With the development of Global Navigation Satellite Systems (GNSS), the quality and anti-jamming capability of satellite navigation signals are crucial. Binary Offset Carrier (BOC) modulation faces issues of false locking due to multi-peak ambiguity in its autocorrelation function, limiting its application. This paper examines FH-BOC modulation, which integrates BOC with frequency hopping technology, significantly improving anti-jamming, anti-multipath performance, and spectral efficiency. To meet the high dynamic tracking demands of FH-BOC signals, this study explores three types of carrier tracking loops: the traditional second-order frequency-locked loop assisted a third-order phase-locked loop, a linear Kalman filter-based tracking algorithm, and an adaptive Kalman filter-based tracking algorithm. A composite code tracking loop is also proposed. Simulations show that the adaptive Kalman filter algorithm achieves high-precision carrier tracking in dynamic environments and quickly converges during transitions. The composite code tracking loop, aided by the carrier loop, ensures precise synchronization of pseudocode and frequency-hopping subcarrier phases, demonstrating the superior performance of FH-BOC modulation in dynamic environments.