Equivalent linearization Kalman filter with application to cubic sensor problems

We revisit the equivalent linearization technique to clarify a relationship between the extended Kalman filter (EKF) and equivalent linearization Kalman filter (EqKF). By deriving the equivalent gain for a static nonlinearity, we show that the equivalent linearization for the EqKF is a global method, though the first-order linearization for the EKF is a local one. Then, we consider discrete-time cubic sensor problems and analyze the Kalman gains and filtered covariances of respective filters, showing that the EqKF is quite close to the Gaussian filter (GF). Moreover, numerical results are included to compare the performances of the EqKF, EKF and GF.