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.
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