This paper is Part VIb of a comprehensive survey of maneuvering
target tracking without addressing the so-called measurement-origin
uncertainty. It provides an in-depth coverage of various
approximate density-based nonlinear filters in mixed time
developed, particularly for handling the uncertainties induced by
potential target maneuvers as well as nonlinearities in the
dynamical systems commonly encountered in target tracking. An
emphasis is given to the more recent results, especially those with
good potential for tracking applications. Approximate nonlinear
filtering techniques for point estimation have been covered in a
previous part. Approximate nonlinear filtering in discrete time and
sampling-based nonlinear filters will be surveyed in forthcoming
parts.