The Closely Spaced Objects (CSOs) unity is treated as an extended target with a random vector and a random matrix to respectively represent the kinematic states of the centroid and the extension state. Then the Gaussian inverse Wishart implementation of extended-target PHD filter is utilized to track CSOs under clutter and miss detection. New recursive expressions are given for the ill modeling of the original GIW-PHD filter. Consequentially, multiple (shape) models can be easily incorporated with the modified GIW-PHD filter to handle extension changes caused by splitting and merging of CSOs. The effectiveness of the proposed method is demonstrated by simulations. Simulation results show that the proposed method not only improves the estimation precision of the states, but also more sensitive to the extension changes of CSOs compared with the original GIW-PHD filter.