To track multiple extended targets in dense clutter, an improved Gaussian processes linear joint probabilistic data association (IGP-LJPDA) method is proposed. This method consists of two stages. In the first stage, measurements are associated with targets, and pseudo-measurements are constructed. By integrating linear JPDA with Gaussian processes, probabilities for each measurement's assignment to each target are determined. Following this, a novel pseudo-measurement model is devised by combining the marginal probability of each target with measurements belonging to their respective basic point neighborhood, enabling more efficient state updates. In the second stage, pseudo-measurements are associated with the contour, and states of extended targets are updated accordingly. By associating pseudo-measurements with Gaussian processes basic points of each target, the algorithm achieves globally optimal association. The proposed algorithm demonstrates a notable improvement in Intersection over Union (IOU) metrics in environments with significantly higher clutter rates compared to existing methods. •A multiple extended targets tracking algorithm that can perform efficiently in dense clutter is proposed.•A new pseudo-measurement model is constructed, resulting in a decreased computational complexity.•A pseudo-measurement to contour association is proposed to achieve a globally optimal association.•The track maintenance process operates without relying on any clustering or partitioning method.