Multiobject tracking (MOT) is the problem of tracking the state of an unknown and time-varying number of objects using noisy measurements, with important applications, such as autonomous driving, tracking animal behavior, defense systems, and others. The MOT task can be divided into two settings, model based or model free, depending on whether accurate and tractable models of the environment are available. Model-based MOT has Bayes-optimal closed-form solutions, which can achieve state-of-the-art (SOTA) performance. However, these methods require approximations in challenging scenarios to remain tractable, which impairs their performance. Deep learning (DL) methods offer a promising alternative, but existing DL models are almost exclusively designed for a model-free setting and are not easily translated to the model-based setting. This article proposes a DL-based tracker specifically tailored to the model-based MOT setting and provides a thorough comparison to SOTA alternatives. We show that our DL-based tracker is able to match performance to the benchmarks in simple tracking tasks while outperforming the alternatives as the tasks become more challenging. These findings provide strong evidence of the applicability of DL also to the model-based setting, which we hope will foster further research in this direction.