Derivative-free Nonlinear Version of Extended Recursive Three-step Filter for State and Parameter Estimation during Mars Entry

Parameter uncertainties which may lead to divergence of traditional Kalman filters during Mars entry are investigated in this paper. To achieve high precision navigation, a Derivative-free Nonlinear version of an Extended Recursive Three-Step Filter (DNERTSF) is introduced, which suits nonlinear systems with arbitrary parameter uncertainties. A DNERTSF can estimate the state and the parameters simultaneously, and Jacobian and Hessian calculations are not necessary for this filter. Considering the uncertainties in atmosphere density, ballistic coefficient and lift-to-drag ratio, a numerical simulation of Mars entry navigation is carried out. Compared with the standard Unscented Kalman Filter (UKF), DNERTSF can effectively reduce the adverse effects of parameter uncertainties and achieve a high navigation accuracy performance, keeping position and velocity estimation errors at a very low level. In all, the DNERTSF in this paper shows good advantages for Mars entry navigation, providing a possible application for a future Mars pinpoint landing.