###### Abstract  
This paper proposes a GPS receiver vector frequency-locked loop-assisted phase-locked loop (VFAPLL) structure based on the maximum likelihood estimation (MLE) method for highly dynamic weak-signal scenarios. In this structure, the loop structure does not include a frequency discriminator, and the signal is directly input to the navigation filter after down-conversion, coherent integration, and other processing to avoid nonlinear noise error. Due to the high dimension and nonlinearity of the cost function of the MLE algorithm, the Levenberg Marquardt (LM) algorithm is used to optimize it. The proposed VFAPLL is compared with the VFAPLL implemented based on the extended Kalman filter (EKF) algorithm and the frequency locked loop assisted phase locked loop (FAPLL) implemented based on MLE. Through simulation verification, it was shown that the VFAPLL (MLE) has higher tracking accuracy, lower loss-of-lock threshold, and better robustness to the input signal than the other two loops. V +
Footnote †: journal: Applied sciences  
Today's vector tracking loops include the vector frequency locked loop (VFLL), vector delay locked loop (VDLL) and vector phase locked loop (VPLL). The combination of a FAPLL and vector tracking technology is a very promising development direction. In this paper, VFLL is used to assist the PLL. The advantages of vector tracking and the FLL are that they are fully utilized in the auxiliary loop, which avoids time-consuming and energy-consuming reacquisition after signal interruption, can tolerate the high dynamic stress of users more robustly, and can track signals with lower signal-to-noise ratios. Scholars have been working to improve the tracking performance and robustness of FAPLLs. This loop essentially aids PLLs by estimating the Doppler frequency shift, whereas Kalman loops or other circuit forms can also be used for assistance in estimating frequency. [PERSON] proposed several carrier tracking loop structures combining vectors and scalars in [8], including the VFLL-assisted PLL, local carrier phase Kalman filter cascaded VDFLL, and cooperative carrier tracking. The VFLL-assisted PLL structure combines the carrier frequency error of the navigation processor with the phase discriminator. The position and clock offset of the navigation processor are predicted and updated by the code discriminator in the VFLL-assisted PLL structure. The speed measurement value is obtained by combining the carrier frequency and discriminator of each channel. [PERSON] proposed a new loop structure called the unambiguous frequency-assisted phase locked loop (UFA-PLL). In terms of tracking ability and antijamming, this loop has the same advantages as commonly used coupled loops, but its design and implementation are simpler. An optimal method for smoothing phase estimation has also been proposed [9]. [PERSON] et al. proposed a vector receiver combined with an FAPLL [10], where the VFLL receiver outputs the frequency error used in the FAPLL. The loop proposed in this paper is more robust to carrier phase tracking than conventional FAPLLs, even in harsh signal environments. [PERSON] et al. in China proposed an iterative FAPLL designed in the state space based on the minimum mean square error algorithm through constructing a high-fidelity carrier signal model [11]. Another study combined the FLL and PLL through an ensemble filter. If a decentralized state estimation framework is used for the FAPLL, then the measurements can be distributed and filtered in the local state estimator and are thus able to combine the local estimates by a weighting matrix to update the global carrier state [12]. To address the problem that the VFLL is not sufficiently accurate and unable to lock the carrier phase and demodulate the received signal correctly, a phase-locked loop-assisted vector frequency-locked loop method was proposed [13]. The method adds the output of the loop filter in the PLL to the prediction of the carrier frequency, which improves the prediction accuracy of the VFLL carrier phase.