In conventional approaches for multiobject tracking (MOT), raw sensor data undergoes several preprocessing stages to reduce data rate and computational complexity. This typically includes coherent processing that aims at maximizing the signal-to-noise ratio (SNR), followed by a detector that extracts "point" measurements, e.g., the range and bearing of objects, which serve as inputs for sequential Bayesian MOT. While using point measurements significantly simplifies the statistical model, the reduced data rate can lead to a loss of critical, object-related information and, thus, potentially to reduced tracking performance. In this paper, we propose a direct tracking approach that avoids a detector and most preprocessing stages. For direct tracking, we introduce a measurement model for the data-generating process of the sensor data, along with state-transition and birth models for the dynamics and the appearance and disappearance of objects. Based on the new statistical model, we develop a factor graph and particle-based belief propagation (BP) method for efficient sequential Bayesian estimation. Contrary to the track-before-detect (TBD) paradigm which also avoids a detector, direct tracking integrates coherent processing within the Bayesian MOT framework. Numerical experiments based on a passive acoustic dataset demonstrate that the proposed direct approach outperforms state-of-the-art conventional methods that rely on multiple preprocessing stages.