In this paper we carried out designing and implementing of a target tracking data fusion algorithm based on a two stages graph solution using the computational model Gamma (General Abstract Model for Multiset mAnipulation). The proposed solution is the first parallel implementation of the method PPTS (Pairs of Plots in Two Stages). For this, we employed three Gamma implementations, where two of them exploited the resources of a parallel hardware environment, one using the MPI (Message Passing Interface) and the other one GPU (Graphics Processing Unit). Thus, the studied algorithm was evaluated from the parallelism exploited and finally was carried out a performance analysis of this algorithm in the three Gamma implementations used. The aim of this study is to provide an implementation on a real problem using for this the paradigm Gamma, which contributes to the implementations of the Gamma computational model, since it enables the performance analysis of these implementations and provides some suggestions for possible improvements. In addition, this work contributes to the PPTS method since it provides the parallelization of the first stage.