Abstract: BOC signals employ binary offset carrier modulation, whose multi-peak autocorrelation characteristic is prone to causing false lock on side peaks in receivers, thereby undermining the stability of the tracking loop. To address the insufficient tracking accuracy of conventional discriminators caused by zero-crossing detection and fixed-step adjustment, this paper proposes an improved Bump-Jump phase discriminator algorithm. The algorithm innovatively combines a dynamic step-size adjustment mechanism with joint decision-making of primary and auxiliary discriminators. By incorporating Very Early (VE) and Very Late (VL) auxiliary branches, it establishes a "main-peak tracking with side-peak monitoring" architecture, which dynamically suppresses side-peak interference through power difference detection between the two branches. Meanwhile, a closed-loop feedback dynamic step-size control mechanism is designed to effectively mitigate sidelobe interference of the autocorrelation function. Simulation results demonstrate that, compared with the conventional discriminator method, the improved algorithm enhances tracking accuracy by an average factor of 4.8, reduces dynamic response time by 67%, and extends the weak-signal tracking threshold to 25 dB·Hz. The study confirms that the proposed scheme effectively resolves the multi-peak false-lock problem of BOC signals and significantly improves receiver tracking performance.