A polynomial chaos based square-root Kalman filter for Mars entry navigation

In order to compute the sequential state estimation of Mars entry dynamic system from noisy observations, a deterministic square-root Kalman filter is developed with the implementation of polynomial chaos expansion. The filter allows for the nonlinearity of dynamic system and observation model without the need for assumption about the Gaussian distribution of state. In the algorithm, a minimum variance based data assimilation scheme is developed. The resulting Kalman type updates of state's mean and deviations are performed separately and the square-root formulation of coefficients of polynomial chaos can be computed directly from the polynomial chaos expansion of forecasted states and observations. Two autonomous navigation scenarios based on the Mars Network are considered to quantify the benefits of polynomial chaos based square-root Kalman filter over the other usual nonlinear filters. Additionally, the contrastive analysis of propagations with non-Gaussian states is conducted. Simulation results show that a more accurate estimation and faster convergence can be achieved from the proposed nonlinear filter. Finally, the accuracy and time efficiency of the polynomial chaos based square-root Kalman filter are further analyzed and the optimal order of polynomial chaos is recommended.