Multi-object tracking (MOT) is a key technology for enabling autonomous navigation of unmanned surface vehicle (USV) as it provides continuous perception of surrounding maritime targets and supports navigation decision-making. However, videos acquired on maritime platforms typically suffer from challenges such as platform-induced jitter and nonlinear object motion, which significantly degrade tracking performance. To address these challenges, this paper builds upon ByteTrack by incorporating an adaptive Kalman filtering scheme and proposing a density-aware association strategy, resulting in a novel tracker termed the Marine-Aware Adaptive Tracker (MAAT). Specifically, an adaptive Kalman filter is introduced to increase the contribution of high-confidence detections during the state update process, thereby enhancing the stability and robustness of state estimation. Furthermore, to better mitigate the frequent identity switches caused by severe platform jitter from the USV observation platform, a density-aware association strategy is proposed. This strategy dynamically adjusts the composition of the cost matrix according to the density of high-confidence targets, enabling more reliable data association under varying scene conditions. Finally, the proposed tracking algorithm is evaluated against several state-of-the-art methods on the Singapore Maritime Dataset. It achieves competitive performance, attaining 44.37 MOTA and 43.857 IDF1. Moreover, MAAT operates in real time, running at 41.4 FPS. The experimental results demonstrate that MAAT is capable of performing accurate and real-time multi-object tracking in dynamic maritime environments with surface fluctuations, thereby providing effective technical support for intelligent maritime surveillance applications.