An Efficient Approximation of the Second-Order Extended Kalman Filter for a Class of Nonlinear Systems

This paper presents an efficient approximation for the second-order extended Kalman filter (SEKF) for nonlinear systems possessing a dominant direction of nonlinearity, which we call the directional second-order extended Kalman filter (DSEKF). Under certain assumptions, it is shown that the second-order terms in the standard SEKF can be accurately approximated with a single function evaluation (n
x
terms). The DSEKF approximation addresses some of the drawbacks of the standard SEKF - namely, that the SEKF requires deriving the second-order state rates for the system, and requires integrating an additional
$n_{x}^{3}$
terms on top of the first-order extended Kalman filter (EKF). The resulting algorithm is an efficient alternative to sampling-based nonlinear filtering methods. The DSEKF can also be easily added onto existing operational systems that already use the EKF.