Application of Discrete Recursive Bayesian Estimation on Intervals and the Unit Circle to Filtering on SE(2)

Many applications require state estimation where possible values of the state are constrained to an interval (say, the valve position in percent) or the unit circle (say, the direction a robot is facing). We present two approaches that rely on a discretization of the state space, which differ in their interpretation of the discretized density. The first option is a piecewise constant density and the second option is a Dirac-mixture density. We show how circular filters can be derived and discuss the advantages and disadvantages of both approaches. In addition, we show how to extend the Dirac-based approach to estimation on the special Euclidean group in 2D, the group of rigid body motions in the plane, using Rao–Blackwellization. All presented the methods are thoroughly evaluated in simulations.

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