For non-ellipsoidal extended targets and group targets tracking (NETT and NGTT), using an ellipsoid to approximate the target extension may not be accurate enough because of the lack of shape and orientation information. In consideration of this, we model a non-ellipsoidal extended target or target group as a combination of multiple ellipsoidal sub-objects, each represented by a random matrix. Based on these models, an improved gamma Gaussian inverse Wishart probability hypothesis density (GGIW-PHD) filter is proposed to estimate the measurement rates, kinematic states, and extension states of the sub-objects for each extended target or target group. For maneuvering NETT and NGTT, a multi-model (MM) approach based GGIW-PHD (MM-GGIW-PHD) filter is proposed. The common and the individual dynamics of the sub-objects belonging to the same extended target or target group are described by means of the combination between the overall maneuver model and the sub-object models. For the merging of updating components, an improved merging criterion and a new merging method are derived. A specific implementation of prediction partition with pseudo-likelihood method is presented. Two scenarios for non-maneuvering and maneuvering NETT and NGTT are simulated. The results demonstrate the effectiveness of the proposed algorithms.