sensors Letter Research on the eLoran Differential Timing Method Yun Li 1,2,*, Yu Hua 1, Baorong Yan 1 and Wei Guo 1 1 National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China; [email protected] (Y.H.); [email protected] (B.Y.); [email protected] (W.G.) 2 Physics Department, University of the Chinese Academy of Sciences, Beijing 100049, China * Correspondence: [email protected]; Tel.: +86-1868-291-1626 Received: 14 September 2020; Accepted: 12 November 2020; Published: 14 November 2020 Abstract: An enhanced long-range navigation (eLoran) system was selected as the backup of Global Navigation Satellite Systems (GNSS), and experts and scholars are committed to improving the accuracy of the eLoran system such that its accuracy is close to the GNSS system. A differential method called eLoran differential timing technology is applied to the eLoran system, which has been used in maritime applications of eLoran. In this study, an application of eLoran differential timing technology in a terrestrial medium is carried out. Based on the eLoran timing service error, the correlation of the timing service error is analyzed in theory quantitatively to obtain the range of the difference station in the ground. The results show that to satisfy the timing accuracy of 100 ns, the action range of eLoran difference station on the land needs to be less than 55 km. Therefore, the eLoran differential method is proposed, and in the difference station, the theoretical calculation is combined with the measurement of the signal delay to obtain the difference information, which is sent to the users to adjust the prediction delay and improve the eLoran timing precision. The experiment was carried out in the Guan Zhong Plain, and the timing error of the user decreased from 394.7287 ns (pre-difference) to 19.5890 ns (post-difference). The proposed method is found to effectively enhance the timing precision of the eLoran system within the scope of action. Keywords: eLoran; difference; timing service; error; correlation 1. Introduction After delaying the instalment of enhanced long-range navigation (eLoran) stations for a certain period of time, the United States announced, on 4 December 2018, that eLoran stations will be used as a backup for Global Navigation Satellite Systems (GNSS). Moreover, simultaneously, a high-precision terrestrial time service system is being developed in China. The effective radiated power of eLoran is in the range of 100 to 1000 kW, and it is nearly impossible to jam over large areas with such high power levels. This is the reason why eLoran is used as an alternative to the GNSS system. Unfortunately, eLoran is less accurate than GNSS. Several studies have been conducted to improve the precision of the eLoran system to match that of the GNSS system. Many experts and scholars focus on the prediction of signal propagation delay, especially the additional secondary factor (ASF) under special topographic conditions [1–4]. By using the ASF grid, the accuracy of the eLoran system can be improved [5–8]. To develop the ASF grid, surveys have been conducted for the ASF values. However, conducting investigation and measurement of ASF for the entire area is expensive. Moreover, ASF depends on the ground conductivity along the propagation path of the signal, and any change in conductivity due to weather and season will affect ASF. To supply the real-time variation of the ASF, the eLoran differential timing method has been proposed, especially for maritime applications, in which numerous experiment and data analysis are performed [5,6]. Sensors 2020, 20, 6518; doi:10.3390/s20226518 www.mdpi.com/journal/sensors Sensors 2020, 20, x FOR PEER REVIEW 2 of 14 Sensors 2020, 20, 6518 2 of 14 In this study, the eLoran differential timing service is analyzed theoretically and this method is mainlyIn this used study, in terrestrial the eLoran media. diff erentialThe correlation timing serviceof eLoran is analyzedtiming service theoretically error is analyzed and this methodin theory isquantitatively, mainly used in and terrestrial the action media. range of The difference correlation station of eLoran on the ground timing is service calculated error with is analyzed an accuracy in theoryof 100 quantitatively, ns. Based on the and correlation the action of range the errors, of difference the eLoran station differential on the ground timing is calculatedservice is proposed. with an accuracyThen an of experiment 100 ns. Based is carried on the correlationout to test ofand the verify errors, the the eLoran eLoran differential differential timing timing method service isby proposed.conducting Then a survey an experiment in the Guan is carriedZhong outPlain to of test the and Shanxi verify province. the eLoran differential timing method by conducting a survey in the GuanZhong Plain of the Shanxi province. 