## 1 Introduction  
The hybrid direct sequence/frequency hopping (DS/FH) spread spectrum technology integrates the strengths of both a direct sequence spread spectrum (DSSS) and a frequency hopping spread spectrum (FHSS), making it a preferred choice for applications in space TT&C (Telemetry, Tracking, and Command), satellite communication, satellite navigation, and various other domains demanding robust anti-interference and anti-interception capabilities [1; 2; 3; 4; 5; 6]. In the hybrid DS/FH spread spectrum system, multiple carriers are transmitted in a time-division pattern. Due to the continuous hopping of the carrier frequency, even if the motion speed remains constant, the carrier's Doppler frequency will experience corresponding variations. When the relative motion speed is high, the Doppler frequency differences across different carrier frequencies become greater. The continuous hopping of the Doppler frequency introduces new frequency step excitations to the carrier tracking loop, necessitating constant adjustments to accommodate these changes. As a result, this ongoing frequency step response poses a severe challenge to steady-state tracking. Particularly in high dynamic environments, such as high-speed mobile communication scenarios, the first-order and second-order rates of change of the Doppler frequency become even more significant. These rates of change not only increase the difficulty of tracking but may also lead to the loss of lock. In response to this challenge, we need to conduct in-depthresearch on the tracking algorithms for hybrid DS/FH spread spectrum signals under high dynamic conditions. In recent decades, the tracking technology for a hybrid DS/FH spread spectrum signal has drawn the attention of scholars at home and abroad. The authors of [7] analyze the effects of multiple interferences on the range and velocity measurement performance of a hybrid DS/FH spread spectrum system, providing a reference for the research on hybrid DS/FH spread spectrum signal tracking. A carrier tracking method aided by a frequency hopping pattern is presented in [8]. The Doppler shift variable introduced by the next frequency hopping point is estimated based on the predicted frequency hopping pattern and the current speed measurement. However, the maximum hopping speed is only 1.2 khop/s. The authors of [9] propose a hybrid DS/FH spread spectrum signal tracking approach. Although the hopping rate reaches 10 khops/s, the coherent integration period only occupies one frequency hopping time slot, which is only applicable to high signal-to-noise ratio (SNR) scenarios. The key technologies for the reception of hybrid direct sequence/fast frequency hopping (DS/FFH) spread spectrum signals are investigated in [10], including signal acquisition, tracking, and group delay equalization methods, in which the signal tracking part adopts the same method as that used in [8]. Although the frequency hopping rate involved is up to 100 khops/s, the information rate is set to be the same as the frequency hopping rate, making it only applicable to scenarios with a higher SNR. The authors of [11; 12] employ a tracking scheme based on a velocity locked loop (VLL), which utilizes the coherent integration results of multiple hops for discrimination. The employed scheme simultaneously achieves the requirements of a high hopping rate and low SNR, yet the involved dynamic is merely 10 g/s, where g = 9.8 m/s\({}^{2}\). Table 1 lists the hopping rates, dynamics, SNR, and loop structures involved in [8; 9; 10; 11; 12]. As indicated in Table 1, the research on tracking algorithms for high dynamic hybrid DS/FH spread spectrum signals has remained relatively scarce in recent years. Nevertheless, it is reassuring to note that numerous research achievements have been made in the tracking of high dynamic DSS signals in recent times.