###### Abstract
After that, the accuracy of the demodulated value is improved by compensating for the residual error of the carrier phase. The loop filter of the FAPLL in [14] is realized by bilinear transformation from the S domain to the Z domain, and a weight adjustment module using an automatic adjustment strategy is designed to calculate the weight factor to adjust the effects of the FLL and PLL. In [15], the authors proposed a tracking loop structure to achieve carrier signal phase tracking in the VFLL, in which a loop filter and reset module in the channel will assist in tracking carrier phase and the signal processing period is matched with a preprocessing filter. Based on fuzzy control theory, an algorithm for the FLL auxiliary PLL structure is proposed, the algorithm uses the output of discriminator as the measured residuals of the Kalman filter [16]. In the above examples from the literature, in-depth research has been carried out on the FAPLL control loop in the receiver, and the performance of the corresponding receiver was improved. However, in the extremely harsh environment of highly dynamic weak signals and some application fields that require extremely high navigation accuracy, further improvement of the loop performance is needed. From the perspective of the algorithm, the performance improvement of the carrier loop generally occurs in one of two ways. One way is to replace the loop filter with a nonlinear filtering algorithm for the traditional discriminator and loop filter structure to adaptively adjust the loop bandwidth. This improves the tracking performance of the system while considering the dynamic performance and steady-state performance of the system [17]. In [18], the authors evaluated the tracking performance of an adaptive third-order look-up table direct state Kalman filter in the loop bandwidth control algorithm FAPLL. Firstly, the system measurement model, state space model, and the transfer function of FAPLL were explained, and the relationship between the direct state Kalman filter and the FAPLL was analyzed. Then, by solving the discrete algebraic Riccati equation, the convergence of Kalman gain was calculated, and the look-up table direct state Kalman filter was derived, thus reducing the complexity of direct state Kalman filter. However, as the discriminator contained in the loop has only a small linear interval, nonlinear noise errors were introduced, and the loop performance degrades. The other way is to design the carrier tracking loop based on parameter estimation theory, which removes the discriminator in the traditional loop and replaces it with a nonlinear filter and uses the coherent integration result of the signal as the input of the navigation filter, which can improve the loop performance, noise immunity, and sensitivity. In the above literature, the FLL or VFLL auxiliary PLL typically uses a discriminator to discriminate the phase or frequency difference between the input carrier and the replica carrier. As the discriminator has only a small linear interval, when the carrier-to-noise ratio C/No falls to an error close to or below the level required for the Kramer-Roman lower bound, the discriminator's measurement error increases rapidly. This leads to a degradation in the tracking performance of closed-loop structures [19]. Therefore, according to parameter estimation theory, this paper proposes a VFLL-assisted PLL based on the maximum likelihood estimation algorithm. The loop no longer uses the discriminator but directly uses the correlation result as the input of the navigation filter and then uses the maximum likelihood estimation to process the input. The nonlinear filtering method can increase the linear interval compared with the direct use of the discriminator, while the nonlinear operational noise is lower [20]. Additionally, unlike Kalman filters, ML estimators are not recursive, and each estimate uses enough signal data to achieve good weak signal performance [19].