states.directional
module unitrack.states.directionalvon 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