Nonlinear Progressive Filtering for SE(2) Estimation

Dual Quaternion Sample Reduction for SE(2) Estimation

“…We compare the sample reduction-based filter (SRF) proposed in Sec. IV with a plain particle filter (PF) and the SE(2)-Bingham filter (SE2BF) with a progressive update step [14], [27]. As the SE2BF relies on the SE(2)-Bingham distribution [12], we exploit 10 5 random samples for fitting the parametric model offline.…”

“…Here, s is expressed in the form of a planar dual quaternion and the last two elements of the vector after the operation are taken out to recover the transformed location. A more detailed introduction about the arithmetic and manifold structure of dual quaternions can be found in [14], [23].…”

“…As shown in Alg. 1, the set of n equally weighted samples X k−1 representing the posterior at time step k − 1 is fed through the system dynamics in (14). Each planar dual quaternion sample x k−1 is propagated by n p random samples from the system noise distribution (Alg.…”

“…In [12], a new distribution was proposed based on the Bingham distribution to directly model uncertain planar dual quaternions while considering correlated real and dual part. Corresponding Bayesian filters [13], [14] were established based thereon by exploiting the unscented transform as well as the progressive filtering scheme [15] and were further applied to simultaneous localization and mapping [16].…”

The State Space Subdivision Filter for Estimation on SE(2)

“…Other general approaches that can be applied to are the invariant extended and unscented Kalman filter [ 12 ] and the unscented Kalman filter on manifolds (UKF-M) [ 13 ]. An approach tailored explicitly to that is based on dual quaternions was proposed in [ 14 ]. A filter based on sample reduction for scenarios in which only samples of the noise are available was presented in [ 15 ].…”