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Carrier phase measurements are essential to high precision positioning. Usually, the carrier phase measurements are generated from the phase lock loop in a conventional Global Navigation Satellite System (GNSS) receiver. However there is a dilemma problem to the design of the loop parameters in a conventional tracking loop. To address this problem and improve the carrier phase tracking sensitivity, a carrier phase tracking method based on a joint vector architecture is proposed. The joint vector architecture contains a common loop based on extended Kalman filter to track the common dynamics of the different channels and the individual loops for each channel to track the satellite specific dynamics. The transfer function model of the proposed architecture is derived. The proposed method and the conventional scalar carrier phase tracking are tested with a high quality simulator. The test results indicate that carrier phase measurements of satellites start to show cycle slips using the proposed method when carrier noise ratio is equal to and below 15 dB-Hz instead of 21 dB-Hz with using the conventional phase tracking loop. Since the joint vector based tracking loops jointly process the signals of all available satellites, the potential interchannel influence between different satellites is also investigated.

Carrier phase is tracked by the phase lock loop (PLL) in a conventional GNSS receiver. Compared to frequency lock loop (FLL) and code lock loop (DLL), PLL is the weakest component which is sensitive to the noise and dynamics. However, to have usable carrier phase measurements, carrier phase tracking must be maintained. There are three error sources in carrier phase tracking [

Except the thermal noise, the oscillator and dynamics stress are dominated by the receiver clock and dynamics, and the satellite dynamics will be compensated for using ephemeris. The receiver oscillator and dynamic stress are common for different channels. If the common error can be estimated before the correlator for individual channels, the bandwidth of channel loop can be reduced without increasing the common error. One idea to handle these common errors is to use vector tracking. Leimer and Kohli [

In this paper, a carrier phase tracking approach based on a joint vector architecture is proposed for GNSS receivers. The proposed joint vector tracking method adds a common loop based on extended Kalman filter (EKF) to estimate the common error for different channels. Compared to the existing architectures mentioned above, the proposed method is able to take the advantage of EKF’s flexibility and Co-Op tracking’s robustness with less process states. A test with a high quality simulator shows that the proposed method can improve the sensitivity of carrier phase tracking by 6 dB. Since the common loop combines all channels, the interchannel influence between different satellites is also investigated. The impact of the channel with lower carrier noise ratios (CNR) on other channels is especially provided. The test result shows that a lower CNR satellite can impose more noise on a higher CNR satellite.

The remainder of the paper is organized as follows. The methodology of the joint VPLL tracking architecture and the theoretical derivations are provided in Section

In this section, the architecture of the joint VPLL is introduced firstly. The transfer function model based on the joint vector architecture is then derived. The implementation of the proposed joint VPLL is finally described.

The architecture of a joint vector phase lock loop (VPLL) is shown in Figure

The joint VPLL architecture for carrier phase tracking.

The IF data is received and processed by the baseband algorithms to generate measurements including carrier phase, pseudorange, and Doppler. The baseband algorithms usually include acquisition and tracking. The fine synchronization of the input signal with the local replica is made by the tracking function which includes DLL, FLL, and PLL. In this paper, DLL is first-order loop aided by the PLL while FLL is not used. In the proposed joint VPLL, we add a vector phase lock loop in addition to the conventional PLLs dedicated to individual channels as shown in Figure

Figure

Transfer function models of the joint VPLL architecture.

The TF model of the common loop based on EKF can be written as follows [

From (

For an individual channel in (

From (

Although the dynamic stress error and oscillator phase noise error can be decreased using the joint VPLL, the joint tracking method will make the errors in one channel spread to other channels. Usually the thermal noise error is derived from the single channel in a conventional receiver. However for the joint VPLL, except the thermal noise error from the channel itself, the thermal noise error in this channel should include the errors generated from the common loop.

As we see in (

Based on the software receiver [

The state vector of the EKF is

The system model is^{2} for

The measurement model is

A Spirent 8000 simulator is used to test the performance of the joint VPLL and compare to the performance using the conventional PLL method. In this research, we focus on the sensitivity improvement using the joint vector based tracking architecture. To isolate other error sources, the test antenna is put in a static mode during the experiments and the dynamics induced by satellite is to be estimated and compensated using the satellite ephemeris. As a result, the carrier phase error mostly would come from the oscillator and thermal noise. IF data for about 6 minutes are collected from the simulator with a CNR of 47 dB-Hz for all satellite channels. In the experiments, Gaussian white noises are added to the last 5 minutes of the data to adjust the CNR for the purpose of assessing the performance using different tracking methods. Except the original data set with 47 dB-Hz, we generate 17 data sets which show that CNR are from 45 dB-Hz down to 13 dB-Hz with 2 dB intervals.

