Accurately tracking an unknown and time-varying number of objects in complex environments is a significant challenge but a fundamental capability in a variety of applications, including applied ocean sciences, surveillance, autonomous driving, and wireless communications. Conventional Bayesian multiobject tracking (MOT) methods typically employ a detect-then-track (DTT) approach, where a frontend detector preprocesses raw sensor data to extract measurements for MOT. The irreversible nature of this preprocessing step can discard valuable object-related information, particularly impairing the ability to resolve weak or closely spaced objects. The track-before-detect (TBD) paradigm offers an alternative by operating directly on sensor data. However, existing TBD approaches introduce simplifications to facilitate the development of inference methods, such as assuming known signal amplitudes or conditional independence between sensor measurements given object states. These assumptions can lead to suboptimal performance and limit the applicability of the resulting TBD methods in realistic scenarios. This paper introduces a novel TBD method that is based on a comprehensive signal model for sensor data. The new model accounts for sensor data correlations and amplitude fluctuations, enabling the accurate representation of the physics of the data-generating process in TBD. The proposed model is suitable for a wide range of problems in active and passive radar, active and passive sonar, as well as integrated sensing and communication systems. Based on a factor graph representation of the new measurement model, a scalable belief propagation (BP) method is developed to perform efficient Bayesian inference. Experimental results, performed with both synthetic and real data, demonstrate that the proposed method outperforms state-of-the-art conventional MOT methods.