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Multi-target tracking in clutter, assuming linear target trajectory propagation and linear target measurement equation, naturally leads to a Gaussian mixture (GM) target tracking solution. This study examines and compares two prominent methods that use the GMs: the probability hypothesis density and the integrated track splitting. Both are recursive Bayes methods and both incorporate the false track discrimination capabilities. They are represented in the form of GM target density filters. The modelling assumptions are translated in the algorithmic requirements. The authors compare the algorithms on the basis of these requirements with the future work indicated to reconcile algorithms and requirements.