module

states.directional

module unitrack.states.directional

von Mises-Fisher directional filter for unit-norm embedding states.

A recursive Bayesian filter for appearance/kernel embeddings that live on the unit sphere (cosine geometry). The belief over a tracklet's embedding is a von Mises-Fisher distribution with mean direction ``mu`` (a unit vector) and concentration ``kappa >= 0`` (larger = more certain). The vMF mean direction has a conjugate vMF prior, so combining the prior with a new observation is exact: the posterior parameter is the *resultant* of the two concentration-weighted directions, .. math:: R = \kappa\,\mu + \kappa_{obs}\,\hat z,\quad \mu' = R / \lVert R \rVert,\quad \kappa' = \lVert R \rVert, which is the directional analogue of a Kalman update. The predict step has no motion model for appearance, so it only *decays* the concentration: confidence in a stale embedding fades with time.

Source: unitrack/states/directional.py:1