Unbiased minimum variance estimator design for scalar quadratic maps

In this paper, we consider the state estimation problem for scalar discrete-time nonlinear systems with second degree polynomial nonlinearities. This research is a follow up to our previous work on suboptimal minimum variance estimator design for quadratic maps. A novel state estimator is proposed where the extended Kalman filter structure is generalized to include quadratic terms and two consecutive measurements. Gains for unbiased minimum variance estimation are derived. It is shown both mathematically and by simulations that the new estimator achieves lower mean square estimation error than the extended Kalman filter. It is also shown in simulations that the new estimator performs better than the recently developed suboptimal estimator.