Poly-topic Filtering Estimation Applied To The On-board GPS Navigation System

Because of the high precision, all-weather and the global service, the satellitenavigation system attracted a lot of attention. As an advanced technology which is omnibus,the satellite navigation has related to many fields in recent times, ranging from the vehiclenavigation to the spacecraft autonomous navigation. The high-precision navigation is thehot topic always which attracts a lot of attention in the research of the satellite navigation.Due to the existence of the observation noise with uncertain character and the process noisehas an influence on carrier during the moving process actually, the estimation accuracy ofposition and velocity will be influenced by the noise above greatly. Therefore, it issignificant to design an effective filtering algorithm used to reduce the influence on satellitenavigation due to the observation noise and process noise and improve the estimationaccuracy of position and velocity. Aiming at problems above, this article carried out therelated research about the nonlinear filtering estimation applied to the on-board GPSnavigation system.Aiming at great influence on the estimation accuracy of position and velocity due toobservation noise and process noise, a poly-topic filtering algorithm is proposed in thisarticle. Firstly, it is demonstrated that the nonlinear estimation error system of on-boardGPS navigation can be modeled as a poly-topic linear differential inclusion system modelaccording to the method of global linearization. Thus, the filtering of a nonlinear systemsimplified to a filtering of poly-topic linear system with coefficients. Secondly,tensor-product (TP) model transformation is applied to determine the poly-topic lineardifferential inclusion system model. The model error introduced by global linearization isreduced and the compromise between computational complexity and modeling accuracy isrealized. Finally, the poly-topic Kalman filtering algorithm and poly-topic H∞filteringalgorithm are proposed, taking the Gaussian noise and non-Gaussian noise which exists inthe on-board GPS navigation system into consideration. The proposed algorithm is morefeasible and easy to implement since it need not update the Jacobian matrixes online.Simulation results demonstrate the same estimation accuracy of poly-topic KF algorithm and poly-topic H∞filtering algorithm as that of EKF and extend H∞filtering algorithmrespectively.