Data association is a crucial part of target tracking systems with clutter measurements. In general, its complexity increases sharply with a number of targets and measurements. Recently, high-resolution sensors have given rise to extended target tracking problems and more than one measurements can emerge from each target, making the association problems more complex. In this study, a tractable algorithm based on the Gaussian process measurement model and truncated joint probabilistic data association technique is proposed for multiple extended target tracking in the presence of measurement origin uncertainty. Based on the marginal association probabilities, the calculation amount is effectively reduced by truncating the association events with low probabilities in the shortest path problem. The effectiveness of the proposed algorithm is verified by the test of multiple extended targets tracking and compared with the linear-time joint probabilistic data association as well as the algorithm on random finite sets. Simulation results show that the proposed algorithm can track multiple extended targets accurately, which is significant in high-resolution radar tracking systems.