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.