Second order state and covariance estimation for nonlinear stochastic systems

The Kalman Filter is one of the most commonly used methods in state and parameter estimation problems in linear and nonlinear stochastic systems analysis. This paper deals with further extensions of the existing Extended Kalman Filter (EKF) approach to study state and parameter estimation problems of nonlinear system of stochastic differential equations. The main focus in this paper is to reduce the magnitude of errors in the existing Kalman Filter schemes. This is achieved by approximating the state conditional mean and covariances using a second degree polynomials. In addition, the drift, diffusion and the observations are approximated using a multidimensional extension of Sterling's interpolation formula.