## 1 Introduction
Simulation results verified the reliable performance of the proposed algorithm during the sounding rocket launch scenario. In addition, adaptive DPLLs using the Kalman filter (KF) are studied in [9; 10; 11; 12]. The key idea of [9] is to properly adjust the equivalent noise bandwidth of the signal tracking KF with the empirical knowledge of the C/N\({}_{0}\) and the signal dynamics. The tuning method for the signal tracking KF using the relationship between the C/N\({}_{0}\) and the equivalent noise bandwidth is introduced in [10]. An adaptive KF structure that adjusts the measurement and process noise covariance (which are fixed in the case of the standard KF) is presented in [11]. These adaptive DPLL algorithms may operate well while maintaining tracking performance even in harsh environments such as low signal power and high dynamic stress. Using the adaptive DPLL for the ionospheric scintillated environment is investigated in [11; 12]. Simulation results showed that the adaptive algorithms outperforming the traditional DPLL during the ionospheric scintillation occurrence. Most of the aforementioned adaptive DPLLs that adopt an optimal manner have a relatively larger computational burden when compared with the traditional DPLL. A projected bandwidth method that uses a look-up table for the determination of noise bandwidth is proposed in [2]. This algorithm does not utilize dynamic stress estimation to reduce the computational burden; therefore, it inevitably has suboptimal performance. Similarly, look up table-based low-complexity adaptive carrier tracking loop is presented in [13]. It uses the direct-state KF for the DPLL combined with the DFLL as the carrier tracking loop filter for robustness. The look-up table approach is utilized to reduce computational complexity. Consequently, the proposed structure has superior dynamic tracking performance and low complexity simultaneously. Moreover, although the GNSS was originally designed for users and applications in terrestrial regions, such as land, maritime, and air, the GNSS signal can also be used in deep space. The space service volume (SSV) is defined as a shell extending from 3000 km to 36,000 km in altitude [14]. For the region with an altitude of less than 8000 km, the signal reception environment is similar to that of the ground users, which indicates that the GNSS receiver does not operate with much difficulty. In contrast, receivers that operate in the higher regions are either near or beyond the satellites. For this reason, these receivers should obtain satellite signals from the nadir direction, which has weak signal power due to the large free-space loss [15]. In addition, the number of visible satellites of the GNSS receivers at such high altitudes is decreased because the Earth blocks most of the main-lobe signal of the transmitter antenna pattern. Consequently, the receivers can only receive the spilled-over signal of the main lobe, which is the reason for the reduced visible satellite numbers. To counter this problem, studies that effectively use the side-lobe signal of a transmitter antenna have been performed [15; 16; 17; 18]. The results showed that the number of visible satellites is increased by utilizing the side-lobe signal. However, the side-lobe signal inherently has a relatively small transmitting gain compared with the main lobe signal, which results in further decreases in the received signal power at the SSV receivers. Additionally, several studies have been performed to assess the feasibility of GNSS signals for Moon exploration [19; 20; 21; 22; 23]. In particular, GNSS-based navigation during lunar exploration has advantages such as fewer ground operations, reduced costs, and decreased payload weight and volume [20]. However, GNSS receivers suffer weakened signal power and high dynamic stress during the transfer orbit mission. The dedicated receiver design and verification for such a challenging environment are presented in [21; 22; 23; 24]. This paper complements and expands the interim result presented in [25].