Conventional tracking algorithms rely upon the hypothesis of one detection per target for each frame. However, very fine spatial resolution radars represent widespread systems that provides data for which this hypothesis could be no longer valid. This problem is often called in the literature extended target tracking. In this paper we propose to use the well-established random matrix theory to deal with this issue. A suitable measurement model to address the radar's measurement noise and its conversion into Cartesian coordinates is proposed. The benefits of the proposed converted measurements - extended target tracking with regard to the problem of the targets' size estimation are demonstrated by using both simulated and real data acquired by an X-band marine radar. Average gains of 75% in the estimation of the targets' cross-range size and 31% for the along-range size are observed by comparing the proposed approach with the one that neglects the sensor's noises.