On the state estimation for non-linear dynamic systems †

The object of this paper is to present an approximate technique for state estimation of non-linear dynamical systems under noisy observations. The conditional cumulant is introduced, by which the conditional probability density can be characterized. A set of dynamical equations satisfied by conditional cumulants is derived, and an approximate method is proposed for computing the cumulants. The relation of the cumulant method to the stochastic linearization technique is also discussed. Finally the state estimation problem for linear stochaatic system with state-dependent disturbance is solved to illustrate the use of the Gaussian approximation.