Asteroid Landing Navigation Based on Invariant Extended Kalman Filter

Optical navigation serves as a critical modality for autonomous guidance during small celestial body landing missions. To address the inherent strong nonlinearities in both the lander’s dynamic model and optical observation model, this paper investigates an invariant extended Kalman filter algorithm based on Lie group structures. First, we establish the state model and optical observation model on the special Euclidean group. Subsequently, a linearized right-invariant error dynamics equation is derived using invariance theory, along with the formulation of state prediction models. Furthermore, the feature vector observation model is modified into a right-invariant observation form, enabling state correction through exponential mapping of innovation vectors. Numerical simulations using asteroid Eros 433 demonstrate that the proposed invariant extended Kalman filter (InEKF) outperforms the conventional extended Kalman filter (EKF) in both estimation accuracy and convergence speed. Notably, the algorithm eliminates the need for online Jacobian matrix computations, satisfying the stringent navigation requirements for autonomous landing operations. The results validate the effectiveness of Lie group-based filtering in handling the nonlinear geometry of pose estimation for irregular celestial bodies.