This paper presents a novel algorithm for the
estimation of planar rigid-body motions. It is based on using a
probability distribution that is inherently defined on the non-
linear manifold representing these motions and on proposing
a deterministic sampling scheme that makes consideration of
complicated system models possible. Furthermore, we show
that the measurement update for a manifold equivalent to
noisy direct measurements can be carried out in closed form.
Thus, the resulting method avoids errors made due to local
linearization and outperforms methods that wrongly assume
Gaussian distributions, which we show by comparing the
proposed filter to the UKF.