Timing Performance Testing and Regularity Analysis of eLoran System

Abstract

Accurate time synchronisation is critical in modern communication, navigation, and scientific research. In this context, the eLoran receiver, which is an advanced timing device, has attracted increasing scholarly attention. This study aims to comprehensively analyse the performance and potential applications of eLoran systems for timing monitoring and to specifically explore the relevant indices of two eLoran receivers. To this end, we evaluated the performance of these receivers in receiving time signals through both simulated and empirical data and conducted a regularity analysis to uncover their potential value in practical applications. The findings demonstrate that the eLoran receiver excels at timing monitoring and provides highly accurate time information. An analysis of the timing performance of the eLoran system improved its accuracy and integrity.

1. Introduction

As modern communication, navigation, and scientific research continue to evolve, the importance of time synchronisation is becoming increasingly apparent. Time is a critical resource for various applications, ranging from network communications and precise scientific experiments to financial transactions [1]. Accurate time synchronisation improves system performance and efficiency while supporting a range of complex applications, including precision navigation, astronomical observation, seismic monitoring, and satellite communications [2,3].

In the field of time synchronisation, accurate timing is essential for several critical applications, particularly in communication, navigation, and scientific research. Time synchronisation plays a vital role in ensuring the accuracy of financial transactions in banks and in maintaining target tracking in precise missile positioning systems [4].

As one of the most effective backups for global navigation satellite systems (GNSSs), the eLoran system primarily transmits signals via ground waves. This system features high signal transmission power, long transmission distance, and strong anti-jamming capabilities [5]. Hence, it significantly reduces the risk to the positioning navigation timing (PNT) services of the system. The eLoran system has been deployed as an independent land-based PNT system in several regions worldwide [6]. Although eLoran and satellite-based GNSSs operate independently, they can complement each other.

Timing monitoring is essential to ensure the reliable operation of timing systems. In November 2007, the eLoran Definition Document V1.0, published by the International Loran Association, specified that the eLoran system comprises eLoran signals, transmitters, control centres, monitoring stations, and user equipment, which collectively form the complete process from signal transmission to monitoring and usage [7,8]. The establishment of an eLoran transmitter requires a timing monitoring station to monitor the quality of the broadcast signal. Hence, the station is a critical component in the design and operation of the eLoran system [9,10].

Recently, with the development of high-precision, ground-based timing systems and China’s plan to establish three eLoran timing stations, many scholars have focused on the timing performance of eLoran systems [11]. According to the literature, research by both domestic and international scholars has primarily focused on evaluating the system’s navigation performance and navigation accuracy.

Lo et al. evaluated the ground-wave propagation, atmospheric noise, transmitter and receiver performance, and overall system engineering in terms of integrity, availability, continuity, and accuracy [12]. Yu et al. examined an additional secondary factor (ASF) and found that the predicted ASF aligned with the measured ASF, displaying an error of approximately 0.8 μs and thereby validating ASF predictions [13]. Son demonstrated the positioning accuracy of eLoran in narrow South Korean waterways using improved ASF maps [14]. Hargreaves established an ASF data grid based on existing data [15].

However, few studies have focused on eLoran timing monitoring and evaluations, with most addressing the navigation performance of a system to determine its viability as a GNSS backup [16,17,18]. Existing studies have not established a comprehensive timing monitoring and evaluation index system based on monitoring data analyses, nor have they provided detailed parameters or evaluation guidelines for eLoran timing monitoring. To address these problems, this study employed measurement methods to test and compare two commercial eLoran navigation timing monitoring receivers. This study also explored the signal reception strength and signal-to-noise ratio of each device and tested their timing accuracy and stability using the Xuancheng station as the benchmark. This approach quantified the timing capability of the eLoran system and provided technical references for enhancing its service capabilities.

2. eLoran Timing Error

2.1. Main Error

The main sources of error in eLoran timing include control errors at the transmitter and broadcaster, propagation path correction errors, receiver errors, and other miscellaneous errors [19,20,21,22,23].

2.1.1. Control Errors at Transmitters and Broadcasters

A transmitter control error refers to discrepancies at the eLoran time station, and specifically the difference between the time broadcast by the eLoran station and standard time, UTC. These errors can be categorised into three main types: synchronisation errors between the reference time of the transmitter and that of the UTC, signal control errors, and antenna phase-centre measurement errors.

The first type of broadcast control error is the synchronisation error between the reference time of the transmitter and the UTC. Variations in the method used by each station to synchronise with the UTC can result in significant errors. Methods such as optical fibres, GNSSs, bidirectional satellites, and satellite co-vision were used to keep the eLoran time correction synchronised with the UTC.

