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Simultaneously estimating the kinematic state and extent of extended targets is a nonlinear and high-dimensional problem. While the extended Kalman filter (EKF) is widely employed to achieve this goal, it may not be sufficient for mobility targets. To address this issue, this paper first proposes to embed unscented Kalman filter (UKF) into Gaussian process regression (GPR) since the superiority of UKF to high nonlinear. Furthermore, given the widely-existed environment with time-varying noise, it is crucial to study the change of measurement noise covariance caused by time-varying noise for high-precision tracking of extended targets. However, traditional UKF filter considers measurement noise covariance as constant value. To this end, an adaptive unscented Kalman filter (AUKF) algorithm combining with GPR model (GPR-AUKF) is proposed to address the issue. Specifically, the GPR-AUKF algorithm is built based on expectation maximization (EM) algorithm to track the target state and covariance, and which updates the measurement noise covariance in real-time. Experimental results show that GPR-AUKF is more accurate and robust than other methods for tracking extended targets.