Recursive Polynomial Minimum Mean-Square Error Estimation with Applications to Orbit Determination

摘要

This paper presents a systematic generalization of the linear update structure associated with the extended Kalmanfilter for high-order polynomial estimation of nonlinear dynamical systems. The minimummean-square error criterionis used as the cost function to determine the optimal polynomial update during the estimation process. The high-orderseries representation is implemented effectively using differential algebra techniques.Numerical examples showthat theproposed algorithm, named the high-order differential algebra Kalman filter, provides superior robustness and/ormean-square error performance as compared to linear estimators under the condition considered.