Many real-world applications of target tracking and state estimation are nonlinear filtering problems and can therefore not be solved by closed-form analytical solutions. In the recent past, tensor-based approaches have become increasingly popular due to very effective de-composition algorithms, which allow a compressed representation of discretized, high-dimensional data. It has been shown that by means of a Kronecker format of the Fokker–Planck equation, the Bayesian recursion for prediction and filtering can be solved for probability densities in a canonical polyadic decomposition (CPD). In this paper, the application of this approach on tracking multiple targets in a cluttered environment is presented. It is shown that intensity or probability hypothesis density-based filters can well be implemented using the CPD tensor format.