Mars entry navigation under biases based on adaptive Huber divided difference filter

To address the problems of unknown disturbances and measurement outliers at Mars entry phase, three integrated navigation schemes are proposed in this study by complying with divided difference filters, that is, integrated navigation schemes based on the Huber first-order divided difference filter (HDDF1), adaptive Huber first-order divided difference filter (AHDDF1), and adaptive Huber second-order divided difference filter (AHDDF2). The novel versions of predictive state estimation error covariance (PSEEC) and measurement noise covariance (MNC) are deduced by adopting the (Formula presented.) function of the Huber case to modify the cost function of the standard Kalman filter. To be specific, the HDDF1 is derived by embedding the novel PSEEC and MNC in the general first-order divided difference filter. To more specifically enhance the performance of the filter under significant biases, an adaptive forgetting factor is introduced in the HDDF1. On that basis, the AHDDF1 is derived. Likewise, the AHDDF2 is yielded. The numerical simulations are presented to verify the effectiveness of the proposed navigation schemes.