 This paper proposes a new method for tracking multiple extended targets in three-dimensional space. It combines the Gaussian process regression measurement model with the probability hypothesis density filter to estimate both the kinematic state and the shape of the targets. The shape of the extended target is described by a 3D radial function and is estimated recursively using the Gaussian process regression model. Additionally, the recursive Gaussian process regression problem is transformed into a state estimation problem by deriving a state space model such that the extent of the target can be integrated into the kinematic part. The predicted likelihood function of the PHD filter is derived and a closed-form Gaussian mixture implementation is provided. The proposed algorithm is compared against the traditional gamma Gaussian inverse-wisert PHD, GGIWPHD filter. Results show that the proposed algorithm outperforms the GGIWPHD filter in terms of estimating both kinematic states and shape. Additionally, the proposed algorithm demonstrates robustness across various measurement rates, while the GGIWPHD filter suffers under low measurement rate conditions. This article was authored by Ziyuan Yang, Xiang Qinli, Xuanzhu and Yao, and others. We are article.tv, links in the description below.