Constrained estimation for autonomous navigation using unknown landmarks

This paper presents a new method for autonomous navigation using unknown landmarks on the surface of an ellipsoidal planet, and geometry constraints of landmarks´ position that satisfy an ellipsoid equation are considered. Both of and unconstrained and constrained estimation are developed. An implicit bias method by augmenting the current state with a delay state to eliminate unknown landmarks positions in the measurement equation is used to form an unconstrained estimation of spacecraft´s state. Once the unconstrained estimation is derived, geometry constraints of landmarks´ position are transformed to constraints of spacecraft´s state. The unconstrained estimation is then projected onto the constrained space to form a constrained estimation. Numerical simulations are also provided to assess the performance of the proposed new method.