# Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service Volume
## 1 Introduction
On the basis of estimating the state of code phase and the third-order state vector of the carrier phase, the principle about how to regulate the filter gain matrix to vary the equivalent LNBW is introduced in this work. Furthermore, the relationship between noise and adaptive bandwidth is also discussed. Actually, the CL form uses a feedback path to make corrections of code phase and carrier frequency errors. In contrast, open loop (OL) tracking updates the local code phase and carrier frequency estimates flexibly, not entirely dependent upon the feedback path [6]. Aided by supplementary measurements, the OL scheme is free of loop instability. Thus, it is suggested that an OL tracking design could be an alternative to be adopted in SSV user receivers to overcome the dilemma of settling the issues of weak-signal and high-dynamics together. Various OL tracking methods have been developed up to now. A US patent (Patent No: US 6633255B2) [7] proposed four kinds of carrier frequency measuring approaches, based on a frequency doubler, a frequency discriminator, a block phase estimator, and a channelized filter, respectively. Some scholars demonstrated quasi-open loop architecture to update the frequency of the local oscillator (LO) every several epochs, instead of updating frequency estimations at each epoch [8], which can be recognized as an interim scheme between closed loop and open loop. Other literatures released an idea of FFT-based frequency-domain tracking [9], which is a novel high-sensitivity tracking method developed to perform accurate frequency parameter estimation by processing the spectral peak line and adjacent lines [10]. Without doubt, an INS-assisted open loop tracking strategy is another effective method to find the true signals with high dynamics and high noise level [11]. However, all of these methods are derived on the basis of some assumption that disregarding the coupling effect between the carrier phase and Doppler frequency. Then the technical matter comes down to put forward an improved methodology to generate the carrier phase and Doppler frequency estimates decoupled with each other for the LO. This paper incorporates a GNSS orbit propagator with INS-assisted open loop tracking together to obtain the aiding information about the Doppler frequency. With the purpose of updating the Doppler frequency estimation that is insensitive to the corresponding carrier phase estimation, a non-coherent maximum likelihood estimator is used to eliminate the coupling relationship in this paper. A new gradient function from the two-dimensional log-likelihood cost function for code delay and Doppler frequency is first established, and the new cost function is totally independent of the carrier phase tracking error. Then we can get the gradient and Hessian expressions of this new cost function with respect to the Doppler frequency. When the frequency correction is computed with the gradient divided by the Hessian, the equation does not contain the component of carrier phase and proves the cancellation of the coupling effect. This paper illustrates the implementation block diagram of the open loop tracking structure using the maximum likelihood estimation (MLE) method, and introduces its detailed operational procedure. In the part of testing, a typical flight mission, with large variation ranges of signal power and dynamic stress, is taken as a destination object. The trajectory of the object is hybrid, which consists of a period of normal status (non-maneuvering) followed with a period of orbital maneuvering. The simulation results verify the fact that the performance of an adaptive KF-based strategy is superior to the classical CL structure, especially when the object operates in a non-maneuvering status. However, in orbital maneuvering conditions, an adaptive KF-based strategy is incompetent to perform well as what the INS-assisted strategy does. Additionally, the non-coherent MLE method in the INS-assisted strategy provides more robustness to track the Doppler frequency.