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This paper is concerned with the development and performances of navigation filters for spacecraft relative pose estimation in a mission around an asteroid. For the sake of comparative study, relative pose is represented using two different sets of parameters: 1) conventional Cartesian coordinates along with the attitude quaternion, and 2) the dual quaternion. The spacecraft is equipped with a navigation camera and a laser ranger for position sensing, and with a star tracker and a rate gyroscope for attitude sensing. A highly realistic Truth model is used that includes polyhedron gravity field modelling of small bodies, polyhedron gravity gradient torque modeling, advanced hardware modeling of the navigation camera and laser ranging observations and errors. Results of extensive Monte-Carlo simulations for various orbital scenarios around two different asteroids, Kleopatra and Itokawa, will be shown. It turns out that not only are the filters able to estimate the relative pose with high accuracy, but that the gyroscope drift and asteroid angular rates have good observability too. The latter depends on the frequency and geometry of the landmarks lines-of-sight detected within the camera field-of-view. In some cases, the dual quaternion filter shows a better transient, when compared to the conventional filter. Their steady-state accuracies are in general similar. The trade-offs in using dual quaternion filters as opposed to standard filters are discussed.@en