Global Positioning System for Accurate Time and Frequency Transfer and for Cost-Effective Civilian Navigation

GLOBAL POSITIONING SYSTEM FOR ACCURATE TIME AND FREQUENCY TRANSFER AND FOR COST-EFFECTIVE CIVILIAN NAVIGATION

James L. Jespersen, Marc Weiss, Dick D. Davis, and David W. Allan

National Bureau of Standards, Boulder, Colorado

ABSTRACT ephemerides are available for GPS and that GPS time is based on atomic clocks. It is assumed This paper described some alternative applications of Global Positioning System (GPS) includ- that the civilian or clear-access code (C/A) is ing a method for very accurate time transfer and available during the observation periods. for civilian position location much less expensively than the designed Department of Defense method. The first part of the paper discusses FOUR METHODS FOR ACCURATE TIME TRANSFER several time transfer techniques with emphasis on what we call the "common-view" approach, and the second part considers the system for position There are four interesting methods to employ location. Both applications depend on the fact that accurate ephemerides are available for GPS GPS for accurate time transfer or for accurate and that GPS time is based on atomic clocks. It time and frequency comparisons (see Fig. 1). is assumed that the civilian or clear-access code (C/A) is available during the observation periods. First. Clock A and a GPS receiver are used to The accuracy of time transfer over a few thousand deduce from a GPS satellite's ephemeris, from km using the "common-view" approach is estimated at about 10 ns, and the accuracy of position clock A's location. and from received GPS time location at about 100 m. decoded from the same satellite, the time difference (Clock A - GPS time) (1). This method is the simplest and least accurate (estimated to be INTRDDUCTIPN better than about 100 ns with respect to GPS time) (21, but has global coverage, is in the receive- This paper describes some altm-native appli- only mode, requires no other data, yields receiver cations of GPS including a mathoa for very accurate prices that could be competitive on a mass produc- time transfer and for civilian position location tion basis, and could service an unlimited audi- which could, In principle, be doni? much less ence. Also, GPS time will be referred to UTC(USN0) expensively less expensively than the designed DO0 and will be know with respect to UTC(BIH), method. The f5rst part of the paper discusses UTC(NBS), and other major timing centers. several time transfer techniques with emphasis on Second, Clock A and Clock B at different what we call the "common-view" approach, and the locations anywhere on earth can be compared by second part considers the system for position making successive observations of the same GPS location. The primary difference between the two satellite clock, at least one of which will appear appllcations is that the time transfer technique above their horizons with delayed view times of requires the use? to know his location, while the less than 12 hours. This is analogous to the position location technique allows the user to clock flyover mode reported by Besson (3) and determine his position (and clock offset from GPS J. others. The time prediction error for the satel- system time, if he desires) by making observations lite cesium clocks to be used in the GPS satel- of signals from several satellites; the usual lites will be about 5 ns over hours. Since the scheme for determining position from signals 12 same GPS satellite clock will be vtewed by both A emanating from several known locations. Both and 8, biases in the satellite ephemeris may tend applications depend on the fact that accurate