The other two components, viz., the signal control error and antenna phase centre measurement error, are primarily hardware-related and challenging to separate. The errors caused by equipment and cable delays can be controlled to within 10 ns if the long-wave timing station is accurately calibrated.

2.1.2. Propagation Path Correction Errors

eLoran timing relies on ground and sky waves. Sky-wave propagation depends on ionospheric reflection, and factors such as solar activity (sunspots, solar flares, geomagnetic activities, sunrise, and sunset), meteorological factors, and solar eclipses affect ionospheric conditions, which lead to propagation errors. However, high-precision timing is primarily achieved through ground-wave propagation, with the primary factor (PF), secondary factor (SF), and ASF being the primary influences on the timing accuracy [24,25].

2.1.3. Receiver Errors

Receiver errors are primarily caused by equipment errors and tracking point errors.

Receiving Equipment Errors: These errors involve time delays between the antenna input and receiver output, including delays in the antenna, cables, and receiver channels. These errors can be corrected through receiver time-delay calibration, as discussed in Section 2.2.

Tracking Point Errors: The receiver tracks the signal at the end of the third cycle rather than at the beginning, necessitating a period correction of 30 μs. Theoretically, this correction ensures that there are no tracking-point errors in the receiver’s output signal.

2.1.4. Other Errors

Other errors include time delays introduced by firmware and other instruments, such as cables, which can be corrected.

Since both receivers received eLoran signals at the same location, we assumed that the propagation path correction errors were consistent for both. Therefore, this study primarily focuses on analysing the control errors at the transmitter and broadcaster.

2.2. Authorization Performance Assessment Metrics

2.2.1. Maximum Timing Deviation

The maximum value of the timing deviation monitored during the valid data period indicates the highest deviation in the eLoran timing system.

2.2.2. Minimum Timing Deviation

The minimum value of the timing deviation was monitored during the valid data period and indicated the lowest deviation in the eLoran timing system. The maximum and minimum values reflect the range of variation in the UTC obtained by the user. To illustrate the dispersion of the timing deviations, this study uses extreme deviation (the difference between the maximum and minimum values) to represent the fluctuation range of the timing deviation.

2.2.3. Timing Accuracy

The average timing deviation values monitored during the valid data period indicate the central tendency of the eLoran timing system in broadcasting the national standard time [24,25]:

$$\stackrel{-}{\tau }={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\tau }_i}}{n}},$$

(1)

where n indicates the number of data points in the valid data period, ${\tau }_i$ indicates the monitoring value of the timing deviation, and $\stackrel{-}{\tau }$ indicates the average value of the timing deviation in the valid data period.

2.2.4. Timing Stability

The timing stability is quantified by the standard deviation of the monitoring value of the timing deviation during the valid data period, which characterises the degree of dispersion of the national standard time broadcast by the eLoran timing system [26]:

$$\sigma =\pm \sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left({\tau }_i-\stackrel{-}{\tau }\right)}^2}}{n-1}}}.$$

(2)

where n indicates the number of data points in the valid data period, ${\tau }_i$ indicates the monitoring value of the timing deviation, and $\stackrel{-}{\tau }$ indicates the average value of the timing deviation in the valid data period.

Currently, China’s eLoran system requires timing accuracy in the order of microseconds (millionths of a second). According to the timing characteristics of the eLoran system and the above analysis, we have stipulated how to use receivers to receive eLoran timing signals; monitor the deviation of the time broadcasted by the eLoran timing system from the national standard time; and analyse indices such as the maximum timing deviation, the minimum timing deviation, timing accuracy, and timing stability, based on the value of the monitoring of deviation, in order to carry out a comprehensive assessment of the performance of the eLoran system’s timing.

3. Measuring Equipment and Tests

3.1. Measuring Equipment

A test platform was constructed to verify the validity and reliability of the two eLoran timing monitoring receivers. The platform was designed to assess the timing performance of the receivers. Two commercial eLoran navigation timing monitoring receivers were used in the test. Both receivers were activated simultaneously, and their timing signals were monitored and compared for consistency using monitoring software (ELEGANT_UN15X_v8.2.3 USA). The two receivers used in this test are existing commercial eLoran receivers. A diagram of the test equipment is shown in Figure 1.

