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A method and algorithms are described which are practically attractive when performing simultaneous state and parameter estimation. The method is based on the use of a non-linear filter and the idea that the state and parameter estimates are properly phased to get good convergence conditions. The algorithms are given in the case where the system non-linearities are approximated by a polynomial, preferably orthogonal expansion. The method itself, however, does not assume such specification and can be applied to the case of given non-linearities as well.