1 to cancel depending upon geometry, etc. Accura- It appears that as GPS becomes fully devel- cies of from 10 ns to 50 ns are anticfpated. This oped, GPS time may become operational world time. method requires communication of the data betwen Methods 1, 2, or 3 above would yield significant A and B, and hence the logistics may limit the improvements in national and international time customers. comparisons. If commerclal vendors take advantage Third (see figures 1 & 2). two users with of some of these methods, receiver costs could be- Clock A and Clock 8 at different locations, but in made reasonable. The same basic receiver could be simultaneous common-view of a single GPS satellite used in methods 1, 2, or 3; the main difference clock. can take advantage of common mode cancella- would be in the software supoort, modems, and tion of ephemeris errors in determining the time local clocks. This method has the most attractive difference (tA- tB), The satellite clock error accuracy/cost ratio and is being pursued by NBS. contributes nothing. Since the GPS satellites are The theoretical advantages and disadvantages are at about 4.2 earth radii (12 hour orbits). for reoorted herein. continental distances between A and B (z 3000 km) the angle L (A-Satellite-B) will be 2 loo, and the SYSTEM ERROR ANALYSIS effects of satellite ephemeris errors will be reduced by a factor of more than 10 over the first Errors Resulting from Satellite Ephemeris Location method. Using a fairly straightforward receiver Uncertainty system, an accuracy of about 10 ns in measuring the time difference (tA- tB) appears probable. The time transfer error is dependent upon the This again requires data communication between A ephemeris or position error of a satellite. and 8. With improved ephemerides and propagation Common-view tine transfer yields a great reduction delay characterization, the potential accuracy in the effect oc thesa errors between two stations, limit for this method appears to be about 1 ns. A and 0, as compared to transfer of Lime from the The receiver should be relatively inexpensive. and satellite to the ground. Common-vie* time transfer given the reasonable costs of data modems and the is accomplished as follows: potential accuracies achievable via this method. Stations A and 9 receibe a commoii signal it makes it very attractive and cost effective for from a satellite and each records the national, and in some instances, for international local time of arrival, t and tBrcspec- A time comparisons. tively. Fourth, a method being developed for Geodesy From a knohledge of station and satel- by JPL (Jet Propulsion Laboratory) (4) has baseline lite position in a common coordinate accuracy goals of about 2 cm over baselines of the system, the range between the satellite order of 100 km. This method can be inverted to and each of the stations is computed, rA do time comparisons with subnanosecond accuracies. and rB respectively. The two clocks A and B separated by abeut 100 kn The time of transmission of the cammon have two broadband receivers with tunable tracking signal according to each station, A and antennae such that sequentially. 4 satellites can 8, is computed by subtracting from the be tracked concurrently at A and 8. The data are times of arrival, the times of propaga- cross-correlated after the fact, the same as fn tion from the satellite to each of the long basel ine interferometry, to determine location respective stations, i.e. , the time to and time difference (tA- ta). The data density travel the distances, rA and rB, are T~ fs higher than with the other approaches and the and T~ (the range delays) and are given baselines are relatively short, but the accuracy by T~ = rA/c and T~ = r B /c where c is is excellent. the speed of light. This speed is subject to other corrections as are treated later.

2 4) Finally, the time difference, rAB, of that location. The current values of ephemeris station A's clock minus station 6's error for the GP5 satellites are estimated at clock at the times the signals arrived about 10 meters in-track, i.e., in the satellite's is: direction of motion; 7 meters cross-track, and 2 meters radial (5). This corresponds to 41.23 ns rms error (square root of the sum of squaredc). The projected values for 1985 are 7 m in-track, 3 in cross-track, and 0.6 m radial, corresponding If the ephemeris of the satellite is off, the to 25.46 ns rms error (5). computed ranges from the stations to the satellite Notice that the rms errors make an elongated will be off an amount dependent on the way the ellipsoid and are dependent on satellite direction. ephemeris is drong and the geometrical configura- Thus, to compute the range errors to a given pair tion of the satellite-station systems. The advan- of stations for a given satellite location, one tage of common-view time transfer is that the needs to know the satellite direction at that computed bias is affected not by range errors to location. The satellite moves in a fixed plane in individual stations, but by the difference of the space with the earth rotating under it. two range errors. Thus, much of the ephemeris The program which computed the figures used error cancels out. To see how this works in an orbital plane making an angle of 63' with the detail, suppose the ephemeris data implies range ecliptic with the satellite moving west to east in delays of 'A and rb, but the actual position of the plane. As an approximation, the orbit was the satellite, if known correctly, would give assumed circular at 4.2 earth radii (12 hour range delays of rA = TA - AT^ and rB= r; - ArB. period). At a given latitude, the satellite direc- Then the error in time transfer would be ArAB = tion in degrees east of north is determined by the ArB - OrA, where rAB= rAB -AxAB is the true time orbital plane and whether the direction is north- difference (clock A - clock B) and where riB is erly or southerly. Corrections for the earth's the computed time difference from tne actual time rotation need to be included. Thus, each figure of arrival measurements and ephemeris data. Thus, was created by: 1) choosing a given pair of

