Combination of iterated cubature Kalman filter and neural networks for GPS/INS during GPS outages.

To improve the performance of the Global Positioning System/Inertial Navigation System (GPS/INS) integrated navigation system, current research studies merely combine neural networks with nonlinear filter methods. Few studies focus on how to optimize the parameters of the neural network and how to further improve the small error accumulated into the next filter step due to the imprecise design of the filter when setting the initial parameters in the GPS/INS integrated system. In this article, a dual optimization method consisting of an iterated cubature Kalman filter-Feedforward Neural Network (ICKF-FNN) and a radial basis function-cubature Kalman filter (RBF-CKF) is proposed to compensate the position and velocity errors of the integrated system during GPS outages. The prominent advantages of the proposed method include the following. (i) The ICKF is designed to optimize the parameters of the introduced FNN adaptively and obtain an appropriate internal structure when GPS is available, which improves the accuracy of the training model. (ii) The RBF establishes the relationship between filter parameters and the optimal estimation errors, reducing the errors caused by inaccurate predicted observation during GPS outages. (iii) The proposed dual optimization method takes advantages over other combination algorithms under different moving conditions or even during long period of GPS outages, which shows its great stability. Experimental results show that the root mean squared error of the east position is reduced by 85.79% to 3.2187 m using the proposed strategy during turning movement and the east velocity error accumulation rate decreases by 92.69% during the long straight movement of 250 s. These results are from offline processing.