For nonlinear state space systems with additive
noises, sometimes the number of process noise signals could
be less than the dimension of the state space. In order to
improve the accuracy and stability of nonlinear state estimation,
this paper provides for the first time the derivation of the
full information estimator (FIE) for such nonlinear systems.
We verify our derivation of the FIE by firstly proving the
unbiasedness and minimum-variance of the FIE for linear time
varying (LTV) systems, then showing the equivalence between
the Kalman filter/smoother and the FIE for LTV systems.
Finally, we prove that the FIE will provide more accurate state
estimates than the extended Kalman filter (EKF) and smoother
(EKS) for nonlinear systems.