Recognizing the existence of identification errors due to variations of system parameters, an approximate method is described of state estimation for nonlinear dynamical systems with state-independent noise. Guided by the state space representation concept in control theory, a mathematical model of the dynamical system is given by the nonlinear vector stochastic differential equation of Itô- type.
The first part is devoted to the verification of the existence of a unique continuons solution for the nonlinear vector stochastic differential equation containing a random parameter. Both the α and β stochastic sensitivity equations are established through the precise definition of stochastic sensitivity.
The remainder of this paper deals with an application of the stochastic sensitivity concept to the state estimation problem. Effects on the state estimator dynamics due to variations in system parameters are considered by a numerical example.