"AB' tke time transfer errw due to ephemeris ground stations, a set of values for ephemeris error, depends not on the magn!tude of the range error, and whether the satellite was moving north errors, but on how much they differ. or south in its orbital plane; 2) for a given The error in time transfer, ArAB. as mention- location on a map containing the ground stations, ed above, depends on the locations of the two finding the satellite direction (a function of stations and of the satellite, as well as the latitude only) and three independent position orientation of the actual position error of the error vectors from the three different types of satellite. Figures 3 through 18 at the end of the ephemeris error; and 3) approximating AT^^ for paper give ArAB for some ground stations of inter- each of the independent position error vectors, est with different discrete levels of error shown then finding the square root of the sum of their as contour graphs dependent on where the satellite squares for the total ArAB at that location. In is. For each pair of ground stations, we have this way a chart of values of AT^^ was computed, selected contour graphs from A possible set of four which were then plotted ir! contour plots super- contour graphs for current and future typical imposed on a world map in cylindrical projection. ephemeris errors and for whether the satellite is Clearly, there are regions shown where the satel- going north or south in its orbital plane. Within lite will be below the horizon for one or both a particular graph, the contour level at a point stations, so the maps are over-inclusive in this corresponds to the root-mean-square value of ArAB regard. when the common view satellite is directly above

3 The AzAB were approximated in the following and were half-way in between the two stations, the way. Let us fix a coordinate system at the earth's effect of the ephemeris errors due to radial and center to define basis vectors. Then let and on-track go to zero! Since the GPS satellites are be the position vectors of stations A and B, so far out, 4.2 earth radii approximately, the repectively, and 2 the position vector of the direction vectors pointing to the satellite tend satellite. Then the range vectors, pointing to to be close to parallel, thus cancelling most of the satellite from the ground stations, are: the ephemeris error in all cases where common-view is available.

Errors Resulting from Ionosphere Let 6, and Sa be the unit vectors in the direc- tions of EA and Ra respectively. Then the ranges The ionospheric time delay is given by At = are: (40.3/cf2) TEC (seconds) where TEC is the total number of electrons, called the Total Electron Content, along the path from the transmitter to the receiver, c is the velocity of light in meters If 2 is the satellite position according to its per second, and f is the carrier frequency in Hz. ephemeris, but the true position is + e then TEC is usually expressed as the number Df electrons the new unit vectors, ii and ii, are the same as In a unit cross-section column of 1 square meter the old to first order: area along the path and ranges from 1OI6 electrons per meter squared to loi9 electrons per meter squared. At the 1.575 GHz C/A carrier frequency for the GPS satellite system and for a TEC of 10l8 where a is the angle between 3, and 'A. So. to electrons per meter squared, one computes the first order, the new ranges are: delay of 54 ns which is possible for low latitude parts of the world. For these low latitudes and solar exposed regions of the world, tine delays exceeding 100 ns are possible especially during Thus, the range errors are approximately: periods of solar maqimmum. Clearly, the TEC para- meter is of great importance in the GPS system. ArA = rA - rA= iA-As and Shown in Fig. 19 is a reproduction of a figure rh ra = gB-hs, Or B = - taken from a paper by J. A. Klobuchar (S), this figure clearly shows during a solar maximum year, so: 1968, that the range of delays vary from about 5 to 40 ns, being maximum near the equator and near the noon path. This figure refers to the extra delay that would be encountered if the satellite We see that the time transfer error increases as was directly overhead. At lower elevation angles, the vectors pointing to the satellite from the the slant path through the ionosphere lengthens. ground statlons become less parallel up to the which increases the ionospheric component of maximum of fl times the ephemeris erfor when they delay. If io is the total path delay when the are p/rpendicular, down to zero when they ate satellite is overhead, then the path delay, T, at parallel. Because of the dot product, some inter other elevation angles, E. is given to a good esting and very helpful situations nay arise. For approximatlon by I example, if the path of the satellite were at right angles to the line between stations A and B

