Aiming at improving the poor real-time performance of existing nonlinear filtering algorithms applied to spacecraft autonomous navigation based on Global Positioning System (GPS) measurements and simplifying the algorithm design of navigation algorithms, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is proposed in this paper. Firstly, it is demonstrated that the nonlinear estimation error system of spacecraft autonomous navigation can be modelled as a polytopic linear differential inclusion system model according to the idea of global linearization. Thus, the filtering of a nonlinear system simplified to a filtering of a polytopic linear system with coefficients. Secondly, Tensor-Product (TP) model transformation is applied to determine the polytopic linear differential inclusion system model. The model error introduced by global linearization is reduced and the compromise between computational complexity and modelling accuracy is realised. Finally, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is designed by combining multi-model Kalman filtering with data fusion. Compared with an Extended Kalman Filter (EKF), the proposed algorithm is simpler and easier to implement since it need not update the Jacobian matrices online. Simulation results demonstrate the same estimation accuracy of the proposed algorithm to that of EKF.