  This work focuses on the critical aspect of accurate weight computation
during the measurement incorporation phase of Gaussian mixture filters. The
proposed novel approach computes weights by linearizing the measurement model
about each component's posterior estimate rather than the the prior, as
traditionally done. This work proves equivalence with traditional methods for
linear models, provides novel sigma-point extensions to the traditional and
proposed methods, and empirically demonstrates improved performance in
nonlinear cases. Two illustrative examples, the Avocado and a cislunar single
target tracking scenario, serve to highlight the advantages of the new weight
computation technique by analyzing filter accuracy and consistency through
varying the number of Gaussian mixture components.
