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This paper analyzes directional tracking in 2D with the extended Kalmanfilter on Lie groups (LG-EKF). The study stems from the problem of trackingobjects moving in 2D Euclidean space, with the observer measuring directiononly, thus rendering the measurement space and object position on thecircle---a non-Euclidean geometry. The problem is further inconvenienced if weneed to include higher-order dynamics in the state space, like angular velocitywhich is a Euclidean variables. The LG-EKF offers a solution to this issue bymodeling the state space as a Lie group or combination thereof, e.g., SO(2) orits combinations with Rn. In the present paper, we first derive the LG-EKF onSO(2) and subsequently show that this derivation, based on the mathematicallygrounded framework of filtering on Lie groups, yields the same result asheuristically wrapping the angular variable within the EKF framework. Thisresult applies only to the SO(2) and SO(2)xRn LG-EKFs and is not intended to beextended to other Lie groups or combinations thereof. In the end, we showcasethe SO(2)xR2 LG-EKF, as an example of a constant angular acceleration model, onthe problem of speaker tracking with a microphone array for which real-worldexperiments are conducted and accuracy is evaluated with ground truth dataobtained by a motion capture system.

On wrapping the Kalman filter and estimating with the SO(2) group