We address the data association problem and propose a Bayesian approach based on a mixture of Gaus-sian Processes (GPs) having two key components, the assignment probabilities and the GPs. In the pro-posed approach, the two key components are simultaneously updated according to observations through an efficient Expectation-Maximization (EM) algorithm that we develop. The proposed approach is thus more adaptive to the observations than the existing approaches for data association. To validate the per-formance of the proposed approach, we provide experimental results with real data sets as well as two synthetic data sets. We also provide a theoretical analysis to show the effectiveness of the Bayesian up -date.(c) 2022 Elsevier Ltd. All rights reserved.