The test equipment provides a precise demodulation of the time, frequency, and data channels based on an eLoran C or Enhanced eLoran system. This receiver is equipped with a serial port, GPIO interface, and both 1PPS and 10 MHz inputs and outputs. It uses a long-wave receiving antenna to capture the long-wave space signal, which is then fed into the receiver host via a coupler. The receiver host captured and identified the long-wave signal and also tracked the third weekly over-zero point of the first pulse in the pulse group. The receiver performed real-time timing monitoring by decoding the messages. This device provided three timing-pulse 1PPS outputs and can communicate via its RS232 serial port or LAN network port to deliver timing monitoring information.

3.2. Internal Delay Calibration

For Receiver 1, the internal delay was caused by the internal circuit and signal processing of the receiver. Following calibration by users, the internal delay of the equipment was 78.21 μs. Therefore, this part of the error should be removed from the timing results obtained from subsequent measurements. For the self-developed domestic equipment, the internal delay system was calibrated to zero at all stations before leaving the factory. Thus, the internal delay of Receiver 2 was zero by default.

3.3. Experimental Design

The test equipment and overall experimental design of this study are illustrated in Figure 2.

To quantify the timing accuracy and stability of the two eLoran navigation timing monitoring receivers, we examined their performance with both real and simulated signal sources. The following sections provide a detailed analysis of their timing performance under various conditions.

4. Testing and Analysis

4.1. Receiver Signal Source: Long-Wave Signal from Analogue Source

4.1.1. Indicators of the Signal Reception Strength and Signal-to-Noise Ratio (SNR) for Each Device

Analogue sources were used to generate signal strengths ranging from 30 to 110 dBμV/m (in 10 dBμV/m intervals) for the 8390 station’s chain positioning and 8390M station’s timing signals. These signals are output through an adapter to various receiving equipment. Upon achieving stable signal reception, the measured signal strength and signal-to-noise ratio (SNR) parameters for each station were recorded, as shown in Figure 3.

As shown in Figure 3, Figure 4 and Figure 5, a repeat test of the simulated signal reception was conducted using Receivers 1 and 2. Figure 3 shows the results of the field strength SNR parameters of Receiver 1 with different analogue source signal strengths, Figure 4 shows the results of the field strength SNR parameters of Receiver 2 with different analogue source signal strengths, and Figure 5 shows a comparison of the field strength and the SNR of Receiver 1 and Receiver 2 with the same analogue source signal strengths. The test results indicate that both receivers exhibited good tracking and reproducibility for different signal strengths in the simulation. Notably, the output signal strength of Receiver 2 was approximately 15 dB higher than that of Receiver 1. This is primarily because the test uses an emulator that bypasses the antenna and antenna coupler. Consequently, the signal goes directly into the receiver, with a larger amplification factor for Receiver 2 than for Receiver 1. However, owing to the non-standardised output signal strength of the simulator, it is currently not possible to directly quantify the reception capability of the equipment.

4.1.2. Receiving Sensitivity of Each Device

According to the mapping in Section 4.1.1, if the equipment presented in Section 4.1.1 cannot lock the station signal at 40 dB μV/m but can lock it at 50 dBμV/m, the analogue source will generate signal strengths ranging from 50 to 40 dBμV/m (with 1 dBμV/m intervals), and the signal searching phenomenon of the equipment will be recorded. If the equipment can still lock the signal at 30 dBμV/m, the measurement will start at 30 dBμV/m, testing at 1 dBμV/m intervals until the device cannot lock the signal. For Receiver 1, the analogue source broadcast field strength is 18 dBμV/m, while that of Receiver 2 is 10 dBμV/m. The test broadcast time differences are TD1 = 14,990.1 μs and TD2 = 33,428.1 μs.

The locations of the test points and each station are shown in Figure 6. The propagation distances from different stations to the receiving points are relatively long, and the propagation paths are quite complex. The field strengths and SNR of each receiver are listed in

Table 1. Indicators for each receiver after an analogue source origination time difference.

Receiver	Station	Receiver Field Strength (dBμV/m)	Receiver SNR (db)
1	8390M	3.72	–2.56
	8390X	8.28	2.65
	8390Y	7.20	2.16
2	8390M	18.6	–9.75
	8390X	18.9	–5.08
	8390M	3.72	–2.56

. The test reduced the signal source strength to its lowest level and both receivers could still track the signal, indicating their high sensitivity. For the simulation, the output of a weak signal could be considered.

4.1.3. Accuracy of 1PPS Measurement

The analogue source generates 8390M station timing signals, with the time differences between broadcasting and transmitting during the test being recorded as TD1 = 14,990.1 μs and TD2 = 33,428.1 μs. The test equipment received these timing signals and, once they stabilised, a counter measured the 1PPS output from the receiving equipment. The mean and standard deviation were calculated to evaluate the timing accuracy and stability. This test was repeated multiple times, and the resulting data are presented in

Table 2. Receiver 1’s time difference measurement accuracy (analogue source).

