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Nonlinear Filters

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Encyclopedia of Systems and Control

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Abstract

Nonlinear filters estimate the state of dynamical systems given noisy measurements related to the state vector. In theory, such filters can provide optimal estimation accuracy for nonlinear measurements with nonlinear dynamics and non-Gaussian noise. However, in practice, the actual performance of nonlinear filters is limited by the curse of dimensionality. There are many different types of nonlinear filters, including the extended Kalman filter, the unscented Kalman filter, and particle filters.

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Bibliography

  • Arasaratnam I, Haykin S, Hurd TR (2010) Cubature Kalman filtering for continuous-discrete systems. IEEE Trans Signal Process 58:4977–4993

    Article  MathSciNet  Google Scholar 

  • Benes V (1981) Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics 5:65–92

    Article  MathSciNet  MATH  Google Scholar 

  • Chorin A, Tu X (2009) Implicit sampling for particle filters. Proc Natl Acad Sci 106:17249–17254

    Article  Google Scholar 

  • Crisan D, Rozovskii B (eds) (2011) Oxford handbook of nonlinear filtering. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Daum F (2005) Nonlinear filters: beyond the Kalman filter. IEEE AES Magazine 20:57–69

    Article  Google Scholar 

  • Daum F, Huang J (2013a) Particle flow with non-zero diffusion for nonlinear filters. In: Proceedings of SPIE conference, San Diego

    Google Scholar 

  • Daum F, Huang J (2013b) Particle flow and Monge-Kantorovich transport. In: Proceedings of IEEE FUSION conference, Singapore

    Google Scholar 

  • Dick J, Kuo F, Peters G, Sloan I (eds) (2013) Monte Carlo and quasi-Monte Carlo methods 2012. Proceedings of conference, Sydney. Springer, Heidelberg

    Google Scholar 

  • Doucet A, Johansen AM (2011) A tutorial on particle filtering and smoothing: fifteen years later. In: Crisan D, Rozovskii B (eds) The Oxford handbook of nonlinear filtering. Oxford University Press, Oxford pp 656–704

    Google Scholar 

  • Gelb A et al (1974) Applied optimal estimation. MIT, Cambridge

    Google Scholar 

  • Ho Y-C, Lee RCK (1964) A Bayesian approach to problems in stochastic estimation and control. IEEE Trans Autom Control 9:333–339

    Article  MathSciNet  Google Scholar 

  • Jazwinski A (1998) Stochastic processes and filtering theory. Dover, Mineola

    Google Scholar 

  • Julier S, Uhlmann J (2004) Unscented filtering and nonlinear estimation. IEEE Proc 92:401–422

    Article  Google Scholar 

  • Kailath T (1970) The innovations approach to detection and estimation theory. Proc IEEE 58: 680–695

    Article  MathSciNet  Google Scholar 

  • Kushner HJ (1964) On the differential equations satisfied by conditional probability densities of Markov processes. SIAM J Control 2:106–119

    MathSciNet  MATH  Google Scholar 

  • Marcus SI (1984) Algebraic and geometric methods in nonlinear filtering. SIAM J Control Optim 22:817–844

    Article  MathSciNet  MATH  Google Scholar 

  • Noushin A, Daum F (2008) Some interesting observations regarding the initialization of unscented and extended Kalman filters. In: Proceedings of SPIE conference, Orlando

    Google Scholar 

  • Ristic B, Arulampalam S, Gordon N (2004) Beyond the Kalman filter. Artech House, Boston

    MATH  Google Scholar 

  • Sorenson HW (1974) On the development of practical nonlinear filters. Inf Sci 7:253–270

    Article  MathSciNet  MATH  Google Scholar 

  • Sorenson HW (1980) Parameter estimation. Marcel-Dekker, New York

    MATH  Google Scholar 

  • Sorenson HW (1988) Recursive estimation for nonlinear dynamic systems. In: Spall J (ed) Bayesian analysis of time series and dynamic models. Marcel-Dekker, New York, pp 127–165

    Google Scholar 

  • Stratonovich RL (1960) Conditional Markov processes. Theory Probab Appl 5:156–178

    Article  Google Scholar 

  • Traub J, Werschulz A (1998) Complexity and information. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • van Handel R (2010) Nonlinear filters and system theory. In: Proceedings of 19th international symposium on mathematical theory of networks and systems, Budapest

    Google Scholar 

  • Villani C (2003) Topics in optimal transportation. American Mathematical Society, Providence

    MATH  Google Scholar 

  • Zakai M (1969) On the optimal filtering of diffusion processes. Z fur Wahrscheinlichkeitstheorie und verw Geb 11:230–243

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Raytheon Company, Woburn, MA, USA

    Frederick E. Daum

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  1. Frederick E. Daum
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Correspondence to Frederick E. Daum .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Daum, F.E. (2014). Nonlinear Filters. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_63-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_63-2

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  • Online ISBN: 978-1-4471-5102-9

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