**Sangeeta Nagrare & M. R. Sivaraman**

Satcom & IT Applications Area

Space Applications Centre

Ahmedabad -380015, India

[email protected]

**Abstract**

Indian Space Research Organisation (ISRO) in collaboration with Airport Authority of India(AAI), is planning to implement Wide Area Augmentation System(WAAS) over Indian Airspace, to meet the requirements of Category I precision approach of aircrafts. Indian WAAS will consist of a network of ground stations called ‘Range & Integrity Monitoring Stations(RIMS), One or two Master Control Centre (MCC), One or two Navigation Land Earth -Stations (NLES), CXL & CXC Navigation Transponders on one or two Geostationary Communication satellites. RIMS,MCC and NLES will have atomic clocks that should be kept synchronised to a network time within 1-3 ns and the clocks at NLES and MCC should be kept synchronised to, 20ns with GPS time. We have already tested Two-Way Satellite Time & Frequency Transfer (TWSTT) Technique and achieved a time synchronisation accuracy of 1ns between two remotely kept atomic clocks.

RIMS are basically GPS dual frequency tracking stations, located at well surveyed points, whose coordinates are well known. Hence at RIMS, in addition to the atomic clocks , a dual channel P code GPS Receiver will be also installed for GPS tracking. They will essentially collect pseudorange and carrier phase measurements, from all the visible GPS satellites. At Space Applications Centre, Ahmedabad, we propose to try out GPS Common View time transfer technique, basically using the simultaneous pseudorange and carrier phase measurements, to synchronise the atomic clocks at two stations separated by thousands of kms. and estimate its accuracy by comparing the stations. We will present in this paper the details of the GPS common view method, the errors involved in the method and some preliminary results obtained in our experiment.

**Introduction**

Global Positioning System (GPS) satellites are capable of providing global time & frequency dissemination 24 hours a day. GPS is slowly evolving into a primary system for the distribution of Precise Time and Time Interval (PTTI), both at national and international level. It has been shown that GPS can be used to synchronize clocks to tens of nanoseconds over large distances.

All GPS satellites carry an atomic clock (either a Cesium beam standard or a Rubidium vapour standard) on board. The GPS Control Segment located in US, monitors the satellite clocks and determines their offset from a GPS System time maintained by US Naval Observatory. The clock offsets are then uploaded to the satellites, which are stored and transmitted as part of the transmitted GPS Navigation message. GPS time is a continuous time usually measured in weeks and seconds, from the GPS time zero point of midnight, January 5, 1980. Controlled by Universal Time Coordinated (UTC), GPS time is not corrected for leap seconds and so it is currently ahead of UTC by a few seconds. With the exception of the integer number of leap seconds, GPS time is steered to within one microsecond of UTC with a difference reported in the GPS Navigation message to a precision of 90 nanoseconds.

In a simple GPS Timing Receiver, a replica of the C/A code transmitted by one of the visible GPS satelllites, synchronised to a local clock 1 PPS, is generated by the receiver and crosscorrelated with the received signal. Since the local clock 1 PPS will be offset from the satellite clock 1 PPS, the local clock 1 PPS will have to be shifted by a time Dt, so that the cross correlation is maximum. By doing this, the GPS Receiver stripes off the C/A code and the carrier has only BPSK modulated Navigation data. In addition , Dt gives pseudorange from the receiver to the satellite (PR). The receiver resets the local clock time to the time given by in HOW (time of week) and the local 1 PPS is synchronised to the beginning of that subframe. Because of the path delay and many other reasons, still the local clock will be running behind the satellite clock, by a few milliseconds. The receiver estimates the time difference between the local clock and satellite clock (GPS time), as given by

Dt’ = PR – (R/C+dS+dI+dT)-dD+dC ………(1)

Where

PR – Measured pseudorange, determined by measuring the time difference between two the transmitted and received identical codes.

R – Geometric range between the satellite and the receiver, computed from broadcast ephemeris and the known coordinates of the GPS receiver antenna.

