Predictive filtering for nonlinear systems

In this paper, a real-time predictive filter is derived for nonlinear systems. This provides a method of determining optimal state estimates in the presence of significant error in the assumed (nominal) model. The new real-time nonlinear filter determines ("predicts") the optimal model error trajectory so that the measurcment-minus-estimate covariance statistically matches the known measurement-minus-truth covariance. The optimal model error is found by using a onetime step ahead control approach. Also, since the continuous model is used to determine state estimates, the filter avoids discrete state jumps, as opposed to the extended Kalman niter. The predictive filter is used to estimate the attitude of a spacecraft with the utilization of attitude sensor measurements and rate integrating gyro measurements. Results using this new algorithm indicate that the real-time predictive filter accurately estimates the attitude of the spacecraft by determining actual gyro bias errors.