The geometry of satellites during the test period is shown in Figure

Geometry of satellites in the test.

In the test, the coherent integration time is set as 20 ms to improve the tracking sensitivity. The dynamics of the satellite is compensated using the ephemeris and the receiver location information. Figure

PLL filter output in the conventional GNSS receiver.

In Figure

In the test, we use the original 47 dB-Hz data to generate the carrier phase measurements

Firstly, to establish a reference for the test, we have tried different bandwidths to process the original data set to find the optimal bandwidth and the corresponding phase lock indicator (PLI) [

Mean of PLI under different bandwidth for the data set with 47 dB-Hz data set.

In Figure

PLI for different satellites with 1 Hz bandwidth.

As shown in Figure

An analysis on the single difference of carrier phase measurements indicates that cycle slips will be present when the CNR is equal to or less than 21 dB-Hz. Therefore, the data sets with 21 dB-Hz and less CNR will be used in the following performance comparison between the conventional scalar tracking and the joint VPLL.

Given in Figure

Single difference of carrier phase between 47 dB-Hz and 21 dB-Hz data sets with PLL.

Shown in Figure

Single difference of carrier phase between 47 dB-Hz and 21 dB-Hz data sets with the joint VPLL.

Shown in Figures

Single difference of carrier phase between 47 dB-Hz and 19 dB-Hz data sets with PLL.

Single difference of carrier phase between 47 dB-Hz and 19 dB-Hz data sets with the joint VPLL.

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. However, it is worth mentioning that all satellite carrier phase measurements would experience cycle slips when the CNR of the data set is equal to or below 15 dB-Hz, even using the proposed method as shown in Figures

Single difference of carrier phase between 47 dB-Hz and 15 dB-Hz data sets with PLL.

Single difference of carrier phase between 47 dB-Hz and 15 dB-Hz data sets with the joint VPLL.

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. However, the interchannel influences between different satellites have to be accounted for using the vector based PLL especially when the channel with lower CNR affects the channels with higher CNR. This will be described in the next section.

To assess the interchannel influence, another data set is collected which is the same as the data described in the previous section except with a different CNR. In this data set, the CNR for satellite PRN27 is set to be 27 dB-Hz while other satellites are with 47 dB-Hz. We call this data set data-set A in the sequel. Gaussian white noise is added to data-set A to adjust the CNR and generate data-set B which shows 12 dB lower compared to data-set A. So in data-set B, CNR of satellite PRN 27 is 15 dB-Hz and other satellites show 35 dB-Hz.

The carrier phase measurement of data-set A is set as reference. We use the same analysis method described in previous section to process data-set A and data-set B. However to explore the influence of the lower CNR satellites, two strategies are used to process the data-set B.

The result of single difference of carrier phase measurements between data-set A and data-set B with two strategies for PRN 27 is shown in Figure

Residuals of satellite PRN 27 using two processing strategies.

In Figure

Residuals of satellite PRN 2 using two processing strategies.

With strategy two, satellite PRN 2 shows better performance than that using strategy one in Figure

In this paper, the influence of the oscillator in the GNSS receiver is analyzed. To address the dilemma problem of loop bandwidth design, a carrier phase tracking method based on a joint vector architecture is proposed. The transfer function model of the proposed method is derived and analyzed. Based on the same oscillator, we test different CNR through adding white noise on the IF data. With the IF data collected from simulator and the data sets with more white noise, the proposed method is proved to improve the carrier phase tracking sensitivity by around 6 dB when compared to the conventional scalar tracking which uses the optimal bandwidth during the test. Interchannel influence of the proposed method is also analyzed. Due to the joint tracking in the joint VPLL, the lower CNR satellite imposes more noise on the higher CNR satellite. However, as

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The first author is supported by the Alberta Innovates Technology Futures (AITF) through The Alberta Doctoral Awards for Chinese Students (ADACS) program. This work is also supported by Tecterra.