Evaluation of a GPS Time and Frequency Reference Receiver as a VLBI Frequency Standard

Tetsuro Kondo1(kondo(AT)nict.go.jp) and Jun Amagai2

1 Kashima Space Research Center
Communications Research Laboratory
893-1 Hirai, Kashima, Ibaraki 314-0012, Japan

2Communications Research Laboratory
4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan

1. Introduction

In recent years a GPS time and frequency reference receiver has shown remarkable progress in performance, and has come to be widely used as a frequency standard supplying highly stable signals (1x10-12/day) at low cost. Although its stability is less than that of H-maser(~1x10-14/day) conventionally used for VLBI, its lower cost is attractive when we consider wide deployment of VLBI and VLBI-like techniques. We have therefore evaluated the performance of the GPS receiver and the possibility of its adoption as a frequency standard in VLBI observations.

2. Method and Results

An HP58503A is one of the GPS receivers commercially sold as a time and frequency reference receiver. It provides 1 pps signals synchronized to UTC within about 100 nsec as well as stable 10 MHz signals. We located two GPS antennas closely to each other; separation between them was only about 7 meters. Two receivers (HP58503A) were connected to the antennas independently. After sufficient running of receivers (3 days) according to the instructions attached with the receiver, we measured the phase difference between 10 MHz signals from two receivers for 6 days starting from June 29, 1997. Analog output from a phase comparator (HP K34-59991A) is converted into digital signals with a sampling period of 1 sec. Digitized data are stored in a notebook PC (Figure 1).

Figure 1. Schematic block diagram of observation system.

Figure 2. Observed phase data for 3 hours. Discontinuities due to a comparator are already removed.

There are 72 discontinuities in raw phase data spanning 6 days due to inherent characteristics of the comparator, i.e., a trip of 360 degree occurs when the phase crosses the 360 or 0 degree boundary. These discontinuities should be removed before further statistical analysis is carried out. Figure 2 shows the observed phase after removal of discontinuity. Small data discontinuities still remain in the data.

The Allan variance is a good measure for evaluating stability of reference signals. We calculated the Allan variance at an averaging time tau from the phase data at 10 MHz as follows,


where phi(tk) is the phase at time tk and nu0 is the frequency at which the phase measurement is made (=10 MHz). We divide phase data into 24 sets of 6 hour spans. Figure 3 shows the Allan variances calculated for each phase data set. The results show stability of better than 10-11 for an averaging time range less than 1000 sec. This is almost the same performance expected from specifications of the receiver. Scatter on the plots seen for time range less than 1000 sec is attributed to small discontinuities still left in the phase data as mentioned before. System noise level is sometimes larger than the receiver performance for the time range less than 10 sec. However we can say that it reaches the level described as typical characteristics in the specifications of the receiver, i.e., ~2x10-12 at 10 sec.

Figure 3. Root Allan variance calculated for 24 sets of phase data. Each data set spans 6 hours. Measuring system noise lebel is represented by symbol "X".

Next we evaluate coherence loss when this frequency standard is applied to S (2.2 GHz) and X (8.8 GHz) band observations. Using measured phase data, coherence after N sec integration is calculated as follows,

where C is a ratio of observation frequency and 10 MHz, i.e., 220 and 880 for 2.2 GHz and 8.8 GHz respectively, and phi(tn) is a phase at time tn. We assume no coherence loss for 1 sec integration. Coherence calculated this way is shown in Figure 4. In this calculation phase data are divided into 48 sets of 3 hour span. As shown in the figure coherence decreases as the integration period increases. Even at 10 sec integration they are down to about 0.7 and about 0.3 for 2.2 GHz and 8.8 GHz, respectively. They are further decreased down to 0.1 for 100 sec integration, which is a typical accumulation period in a geodetic VLBI. Therefore it seems to be difficult to adopt for VLBI observations.

Fringe searches in VLBI correlation processing are relevant to this problem. Correlator outputs integration results every second or every several seconds. These time segmented data are further integrated with phase change being adjusted by a time-linear function to maximize integrated correlation amplitude. This process is called a "fringe search". We adopt a similar technique in a calculation of coherence. Firstly phase variation during accumulation period is fitted by a polynomial function using a least squares method. Then we calculate coherence using residual phase after fitting. We use a polynomial of degree 1 to 3.

Figure 5 shows results in case of the first order polynomial being adopted. This is the case just like a "fringe search" in geodetic VLBI processing. We can see remarkable increase in coherence. At 100 sec, almost no loss can be seen for 2.2 GHz. Even for 8.8 GHz, coherence keeps value of 0.3. Figure 6 presents results when a third order polynomial is adopted. It is seen that an integration period without loss can extend to about 300 sec for 2.2 GHz and about 100 sec for 8.8 GHz. Thus adopting the fringe search process for integration, the GPS Time and Frequency Reference Receiver can be used as a frequency standard for VLBI observations made at S and X bands. However, the \pagebreak observed delay time obtained this way should be carefully examined for utilization in further analysis such as a baseline length analysis, because clock stability is an important factor to connect a scan, which is a continuous observation of a radio source, between neighboring observations in further analysis, and fluctuation of the clock between observations remains as an unknown parameter.

3. Conclusion

We have evaluated the performance of GPS Time and Frequency Reference Receiver (HP58503A) to determine whether it is adoptable as a frequency standard in VLBI observations. Firstly we measured phase difference between 10 MHz signals output from two independent receivers. Then we calculated the Allan variance to evaluate the stability at average times ranging from 1 to 10000 sec. Coherence loss was also calculated from the actual phase data. As a result it is demonstrated that the GPS Time and Frequency Reference Receiver can be used as a frequency standard if we expand the fringe search process to account for third order variations with time.


The authors would like to thank Hiroo Kunimori, KSP/SLR group leader, for offering two GPS time and frequency reference receivers (HP58503A) for this study.

Figure 4. Coherence calculated from the phase data versus integration time %\caption{Coherence calculated from the phase data versus integration time for 2.2 GHz (left panel) and 8.8 GHz (right panel).

Figure 5. Coherence calculated using residual phase data after a linear drift is removed versus integration time for 2.2 GHz (left panel) and 8.8 GHz (right panel).

Figure 6. Coherence calculated using residual phase data after a third order polynomial fit versus integration time for 2.2 GHz (left panel) and 8.8 GHz (right panel).

Updated on November 20, 1997. Return to CONTENTS