Shown in Figure 8 are the single differences of carrier phase measurements using the proposed joint VPLL method.
Shown in Figures 9 and 10 are the results when the CNR is 19 dB-Hz, using the conventional PLL and the proposed joint VPLL methods, respectively.
Similar results are gotten when the CNR is 17 dB-Hz and no cycle slips are observed using the joint VPLL but all satellites experience cycle slips with conventional PLL.
Based on the test results described above, the proposed joint VPLL architecture can improve the carrier phase tracking performance by about 6 dB when compared to the conventional PLL architecture.
Using the joint VPLL method: set measurements variances for different satellites in the R matrix are the same which means all the measurements variances are calculated based on 35 dB-Hz.
Using the joint VPLL method: calculate measurement noise variance of satellite PRN 27 using 15 dB-Hz and other satellites using 35 dB-Hz.
The influence of PRN 27 for the joint VPLL is reduced in the second strategy since the covariance of PRN measurements is calculated using 15 dB-Hz rather than 35 dB-Hz compared to the first strategy.
In the joint VPLL tracking, since R matrix of EKF is calculated based on the CNR, the influence of lower CNR satellite can be reduced which is similar to strategy two.
Due to the joint tracking in the joint VPLL, the lower CNR satellite imposes more noise on the higher CNR satellite.
Caption: Figure 1: The joint VPLL architecture for carrier phase tracking.
Caption: Figure 2: Transfer function models of the joint VPLL architecture.
Caption: Figure 8: Single difference of carrier phase between 47 dB-Hz and 21 dB-Hz data sets with the joint VPLL.