C – Speed of light

dS – Correction due to Sagnac Effect

dI – Propagation delay due to Ionosphere

dT – propagation delay due to troposphere

dD – Receiver delay

dC – Difference between the onboard clock and GPS time.

Basically GPS can be used for time synchronisation, in two different ways. They are (1) One-way mode (2) Two-way Common-mode ,Common-view Time Transfer.

**Single Station Time Transfer Technique**

A single GPS receiver can deduce GPS time, from measurements according to (1). A typical GPS receiver performs the above process, during 13 minute tracking session as follows.

- The receiver synchronises its local 1 PPS to the first bit of a subframe and resets its clock reading to the time given in the corresponding HOW, in that subframe.
- The receiver then processes the short term raw pseudorange measurements, smoothing them over a period of seconds (typically 6 to 15) through use of a second degree fit or phase accumulation
- These short term smoothed pseudoranges are corrected by the geometrical range R and other corrections .
- A linear fit of the short term data is used to deduce the time difference between the satellite and receiver clocks over the 13 minute track in terms of a slope, an intercept and a standard deviation.
- The receiver 1 PPS, is now corrected for this time difference.

This technique is simplest. It has a global coverage and requires no other data than those provided by the receiver.The major sources of errors and their contribution are as given. **Table. 1: Typical error budget for Single Station GPS technique.**

No. | ERROR (1s) | ERROR (1s) | |

(C/A CODE) | (P CODE) | ||

1. | Satellite Onboard Atomic Clock Error | 10 ns | 10 ns |

2. | Satellite Coordinate determination from Satellite Broadcast ephemeris | 15 ns | 15 ns |

3. | User Receiver antenna coordinate uncertainty | 33 ns | 33 ns |

4. | Ionospheric effect | 15 ns | 7.5 ns |

5. | Tropospheric effect | 3.0 ns | 3.0 ns |

6. | Receiver Delay | 5.0 ns | 5.0 ns |

7. | Receiver Software | 5.0 ns | 5.0 ns |

8. | Receiver Noise | 50.0 ns | 5.0 ns |

9. | MultipathPropagation | 10 ns | 10 ns |

Total Error | 65 ns | 40 ns |

The error due to receiver coordinates and satellite coordinates, causes error in calculation of geometric range (R) in eq. 1 above. In addition they are responsible for the error due to Sagnac effect.

The accuracy to which an atomic standard can be synchronized to GPS time depends on local conditions of observations, mainly on the accuracy of the receiver antenna coordinates and on the amount of acquired data. If the antenna coordinates have an uncertainty of 10 m, the accuracy ranges on an average from 40-65 ns, for 13 minute track, to a few tens of nanoseconds for averaging times of one day or more. The accuracy of time synchronisation, using P code receiver, in single station mode is better than C/A code receivers, because (1) P code receivers uses dual frequency measurements, to remove ionospheric effects and (2) the receiver noise in P code receivers is 1/10 times less than C/A code receivers.

**Two Station Common View Time Transfer Technique**

The principle of this technique is illustrated in Fig. 1. Two GPS receivers are kept at stations A and B, separated by a distance of 1000 kms or more. Both the stations receive the signals of the same satellite at the same time, and synchronize their clocks to the satellite clock. At both the stations, the 1 PPS of the local clock of the GPS Receiver is compared with the 1 PPS of an atomic time standard, by measuring the time delay between the two 1 PPS, using a time interval counter. If these time interval measurements at stations A and B are respectively, DT A and DT B, , then (DT A -DT B ) will be the offset of one atomic standard with respect to the other.

In this approach, the satellite clock error contributes nothing. Some of the other errors like satellite ephemeris error, ionospheric effect, tropospheric effect, receiver delay are reduced. Because of this, there is an improvement in time synchronization accuracy between two station clocks.

