-overlapping camera views. Patt. Recogn. 44, 1121–1136 (2011)
Maskell, S.: Sequentially structured Bayesian solutions. PhD thesis. Cambridge University (2004)
Manfredi, V., Mahadevan, S., Kurose, J.: Switching Kalman filters for prediction and tracking in an adaptive meteorological sensing network. In: 2nd Annual IEEE Commun. Soc. Conf. Sensor and Ad Hoc Commun. and Networks, SECON 2005, Santa Clara, California, USA (2005)
Mardia, K.V., Goodall, C., Redfern, E.J., Alonso, F.J.: The Kriged Kalman filter. Test 7, 217–284 (1998)
Meinhold, R.J., Singpurwalla, N.D.: Understanding the Kalman filter. Am. Stat. 37, 123–127 (1983)
Murphy, K.P.: Switching Kalman Filters. Unpublished Rept. Available from homepage of K. P. Murphy (1998)
Murphy, K.P.: Dynamic Bayesian networks: representation, inference and learning, PhD thesis. University of California, Berkeley, USA (2002)
van der Merwe, R.: Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. PhD thesis. Oregon Health and Science University (2004)
Moore, J.R., Blair, W.D.: Practical aspects of multisensor tracking. In: Bar-Shalom, Y., Blair, W.D. (eds.) Multitarget-Multisensor Tracking: Applications and Advances, vol. III, pp. 1–78. Artech House, USA (2000)
Moore, M., Wang, J.: An extended dynamic model for kinematic positioning. J. Navig. 56, 79–88 (2003)
Pulford, G.W.: Taxonomy of multiple target tracking methods. IEEE Proc-Radar, Sonar, Navig. 152, 291–304 (2005)
Shin, V., Lee, Y., Choi, T.-S.: Generalized Millman’s formula and its application for estimation problems. Sig. Proc. 86, 257–266 (2006)
Wang, C., Kim, J.-H., Byun, K.-Y., Ni, J., Ko, S.-J.: Robust digital image stabilization using the Kalman filter. IEEE Trans. Consum. Elec. 55, 6–14 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mitchell, H.B. (2012). Sequential Bayesian Inference. In: Data Fusion: Concepts and Ideas. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27222-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-27222-6_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27221-9
Online ISBN: 978-3-642-27222-6
eBook Packages: EngineeringEngineering (R0)