2. eLoran Signal and Propagation Delay 2. eLoran Signal and Propagation Delay 2.1. eLoran Signal 2.1. eLoran Signal eLoran is a low frequency (100 kHz) terrestrial navigation and timing system. The transmitters are eLoranorganiz ised a lowinto frequencychains, with (100 one kHz) master terrestrial station navigation and several and secondary timing system. stations The in transmitters each chain. areThe organizedmaster station into chains, transmits with nine one masterpulses stationand second and severalary station secondarys transmit stations eight in pulses each chain. at a time The. Figure master 1 stationillustrates transmits the shape nine pulsesof the andsignal secondary, and the stationsred dot transmitrepresents eight standard pulses z atero a time.-crossing Figure (SZC1 illustrates), which is thethe shape point of at thewhich signal, the andsignal the is redtracked dot represents by an eLoran standard receiver zero-crossing and it is use (SZC),d to calculate which istime the-of point-arrival. at which the signal is tracked by an eLoran receiver and it is used to calculate time-of-arrival. SZCSZC FigureFigure 1. 1.The The enhanced enhanced long-range long-range (eLoran) (eLoran pulse) pulse shape. shape The red. The dot red represents dot represents standard standard zero-crossing zero- (SZC),crossing which (SZC), is thewhich point is the at point which at the which signal the issignal tracked is tracked by an by eLoran an eLoran receiver receiver and and it is it usedis used to to calculatecalculate time-of-arrival. time-of-arrival. 2.2. eLoran Propagation Delay 2.2. eLoran Propagation Delay The eLoran signal is transmitted radially from the transmitter to the receiver, and travels parallel The eLoran signal is transmitted radially from the transmitter to the receiver, and travels parallel to the surface of the earth. During this propagation, the signal does not travel at the speed of light, to the surface of the earth. During this propagation, the signal does not travel at the speed of light, but it is slowed by the atmosphere and the surface of the earth. The time taken for the eLoran signal to but it is slowed by the atmosphere and the surface of the earth. The time taken for the eLoran signal reach the receiver is called propagation time (Tp), which is shown in the following equation to reach the receiver is called propagation time (푇푝), which is shown in the following equation = + Tp푇푝 =PFPF +ASF,ASF, (1)(1) wherewhere if theif the signal signal propagates propagates in the in infinitethe infinite air medium, air medium, the time the taken time to taken reach to the reach receiving the antennareceiving fromantenna the transmitting from the transmitting antenna is calledantenna the is primary called factorthe primary (PF). Owing factor to(PF the). dielectricOwing to properties the dielectric of theproperties earth surface, of the the earth signal surface, will travel the signal relatively will slowlytravel asrelatively compared slowly to that as incompared the atmosphere. to that in This the delayatmosphere. is termed Th asisan delay ASF. is termed as an ASF. Sensors 20202020,, 20,, 6518x FOR PEER REVIEW 3 of 14 The refractive index of the atmosphere 푛푠 implies that the speed of the signal is a fraction slower than Thethe speed refractive of light index in ofvacuum. the atmosphere The PF is nrelateds implies to the that distance the speed S, ofand the this signal is expressed is a fraction as follows slower than(Equation the speed (2)) [9,10] of light. in vacuum. The PF is related to the distance S, and this is expressed as follows (Equation (2)) [9,10]. R∫ 푛푠 푑푆 PF = nsdS (2) PF = 퐶 (2) C where 퐶 is the speed of light in a vacuum and is equal to 0.299792458 km/μs, S is the distance of where C is the speed of light in a vacuum and is equal to 0.299792458 km/µs, S is the distance of signal signal propagation, and 푛푠 is the atmospheric refraction index of the ground, which varies with propagation, and n is the atmospheric refraction index of the ground, which varies with temperature temperature humiditys and air pressure. humidity and air pressure. The earth surface medium (seawater and land) delay signal transmission, and the time taken for The earth surface medium (seawater and land) delay signal transmission, and the time taken the eLoran signal in the procedure is ASF. With the decrease in the electrical conductivity of the for the eLoran signal in the procedure is ASF. With the decrease in the electrical conductivity of the surface, a high proportion of the signal will penetrate the ground and the wave-front will propagate surface, a high proportion of the signal will penetrate the ground and the wave-front will propagate more slowly. The calculation formula of ASF is shown in Equation (3) [9,10]. more slowly. The calculation formula of ASF is shown in Equation (3) [9,10].