In summary, the common view concept is as follows. If a transmitted event (like 1 PPS synchronized to the Navigation data stream) from a GPS satellite is viewed simultaneously from two stations A and B, each maintaining an independent clock, then the coordinate times of the event can be computed at sites A and B as t’GA and t’GB respectively. If the true coordinate times of the transmitted events are tGA and tGB, respectively, then one can write

tGA= t’GA + tDA ———————— (2)

tGB= t’GB + tDB ———————— (3)

where the error terms tDA and tDB include errors in both measurement and calculation. These errors arise principally from errors in knowledge of the satellite position, and of the time delays in the propagation paths and the receivers. Taking the difference between (2) and (3) yields an estimate of the true coordinate time difference between the A and B site clocks,

where

tGA-tGB) = t’GA-t’GB+DtD ………………… (4)

DtD=tDA-tDB ……………….. (5)

Experimentally it has been found that the size of the errors on the left hand side of (5) are about an order of magnitude smaller than those in either term on the right hand side, due to common mode cancellation of errors. Thus one sees the significant advantage of the simultaneous common-view approach.

In Table 2 below, typical error budgets of GPS time comparisons in Common View (CV), between two stations at a distance d, using C/A code receivers is given **Table. 2: Typical error budget for GPS time comparison in Common View (CV) Time Transfer Technique, between two stations using C/A code receivers**

For a single CV | For 10 CV | ||||

averaged over one day | |||||

No. | Error Source | d=1000 km | 5000 km | 1000 km | 5000 km |

1. | Satellite Clock error (cancels in CV) | 0 | 0 | 0 | 0 |

2. | Satellite Coordinates | 2 | 8 | 1 | 3 |

3. | Antenna Coordinates | 20 | 20 | 7 | 7 |

4. | Ionospheric effect | 6 | 15 | 1 | 3 |

5. | Tropospheric effect | 2 | 2 | 0.7 | 0.7 |

6. | Receiver Delay | 2 | 2 | 2 | 2 |

7. | Receiver Software | 2 | 2 | 2 | 2 |

8. | Receiver Noise (13 minute average) | 3 | 3 | 1 | 1 |

9. | Multipath propagation | 5 | 5 | 2 | 2 |

Total Error | 22 | 27 | 8 | 10 |

It is assumed in this table 2, that the noise of the laboratory clocks and the rise time of reference pulse bring unintelligible contributions, which are not considered here. The uncertainty in the antenna coordinates are assumed to be of the order of 3 m. In practice, errors of coordinates can sometimes reach 30-40 m. Two cases are considered : a single common view of about 13 minute duration and a daily average of 10 common views. This budget is established for normal operating conditions. Much large errors may occur in the case of a defective receiver, lack of delay calibration, poor environment of the antenna, adoption of wrong antenna coordinates etc.

**Time Synchronisation Implementation in Wadgps**

In US WAAS, GPS Common-View Time Transfer Technique is used to estimate the difference between the Reference Station Clocks and the Master Clock, located at MCC. The basic equation used to estimate, the clock offset is the following pseudorange residual equation :

{(Dk,m= Drk.1k,m+Dbm-DBk+nk,m)k=1,K}m=1,M ………..(6)

In eq .(6) above, Drk is the vector that connects the true location of the kth satellite, to its location according to the broadcast navigation message. In eq. (6), 1 k,m denotes the unit vector from the k th satellite to the m th reference station. Additionally, Dbm and DBk are the offsets in the Reference Station and satellite clocks to the GPS time. The measurement noise is given by nk,m . K is the number of satellites in view of the m th Reference station and M is the total number of Reference Stations.

The GPS Pseudoranges at the Reference Stations, can be corrected for ionospheric effects, because dual-frequency measurements can be used to estimate the ionospheric delay accurately and removed. In addition, the Reference Stations also collect meteorological parameters, Pressure, Temperature and Relative Humidity and the tropospheric delay can be estimated accurately and corrected for.

Basically there are three possible approaches to estimate, the difference between the Reference Station clocks and the Master clock located at MCC. They are discussed below in detail.

In one of the methods, Enge & Vandierendonck have discussed a methodology to be implemented in US WAAS, which is as folows.

Eq. (6) above can be rewritten as follows for an MCC.