4 Fig. 20 is also from Klobuchar's paper and Errors Resulting From Troposphere shows the actual vertical electron content at Hamilton. MA looking towards the ATS-3 satellite In transferring time between ground stations for every day of the year, and here again one sees via common-view satellite, one records the time of the variations from the order of 5 ns to 40 ns. arrival of the signal and computes the time of In studying these graphs, one observes two transmission by subtracting the propagation time. very important things: 1) the total delay at The propagation time is found by dividing the nighttime and/or high latitude is much smaller range to the satellite by the velocity of light. . than at daytime, and 2)the correlation in absolute However, moisture and oxygen in the troposphere delay time covers much larger distances when one have an effect on the velocity of propagatton of moves away from the equator and the vicinity of the signal, thus affecting the computed time of noon; the conclusion being that a significant transmission and therefore, the time transfer. amount of common-mode cancellation will occur This effect is dependent on the geometry, the through the ionosphere at short or long baselines latitude, the pressure, and the temperature, and between A and B if observations are made at either may vary in magnitude from 3 ns to 300 ns (7). high latitudes and/or at nighttime. These cancel- However, by employing reasonable models and using lation effects, as can be seen from Fig. 20 over high elevation angles, the uncertainties in the several thousand km, will cause errors of less differential delay between two sites should be than 5 ns. For short baselines less than 1000 km, well below 10 ns. Later on, if needed, the magni- this common-mode cancellation will cause errors of tude of the troposphere delay can be calculated the order of or less than about 2 ns. with uncertainties which will approach a nano- Clearly, this gives a definite direction as second. to how one should proceed using the common-view GPS time and frequency transfer technique proposed Relativistic Corrections in this paper. Even though the total ionospheric delay may be very large at certain times and In navigational and time transfer systems places, there are ways to pick and choose, which where great accuracy is required, relativistic would allow one to get large amounts of common- effects become important. The relativistic cor- mode cancellation and which would allow one to rection is comprised of three components: a achieve with some care, time and frequency transfer correction for gravitational potential; another accuracies approaching a nanosecond. for clock motion; and finally, for earth rotation. Beyond the common-mode Cancellation, if one In many instances, all three components must be had access to the measurements of the total elec- considered. We refer the reader to ref. (a), tron content, then clearly one could use the model which provides numerous examples in a variety of to actually calculate the delay over the two paths applications. However, in this paper, which of interest, or if the monitor stations for the focuses on the common-view time transfer technique TEC were nearby, given reasonable correlations and on passive reception of GPS signals for posi- from one monitor station to another. one could tion location, only the last component is important interpolate the TEC so that on an ongoing basis, --the correction for earth rotation. Figure (21) the differential delay variations could be calcu- illustrates why this correction is needed. lated again to the order of a nanosecond. Also, Let be the position of+the satellite at if one used both the L1 and L2 frequencies from the instant of transmission and zA be the earth the GPS satellite, the TEC could be calculated. station position at the same instant. The differ-

ence between T and the time, TI, it would take for the signal to propagate if the ground station had not moved due to earth rotation is given approxi- A way to calculate and to conceptualire this mately by correction due to earth rotation (sometimes called the Sagnac effect) iS the following. Consider a

-10 k x rA/c2 T - T' = -Ar' vector with its tail at the center of the earth and its head at the location of the GPS satellite where T and T' are as shown in figure 21, and at the time of transmission of a signal. Let the where w is the rotational angular velocity- of the head of the vector follow the signal to its recep- earth, c the speed of light, and k is a unit tion point--say at some ground station receiver. vector in the direction of the earth's rotation The vector in so doing will sweep out an area, A. axis. If there wre no earth rotation (w = 0). which has a projection on the equatorial plane,

T = TI as one would expect. As the equation shows, A'. The correction is given by: the magnitude of T - T' depends upon the relative positions of the earth station, the satellite, and the direction of the axis of earth rotation. For GPS satellites with a nominal 12 hour circular where A' is measured in kilometers squared and is

orbit. if one assumes T = TI, then errors of considered positive (negative) when the area swept nearly 100 ns for the "worst case" geometry could Is eastward (westward). result. This calculation can be reduced to a few Error Consideration in Receiver Design simple operations. The satellite position vector, $, can be computed in earth-fixed coordinates Since the primary goal of the NBS receiver from the GPS C/A data. The earth station position design is accuracy in time and frequency transfer, vector, tA,should be known. Then the distance the approach taken tends to be somewhat different between them at the instant of transmission is: than perhaps may be considered in a navigation receiver. The fundamental concern is that whatever time delay exists within the receiver be extremely stable (of the order of a nanosecond). This, of The correction term can be simplified if we con- course, can be most easily accomplished if the sider the vector identity: total additional delay (beyond cables) is minimized through the receiver. We also are working toward minimum parts cost, while still providing full automation capability. In addition, we are design- The term on the right is simply the z-component of ing into the current units being built by NBS, the cA x cross product which equals: self contained microprocessor control and a (1 ns) time interval counter. 'Ax 'by - rAy rbx The total receiver will have high accuracy, is designed to be very stable, and will be totally Thus, we find: automated and self-contained. This allows one to take maximum advantage of appropriate seeing time of the satellites, minimize ionospheric delay and delay variations. and maximize the common-mode cancellations between two sites. We estimate a For this, the values total receiver delay, excluding cables, to be less known. All we need compute is 16 and perform the than 30 ns and the receiver instability to be less few indicated operations. than 2 ns. This stability assumes a 16 db antenna, which tracks the satellite. and a 1 Hz receiver

