This article presents the application of a track before detect (TBD) technique for multiple extended object tracking (EOT) in a heavy-tailed cluttered environment using a high-resolution marine inverse synthetic aperture radar system. In high sea states, the ship EOTs make complex maneuvering motions due to strong disturbances, such as sea waves and sea winds. In this work, we utilize emergent maneuvering EOT (M-EOT) methodologies in real-time scenarios based on the popular multi-Bernoulli (MB)-TBD filter, and in particular, we describe the ship M-EOT's state through the subrandom matrices model (sub-RMM). In sub-RMM, scatter centers are distributed symmetrically around the M-EOT's centroid. However, in the ship M-EOT scenario, the distribution over the whole object is not symmetrical, but distributed and skewed in some portions while a target maneuvers. To solve this problem, a novel robustness observation model is represented using a nonsymmetrically skewed normal distribution and multiple model MB-TBD with more than one ellipse. Simulation and experimental results illustrate that the proposed filter outperforms the existing filters for M-EOTs.