User:Ferrofield/Masreliez’s theorem: Difference between revisions
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'''Masreliez teorem''' describes a [[Recursion (computer science)|recursive algorithm]] within the technology of extended [[Kalman filter]], named after the Swedish-American [[physicist]] [[C. Johan Masreliez|John Masreliez]], who is its author.<ref>Adlibris;[http://www.adlibris.com/se/product.aspx?isbn=1456574345 ''The Progression of Time''], med CV för Masreliez (2013).</ref> The algorithm estimates the state of a [[Dynamical system|dynamic system]] with the help of often incomplete measurements marred by [[distortion]].<ref>T. Cipra & A. Rubio; [http://www.springerlink.com/content/k638271765473144/ ''Kalman filter with a non-linear non-Gaussian observation relation''], Springer (1991).</ref>. |
'''Masreliez teorem''' describes a [[Recursion (computer science)|recursive algorithm]] within the technology of extended [[Kalman filter]], named after the Swedish-American [[physicist]] [[C. Johan Masreliez|John Masreliez]], who is its author.<ref>Adlibris;[http://www.adlibris.com/se/product.aspx?isbn=1456574345 ''The Progression of Time''], med CV för Masreliez (2013).</ref> The algorithm estimates the state of a [[Dynamical system|dynamic system]] with the help of often incomplete measurements marred by [[distortion]].<ref>T. Cipra & A. Rubio; [http://www.springerlink.com/content/k638271765473144/ ''Kalman filter with a non-linear non-Gaussian observation relation''], Springer (1991).</ref>. |
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Masreliez's theorem produces estimates that are quite good approximations to the exact [[Conditional expectation|conditional mean]] in [[Non-Gaussianity|non-Gaussian]] AO situations. Some evidence for this can be had by [[Monte Carlo method|Monte Carlo simulation]]s.<ref name=jasa87>{{Citation|author=R. Douglas Martin and Adrian E. Raftery |accessdate=2016-03-27 |date=December 1987 |publication-date=2003-10-15 |title=Robustness, Computation, and Non-Euclidean Models |trans-title= |pages=1044-1050 |publisher=[[Journal of the American Statistical Association]] |language= |url=https://www.stat.washington.edu/raftery/Research/PDF/martin1987.pdf |quote= }} (PDF 1465 kB)<!--Journal of the American Statistical Association December 1987. Vol. 82. No. 400, Theory and Methods--></ref> |
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The key approximation property used to construct these filters is that the [[Density (disambiguation)#Mathematics|state prediction density]] is approximately [[Gaussian function|Gaussian]]. Masreliez discovered in 1975 that this approximation yields an intuitively appealing [[Non-Gaussianity|non-Gaussian]] filter recursions, with [[Data dependency|data dependent]] [[covariance]] (unlike the Gaussian case) this derivation also provides one of the nicest ways of establishing the standard Kalman filter recursions. Some theoretical justification for use of the Masreliez approximation is provided by the "continuity of state prediction densities" theorem in Martin (1979).<ref name=jasa87/> |
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== See also == |
== See also == |
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Revision as of 21:59, 27 March 2016
Masreliez teorem describes a recursive algorithm within the technology of extended Kalman filter, named after the Swedish-American physicist John Masreliez, who is its author.[1] The algorithm estimates the state of a dynamic system with the help of often incomplete measurements marred by distortion.[2].
Masreliez's theorem produces estimates that are quite good approximations to the exact conditional mean in non-Gaussian AO situations. Some evidence for this can be had by Monte Carlo simulations.[3]
The key approximation property used to construct these filters is that the state prediction density is approximately Gaussian. Masreliez discovered in 1975 that this approximation yields an intuitively appealing non-Gaussian filter recursions, with data dependent covariance (unlike the Gaussian case) this derivation also provides one of the nicest ways of establishing the standard Kalman filter recursions. Some theoretical justification for use of the Masreliez approximation is provided by the "continuity of state prediction densities" theorem in Martin (1979).[3]
See also
- Control engineering
- Hidden Markov model
- Bayes' theorem
- Robust optimization
- Probability theory
- Nyquist–Shannon sampling theorem
References
- ^ Adlibris;The Progression of Time, med CV för Masreliez (2013).
- ^ T. Cipra & A. Rubio; Kalman filter with a non-linear non-Gaussian observation relation, Springer (1991).
- ^ a b R. Douglas Martin and Adrian E. Raftery (December 1987), Robustness, Computation, and Non-Euclidean Models (PDF), Journal of the American Statistical Association (published 2003-10-15), pp. 1044–1050, retrieved 2016-03-27 (PDF 1465 kB)