Analogue Source Signal Strength (dBμV/m)	Maximum Value of Timing Deviation (ns)	Minimum Value of Timing Deviation (ns)	Timing Accuracy (ns)	Timing Stability (ns)
118	337.3	262.4	267.2	32.3
114	322.8	225.2	229.9	35.6
100	336.4	261.5	265.0	32.3
90	323.1	200.0	255.5	32.0
80	348.1	204.6	275.2	35.4
70	391.4	321.5	325.7	32.9
60	393.8	284.8	332.0	33.7
50	359.9	223.4	282.6	33.9
40	360.2	228.6	279.9	33.1
30	348.5	235.6	285.9	30.9

and

Table 3. Receiver 2’s time difference measurement accuracy (analogue source).

Analogue Source Signal Strength (dBμV/m)	Maximum Value of Timing Deviation (ns)	Minimum Value of Timing Deviation (ns)	Timing Accuracy (ns)	Timing Stability (ns)
118	1018.9	768.9	865.5	60.3
114	938.8	698.4	777.5	49.9
100	936.9	636.3	754.3	54.2
90	1143.2	861.9	995.1	57.9
80	1142.2	896.8	1003.7	49.1
70	1127.8	859.1	976.1	49.7
60	921.6	680.5	793.1	48.7
50	940.6	694.9	797.9	49.5
40	935.9	665.5	765.4	51.4
30	1142.9	824.4	958.9	51.1

.

The experimental data indicate that under a pure signal analogue-source output, the timing stability of Receiver 2 is approximately 60 ns or less, whereas that of Receiver 1 is ~30 ns. This demonstrates that Receiver 1 has a higher tracking accuracy. Consequently, the tracking accuracies of foreign receivers surpassed those of domestic receivers, suggesting room for improvement.

4.1.4. Ability of Receiver 2 to Accurately Measure 1PPS Source

To further explore the actual timing accuracy of the domestic receiver, a long-wave analogue source was used to generate signals from each station to measure the 1PPS accuracy of Receiver 2. The test results are presented in

Table 4. Receiver 2’s 1PPS measurement accuracy (first time for analogue sources).

Station	Timing Accuracy (ns)	Timing Stability (ns)
8390M	890.8	72.7
7430M	837.3	92.7
6780M	849.5	88.6
6000M	889.7	103.0

,

Table 5. Receiver 2’s 1PPS measurement accuracy (second time for analogue sources).

Station	Timing Accuracy (ns)	Timing Stability (ns)
8390M	863.9	85.8
7430M	819.8	82.9
6780M	860.5	72.9
6000M	892.5	78.2

and

Table 6. Comparison of the accuracy of two 1PPS measurements (analogue sources).

Station	Difference in Accuracy between Two Tests (ns)	Difference in Stability between Two Tests (ns)
6000M	–26.8	±13.1
6780M	–17.5	±9.8
7430M	11.1	±15.7
8390M	2.8	±24.9

.

Figure 7 indicates that the timing accuracy and stability of the domestic receiver at the source stations were generally consistent, with the timing stability fluctuations being within hundreds of nanoseconds. The difference in accuracy between the two tests remained stable for 30 ns.

4.2. Receiver Signal Source: eLoran Transmitter (Actual Station)

The receiving antenna was installed on the roof to receive the timing signal from the Xuancheng station (8390M) and test its timing accuracy and stability. Once the signal stabilised, a counter recorded the 1PPS timing output to calculate its average value and stability. This test spanned two weeks, and data were collected over 24 h each day. To better assess the timing accuracy and stability of each device, the data from 2 September 2023 were analysed in detail for three time periods: morning, midday, and evening. The timing accuracy and stability results are shown in Figure 8 and detailed in

Table 7. Accuracy and stability of signal received from Xuancheng station for each device (05:30–06:30 time period).

Receiver	Maximum Value of Timing Deviation (ns)	Minimum Value of Timing Deviation (ns)	Timing Accuracy (ns)	Timing Stability (ns)
1	482.9	260.4	362.9	40.2
2	1054.5	686.9	851.1	57.7

,

Table 8. Accuracy and stability of signal received from Xuancheng station for each device (12:30–13:30 time period).

Receiver	Maximum Value of Timing Deviation (ns)	Minimum Value of Timing Deviation (ns)	Timing Accuracy (ns)	Timing Stability (ns)
1	374.4	193.4	288.3	35.2
2	950.5	645.2	761.2	49.1

and

Table 9. Accuracy and stability of signal received from Xuancheng station for each device (19:50–20:50 time period).