(DK,MCC = Drk.1k,MCC + DbMCC -DBk + nk,MCC)k=1,K ……. (7)

In equation (7) above, Drk is the vector that connect the true location of the kth satellite, to its location, according to the Broadcast Navigation Message. 1k,MCC denotes the unit vector from the kth satellite to the MCC. Additionally, DbMCC and DBk are the offsets in the MCC and satellite clocks with respect to GPS Time. nk,MCC is the measurement noise. For each satellite of common visibility between a Reference Station,m and an MCC, we can have a pair of equations (6) and (7). Substracting one from the other, we can write,

where N is the number of satellites in common view of the MCC and the m th Reference Station. This can be written as approximately as equal to

= DbMCC- Dbm

This family of estimated clock offsets (Dbm,MCC)m=1,M is used in US WAAS to eliminate the clock differences in the observations from the M Reference Stations. It should be made sure that the MCC clock is kept in close synchronism with GPS time. This can be done by averaging the GPS observations at MCC to steer an atomic clock or an ensemble of atomic clocks at MCC. Alternatively (which is more accurate) it could be done if there were a more direct connection from the MCC Master Clock to GPS Time as kept by US Naval Observatory, through some means like a Two Way Satellite Time & Frequency Transfer Technique. Once the Reference Station clock differences are eliminated, one can determine the satellite ephemeris correction (along track, cross track and radial error) as well as satellite clock correction, using ranging data from M (M>4) Reference Stations.

IN EGNOS, a slightly different scheme, as described below, is followed. The individual pseudorange measurements from each RIMS to each satellite can be expressed as

riA=RiA+AiA+C(Dtis-DtuA) + e …….. (9)

**where**

riA is the pseudorange measured from RIMS site A to the satellite i

RiA is the range calculated from the RIMS known position (well surveyed point) to the satellite, i, using broadcast ephemeris

AiA is the atmospheric delay (ionospheric and tropospheric delay)

C is the velocity of light

Dtis is the ith satellite clock offset (relative to GPS time)

DtuA is the RIMS clock offset relative to GPS time

e is the random error term

The pseudorange measurements are corrected for ionospheric and tropospheric delays by MCC using models. By applying double difference technique, requiring simultaneous tracking of two satellites, i and j, from two RIMS, A and B, we get

FijAB=((riA-rjA)-(riB-rjB)) = ((RiA-RjA) – (RiB-RjB)) – (10)

This equation is used to estimate the satellite ephemeris errors as it is free from satellite clock and RIMS clock errors. After this using a common pseudorange observations for a satellite, i, between one RIMS, say and MCC, a single difference equation is formed as follows.

FiAM=(riA-riM)+(DtuA-DtuM) (11)

**where**

FiAM is the single difference between RIMS,A and MCC,M.

(DtuA-DtuM) is the clock offsets between RIMS, A and MCC, M, that can be determined.

A third approach is based on using Kalman Filter Technique. Each measurement from a RIM, given by eq. (8) has 5 unknowns viz. three components of satellite ephemeris error (i.e. along track error, cross tack error and radial error), satellite clock error (Dtis) and RIMS clock error (DtuA). If there are n RIMS, we have n equations for a single satellite but (n+4) unknowns (viz. 3 components of satellite ephemeris error, satellite clock error & RIMS clock error in n RIMS.). Kalman Filter approach can be used to solve n equations for (n+4) unknowns.

**Experimental Plan**

The experimental setup to demonstrate GPS Common View Time Transfer Technique is shown in Fig. 2. Two GPS P code receivers, whose specifications are given in Table 4 below will be the main equipment required.

The two GPS receivers would be installed at Ahmedabad (AES) and Delhi Earth Stations (DES), along with modems used in TWSTFT Experiment. The built in Rubidium Clocks in the modems are used as Station clocks. The time interval between the 1 PPS derived from Rubidium clocks and the 1 PPS derived from GPS receivers are measured at AES and DES (DT A and DT B respectively) and recorded as time tagged data in a PC. A GPS C/A code receiver is used at AES and DES, for initial coarse synchronisation of the Rubidium clocks. This will make sure that the two atomic clocks are synchronised to **Table. 4: Specifications of GPS Receivers Required**

