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**Masreliez theorem**^{[1]} describes a recursive algorithm within the technology of extended Kalman filter, named after the Swedish-American physicist John Masreliez, who is its author. 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 additive outlier (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^{[1]} 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]}

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^{a}^{b}Masreliez, C. (1975). "Approximate non-Gaussian filtering with linear state and observation relations".*IEEE Transactions on Automatic Control*.**20**(1): 107–110. doi:10.1109/TAC.1975.1100882. ISSN 0018-9286. **^**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)