  We present a particle vertex fitting method designed for B factories. The
presented method uses a Kalman Filter to solve a least squares estimate to
globally fit decay chains, as opposed to traditional methods that fit each
vertex at a time. It allows for the extraction of particle momenta, energies,
vertex positions and flight lengths, as well as the uncertainty estimates of
these quantities. Furthermore, it allows for the precise extraction of vertex
parameters in complex decay chains containing neutral final state particles,
such as ${\gamma}$ or $K^0_L$ , which cannot properly be tracked due to limited
spatial resolution of longitudinally segmented single-layer crystal
calorimeters like the Belle II ECL. The presented technique can be used to
suppress combinatorial background and improve resolutions on measured
parameters. We present studies using Monte Carlo simulations of collisions in
the Belle II experiment, where modes with neutrals are crucial to the physics
analysis program.
