<p>In order to track multiple maneuvering extended targets accurately, an adaptive interacting multiple model algorithm based on variational inference (AIMM-VI) is proposed. An augmented state is constructed to cater for time-varying orientation angle and track realistic shape changes, resulting in better elliptical shape estimation and tracking accuracy. Multiple measurements from multiple extended targets are effectively assigned to corresponding targets through the marginal association probability distribution criterion, and the variational inference is used to accurately estimate the augmented state and shape information, which greatly improves the parameters estimation performance. The residual and likelihood functions are updated in real-time according to the results of variational inference, allowing for the updating of the model probability in real-time. The Markov probability transfer matrix is subsequently adaptively updated by the compression ratio, which makes the algorithm more adaptable to maneuvering target and significantly improves the adaptability and robustness of the algorithm. The final simulation and experiment results show that the proposed algorithm can effectively improve the tracking performance of multiple maneuvering extended targets.</p>