An Improved Adaptive Multi-Frequency GPS Carrier Tracking Algorithm for Navigation in Challenging Environments
Rong Yang, University of Colorado, Boulder; Dongyang Xu, Colorado State University; Yu Morton, University of Colorado, Boulder
Contemporary navigation satellite systems are designed to broadcast multiple open signals at different frequencies. For example, the modernized GPS block IIF satellites simultaneously broadcast signals at L1 (1575.42MHz), L2 (1227.6MHz), and L5 (1176.45MHz) bands. Multi-frequency receivers can take advantage of the diversity in signal frequency to achieve improved robustness and accuracy for applications in challenging environments. For example, reference  shows that the amplitude fading and random phase fluctuations caused by the ionosphere scintillation do not occur simultaneously across frequency bands. Study in  shows that the multipath induced deep fading observed on different frequencies are also independent of each other. Therefore, when the signal on one frequency experiences fading, unaffected signals transmitted from the same satellite on other frequencies can be utilized to aid carrier tracking of the challenged frequency to improve the tracking loop accuracy and robustness. This paper presents an adaptive GPS multi-frequency tracking algorithm designed to handle the signal tracking with frequency selective deep fading in challenging environment.
There have been several multi-frequency tracking algorithms discussed in literatures. For example, reference  proposed a multi-carrier vector PLL (MC-VPLL) algorithm for joint tracking of carrier phase from all satellites on multiple frequencies. This algorithm was demonstrated to enhance the robustness during ionospheric scintillations, in the presence of carrier phase multipath, and when there are jamming and interferences. However, it exploits not only frequency diversity but also the spatial diversity. Reference  combines GPS L1 and L2C carrier measurements to enhance the carrier tracking performance with deep fading in a multipath environment, however, GPS L5 carrier was not considered in the implementation. Reference  proposed the adaptive multi-frequency (AMF) algorithm that utilizes the triple GPS carrier signals to estimate the fundamental frequency which is then aid the carrier tracking channel that has deep fades due to strong ionospheric scintillations. The AMF algorithm assumed that Doppler frequencies for different carrier signals follow the Doppler shift relationship. However, it treats the frequency rates on different carriers to be an equal bias term. Recently, we developed an inter-frequency adaptive carrier tracking (I-FACT) algorithm  which combines the inter-frequency aiding strategy with the adaptive optimal tracking loop parameter adjustment  and applied this technique to track radio occultation signals experiencing strong water vapor scattering when traversing moist lower troposphere. In the experiment validation, the L2C carrier is used to assist L1 and L5Q tracking.
In this paper, we present an improved adaptive multi-frequency (AMF) carrier tracking loop. This AMF is based on the optimization of the tracking loop error variance. The optimization is achieved by deriving analytical closed-form expressions of the tracking error variance for the single-frequency tracking (ST) mode and the joint-frequency tracking (JT) mode. The ST mode only considers measurements from a single carrier, while in the JT mode, states for multiple carriers are modeled and estimated based on measurements obtained utilizing the inter-frequency Doppler relationships among the carriers.
Our analysis and simulation results demonstrate that when all carriers are extremely weak, such as below 25dB-Hz, the JT mode outperforms the ST mode. If both strong signal and weak signal co-exist in the input, the JP mode can significantly reduce the weak carrier tracking error due to aiding from the strong carrier measurements. However, this improvement comes with a cost at the strong signal tracking performance as the latter can be degraded by the less liable weak signal measurements. To overcome the degradation of strong signal tracking performance, we created an indicator based on the signal strengths’ estimation to adaptively switch between ST and JT mode of operation for a carrier tracking.
To evaluate the performance of the AMF algorithm, we simulated intermediate frequency (IF) data at GPS L1, L2, and L5 frequencies with different combinations of carrier signals’ strength. Simulation results demonstrate the accuracy of the theoretical analysis and validate the improved performance of the AFM. The AFM does not require a prior information on receiver PVT solutions and it is easy to implement and can be applied for the signal tracking with strong ionosphere scintillations or severe multipath effect.
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