1. | Receive Frequencies | : 1575.42 & 1227.6 MHz (L1 & L2) |

2. | Codes used | : C/A code on 1575.42 MHz, P code on 1227.6 & 1575.42 MHz,(BW = 20.46 MHz) |

3. | Operation Mode | : The receiver should automatically acquire GPS satellites and synchronise its clock with GPS time, transmitted from the satellite. |

4. | Timing Pulse | |

(a) Accuracy of timing pulse | : The receiver should output 1 PPS pulse accurate to less than 40 ns to GPS time, transmitted from the satellite. | |

(b) Programmable Rate | : 0.1 sec. to 20 sec. | |

(c) Specifications of Pulse | : + 12 V DC, 25 msec rise time | |

5. | Antenna | : Choke Ring |

6. | Data Logging | : Internal data logging of Satellite Navigation data received as well as pseudorange & carrier phase measurements on L1 and L2. |

7. | Additional Features | : (1) A built in software to remove ambiguity in carrier phase measurements in L1 & L2 and compute ionospheric propagation delay (2) A built in software for relative precise antenna coordinate determination (of the order of few cms.) from carrier phase measurements. |

each other within about 60-80 ns. It is made sure that the Rubidium clocks are allowed to run freely, after initial synchronisation. It is also made sure during the experiment that the GPS P code receiver are locked to a common GPS satellite and its 1 PPS locked to the received 1 PPS from that satellite. Along with time tagged data, the GPS Navigation Data is also recorded. The data collection for GPS Time transfer Experiment is carried out round the clock for atleast about 3 months. .The TWSTFT experiment & data collection is done for about 1-2 hours daily during the period of GPS data collection. During the experiment, meteorological data (viz. Pressure, Temperature & Relative Humidity) are also recorded atleast at intervals of 15 minutes, using automatic meteorological sensors.

The following are the major equipments required for conducting the experiment.

Two Dual channel P code GPS Receivers (According to specifications laid down in Table 4).

Two Time Interval counters (With a precision of time interval measurement better than 1 nsec).

Two modems with built in Rubidium Clock, a GPS Single Channel C/A code receiver for Coarse time synchronisation of atomic clocks & Time interval counter.

Four PCs with printers.

Two Earth Stations and a satellite transponder.

A software for data analysis (To be developed).

Automatic Meteorological data recorder

The specifications of Time Interval Counter, required for the experiment are given in Table 5.

The specifications of the meteorological data recorder is given in Table 6. **Table. 5: Specifications of Time Interval Counter Required**

1. | Internal Oscillator Frequency | :5 MHz (Should be able to phase lock to an external atomic frequency standard) |

2. | Oscillator Stability | : Better Than 5X10-11 |

3. | No. of Channels | : Min. 2 |

4. | Time Interval Measurement accuracy | : 25 to 100 ps |

5. | Range | : 100 ps to 10 s |

6. | Sample size | : 1 to 100 per second |

7. | Interface | : RS 232 or IEEE 488 |

8. | Power Supply | : 230 V AC, 50 Hz. |

9. | Temperature | : 0 to 550C (Operational) |

-40 to 700C (Storage) | ||

10. | Humidity | : 5% RH @ 400C |

**Table. 6: Specifications of Meteorological data Recorder**

A) | Pressure : | |

1. | Range | : 700 to 1050 mbar |

2. | Accuracy | : 0.1 mbar |

3. | Resolution | : 0.1 mbar |

4. | Operating temperature | : 0 to +550 C |

5. | Response Time | : |

6. | Output | : 0 to 2.5 V digital for 700 to 1050 mbar RS 232 Compatible |

7. | Power Supply | : 5 V DC |

B) | Temperature : | |

1. | Range | : 0 to +550C |

2. | Accuracy | : 0.10 C |

3. | Resolution | : 0.10 C |

4. | Operating temperature | : 0 to + 550C |

5. | Response Time | : |

6. | Output | : 0 to 2.5 V digital for 0 to +550 C RS 232 Compatible |

7. | Power Supply | : 5 V DC |

C) | Relative Humidity : | |

1. | Range | : 0 to 100 % RH |

2. | Accuracy | : +/- 0.5% |

3. | Resolution | : 0.5 % |

4. | Operating Temperature | : 0 to + 550 C |

5. | Response Time | : |

6. | Output | : 0 to 1 V digital for 0 to + 100 % RH RS 232 compatible |

7. | Power Supply | : % v DC |

**Method of Data Analysis**

All Common view measurements, between two GPS receivers, satisfying the following conditions are only selected for data analysis.

