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.