A second-order method for state estimation of non-linear dynamical systems†

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Abstract
The paper is concerned with further elaboration of the concept of statistical approximation of a given nonlinear function and its application to the problem of state estimation of a non-linear noisy dynamical system from noise-corrupted observations. It is shown that under the assumption that the conditional probability density of the state variable is gaussian, it is possible to approximate a non-linear function of the state by a polynomial of arbitrary order. Using the second-order approximation, an algorithm is then developed for the problem of state estimation. Results obtained from this algorithm are compared with those obtained from a second-order algorithm based on Taylor's series expansion of the non-linear function.

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