All Common view data are of duration more than 15 minutes.

The elevation angles of the common GPS satellite, is more than 15°.

The standard deviation of the measurements, without applying any corrections is less than 40 ns.

Now the following corrections are applied to the observations. The coordinates of GPS antenna, at AES and DES (relative to each other) should be determined using the same GPS P code Timing receivers, with built in survey software and recorded carrier phase measurements & Navigation data). Using the broadcast ephemeris (recorded by the Receiver) and the accurate antenna positions determined, corrections are applied to the geometrical delay difference to the satellite between the two stations, for the observed measurements. This reduces the error due to satellite coordinates (because of common view) and station coordinates.

Precise ephemeris of the GPS satellites are available on WEB sites iscb.jpl.nasa.gov and lox.csd.edu, with a delay of 2-3 days. These values would be used to calculate satellite coordinates, instead of broadcast ephemeris. This would further reduce the geometrical delay difference.

The receivers also compute ionospheric propagation delay at AES and DES, using dual frequency measurements. The difference in the ionospheric propagation delay between the two stations is computed and also corrected in the observations.

Using the meteorological data collected during the experiment at AES and DES, tropospheric corrections are calculated at AES and DES, using the methodology described by Kirchner et al (1993). The difference between the tropospheric delay between the two stations is computed and corrected for in GPS observations. The relative calibration of receiver delays can be done by colocating the two GPS receivers and tracking common GPS satellites for about 1-2 days. The difference in time delays, for the two receivers A and B, for common GPS satellites (viz. (DT A – DT B ) will essentially give differential receiver delay, which can be applied as correction to the observations.

After applying the above corrections to the GPS observations, the inter comparison of GPS Common View and TWSTFT Techniques is done as follows.

The various steps involved in intercomparison are as follows.

The accuracy of time transfer using TWSTFT Technique can be determined using Allan Variance estimation. The values of corrected (DT A -DT B ) for common view of GPS satellites, computed only for the midpoint of the satellite track is used for data analysis. This is done through a linear regression of 15 minutes of data, through the second to second differences divided by two and computation of the average standard deviation.

Later Vondrak smoothing is performed on the midvalues over a period of 30-40 days, which acts as a low pass filter with a cut off period ranging from 0.5 to 2 days as given in Fig.3.

**Fig 3. Typical raw GPS data and Vondrak smoothed plot (Davis et al, 1995)**

The smoothed values are interpolated (using Lagrangian interpolation) for the time when TWSTFT measurements are available. Next the differences between the TWSTFT and GPS Common View values are plotted as given in Fig.4.

**Fig 4. (TWSTFT – GPS Common View) differences between PTB. Germany and NPL. UK (Davis et al. 1995)**

The Square root of Allan Variance of the GPS and TWSTFT data and their differences has been also used for evaluation of the performance of GPS and TWSFT Techniques.

**Conclusion**

In this report, the Principle of GPS Time Transfer Technique is described in detail. Two techniques viz. (1) Single Station Time Transfer Technique and (2) Two Station Common View Time Transfer Technique are described in detail. Typical error budgets and accuracies that can be achieved, using both techniques, are also discussed. It has been shown by several experiments conducted that GPS Timing accuracies achieved are between 2-5 ns. A brief description of Time Synchronisation implementation proposed in WADGPS in US WAAS and European EGNOS systems are also given, in this report. A brief outline of an experimental plan is given at the end, along with broad specifications of the GPS receivers required for Time synchronisation experiment. It is suggested that GPS Common View Time Transfer and TWSTFT Experiment should be conducted for atleast one month between Ahmedabad and Delhi, to study the comparative merits and demerits of both methods, before implementation in Indian WADGPS Programme.