Receiver	Maximum Value of Timing Deviation (ns)	Minimum Value of Timing Deviation (ns)	Timing Accuracy (ns)	Timing Stability (ns)
1	424.9	221.9	336.3	39.6
2	1028.1	623.3	795.3	61.2

.

The results presented in Table 7 indicate that Receiver 1 had a timing error accuracy of 362.9 ns and a stability of 40.2 ns, whereas Receiver 2 had a timing error accuracy of 851.1 ns and a stability of 57.7 ns. Although the timing stability of Receiver 2 is not significantly different from that of Receiver 1, it exhibits a “jumping weekly” phenomenon, which suggests that its tracking stability under weak signal conditions needs improvement. The results presented in Table 8 indicate that Receiver 1 had a timing error accuracy of 288.3 ns and a stability of 35.2 ns, whereas Receiver 2 had a timing error accuracy of 761.2 ns and a stability of 49.1 ns. The results presented in Table 9 indicate that Receiver 1 has a timing error accuracy of 336.3 ns and a stability of 39.6 ns, whereas Receiver 2 has a timing error accuracy of 795.3 ns and a stability of 61.2 ns.

A comprehensive comparison of the actual test results and the simulation results shows that they are basically the same. Specifically, the actual results are slightly higher in some cases, which may be caused by the fact that certain environmental factors and disturbances were not fully considered in the simulation.

As indicated in Figure 8 and Table 7, Table 8 and Table 9, we analysed in detail the reasons that the eLoran receiver has basically the same timing accuracy in the morning, midday, and evening time slots and found that the following factors may play a role:

(1)

Signal stability: the eLoran system has high signal stability and an anti-interference capability, which enables it to maintain consistent timing accuracy in different time periods.

(2)

Environmental conditions: although there may be variations in environmental interference from one time period to the next, the overall environment at the receiver’s location is relatively stable, with no significant changes in signal propagation paths or conditions, so timing accuracy remains consistent.

(3)

Equipment performance: eLoran receivers are equipped with high-performance equipment and antennas that can effectively capture and process signals to maintain high timing accuracy even in different time periods.

For both tested receivers, the test site environments were the same, but Receiver 1 outperformed Receiver 2 in terms of timing accuracy and stability. This may be caused by the fact that Receiver 1 may be equipped with higher performance antennas and boards that are able to capture and process eLoran signals more efficiently. This gives Receiver 1 better immunity to interference and higher sensitivity.

These results indicate that when the long-wave timing signal’s quality is good, the short-term stability of these long-wave timing monitoring results is reliable, making this a valuable supplementary method for satellite timing, when necessary.

5. Conclusions

The following conclusions were derived from the study of the timing performance indices of two receiver types using real measurement methods.

The timing performances of the different receivers under various signal sources were quantified. Relevant data from multiple timing tests, including the received time signals and other pertinent information, were presented. Timing metrics were visualised using charts and images, and the test results were analysed to identify patterns. Different subsections explored performance variations under various conditions and examined the stability and accuracy of time synchronisation.

The eLoran receiver has basically the same timing accuracy in the morning, midday, and evening time slots. Receiver 1 had a timing error accuracy of 329.2 ns and a stability of 38.3 ns, whereas Receiver 2 had a timing error accuracy of 802.5 ns and a stability of 56 ns. The eLoran receiver demonstrated superior timing monitoring capabilities and exhibited high stability as well as accurate time synchronisation. The eLoran receiver provides reliable temporal information under diverse environmental conditions, making it suitable for a wide range of applications.

eLoran receivers require less than 100 nanoseconds for high-precision applications, 100 nanoseconds to 1 microsecond for moderate precision applications, and 1 to 10 microseconds for low-precision applications. Receiver 1 is best suited for telecommunications, financial transactions, and power grid management owing to its superior timing accuracy and stability. Receiver 2 is suitable for navigation, positioning, general scientific research, and industrial timekeeping, where slightly larger timing errors and less stability are acceptable.

The eLoran system has high signal stability and an anti-interference capability, which enables it to maintain consistent timing accuracy in different time periods. Although there may be variations in environmental interference from one time period to the next, the overall environment at the receivers’ location was relatively stable, with no significant changes in signal propagation paths or conditions, so their timing accuracy remained consistent. eLoran receivers are equipped with high-performance equipment and antennas that can effectively capture and process signals to maintain high timing accuracy even in different time periods. Future studies should conduct long-term time monitoring to further explore and utilise the potential of eLoran receivers.