  We present a novel method called Kernel-SME filter for tracking multiple
targets when the association of the measurements to the targets is unknown. The
method is a further development of the Symmetric Measurement Equation (SME)
filter, which removes the data association uncertainty of the original
measurement equation with the help of a symmetric transformation. The
underlying idea of the Kernel-SME filter is to construct a symmetric
transformation by means of mapping the measurements to a Gaussian mixture. This
transformation is scalable to a large number of targets and allows for deriving
a Gaussian state estimator that has a cubic time complexity in the number of
targets.
