Firstly, the transfer function and measurement function are transformed into a nonlinear random dynamic model with a polynomial form via system identification through the multidimensional Taylor network. 
the multidimensional Taylor network
Finally, as we only know the results of the limited sampling of the random modeling error, we use the combination of the maximum correlation estimator and the Kalman filter to establish a new higher order extended Kalman filter. 
the maximum correlation estimator
Finally, as we only know the results of the limited sampling of the random modeling error, we use the combination of the maximum correlation estimator and the Kalman filter to establish a new higher order extended Kalman filter. 
the Kalman filter