An adaptive target tracking method based on extended Kalman filter (TT-EKF) is proposed to simultaneously estimate the state of an Autonomous Underwater Vehicle (AUV) and an mobile recovery system (MRS) with unknown non-Gaussian process noise in homing process. In the application scenario of this article, the process noise includes the measurement noise of AUV heading and forward speed and the estimation error of MRS heading and forward speed. The accuracy of process noise covariance matrix (PNCM) can affect the state estimation performance of the TT-EKF. The variational Bayesian based algorithm is applied to estimate the process noise statistics. We use a Gaussian mixture distribution to model the non-Gaussian noisy forward speed of AUV and MRS. We use a von-Mises distribution to model the noisy heading of AUV and MRS. The variational Bayesian algorithm is applied to estimate the parameters of these distributions, and then the PNCM can be calculated. The prediction error of TT-EKF is online compensated by using a multilayer neural network, and the neural network is online trained during the target tracking process. Matlab simulation and experimental data analysis results verify the effectiveness of the proposed method.