6 loop bandwidth. Receivers can be straightforwardly The future accuracy potential is quite excit- calibrated in a side-by-side mode as to the dif- ing because there is significant anticipated ferential delay, and since one uses the concept of improvement in the accuracy of the ephemerides for common-mode between two sites, only the differen- the satellites, and that error contribution should tial delay is important for accurate time and be reduced considerably. The ionospheric delay frequency transfer between sites A and B. can, in fact, be calibrated at or below the nanosecond level, and the tropospheric delay can also CURRENT AND FUTURE SYSTEM ACCURACY POTENTIAL be modeled to a few nanoseconds. As we gain more AND SYSTEM COST experience with receiver design and total delay and delay stability, it is believed that its When all of the estimated errors from any of accuracy can also be improved to the nanosecond the potential error sources are combined, one level or below. Ultimately, over the next several obtains an absolute accuracy of time transfer of years this common-view approach could be developed better than 10 ns, and a time stability of the with accuracies of the order of a nanosecond. order of a nanosecond. This means that on a 24 hour basis, one could measure absolute frequency POSITION LOCATION differences between remote sites to a few parts in lo1'. We anticipate a front end parts and assembly In the timing mode, it is assumed that the cost (not including development costs) of well satellite and the user's geographic locations are under $10,000. This includes the computer and known, so that range delay can be calculated. In automatic control system as well as a 1 ns time the navigation mode, the user's position is deter- interval counter; but, of course, does not include mined by making observations of signals from the necessary testing, documentation, and costs several satellites. incurred by a vendor if they are to develop and If the user's clock is synchronized to GPS put into production such a system. The concept system time (or the equivalent if the offset is being developed has the significant advantage that known), the range between user and a particular the main costs will be front end costs as the satellite can be determined directly by simply system should not be labor-intensive after being measuring the time it takes a signal to travel set in operation. It also has the significant from the satellite, whose position is known, to advantage over two-way satellite systems of operat- the user. One such measurement puts the user on ing in the receive only mode, which should allow a the surface of a sphere concentric with the satel- much larger user audience for this kind of receiver lite and with radius equal to the range to the as well as avoiding all of the problems of clear- satellite. Three such measurements to three ances for operating a transmitter, which are different satellites determine the user's position necessary for a two-way satellite system. There as being at the point of common intersection of have been some indications that, because of the the three spheres. excellent signal-to-noise on the C/A code, the If the user does not know GPS system time, signal strength would be degraded, so that adver- then his position, as well as the relation of his sary users would be denied the full accuracy of clock to system time, can be determined from the system. From a time and frequency point of observations of signals from four satellites. In view, this may or may not be a serious problem mathematical terms, there are four unknowns (the depending on how and when all this is done. For user's location in space (x, y, and z) and the example, if there was a degradation in signal-to- unknown time offset) and four equations which noise, one could simply do averaging since there relate the user's position, the satellite posi- is plenty of time to average over a pass, and in tions, and the clock offset, so that x, y, z, and this case, one would still get comparable accuracy t can be determined uniquely. resu 1ts .

7 Ideally, one would like to make all measure- always mare unknowns than there are measuntnts, ments simultaneously. However, this, in effect, and the user's location cannot be determined. requires as many receiving and processing channels However, a good deal is known about the clock as there are satellites to be measured. The performance, and it is usually possible to express alternative is make measurements serially in time the amount of clock offset change between two with just one receiver. However, this requires measurements. that the several measurements be "coherent" in There is much in the literature on clock time. As a simple illustration, consider a user performance, so we will not pursue it here, except at locations x, y, and z and two satellites , S1 to say that most models include terms for systema- and S2, at xsl, YS1,rS1 and xs2, yS2, zs2 (see tic and random effects. Thus, formally there may figure 21). Suppose the user first measures a be some initial fractional frequency offset, which signal from S1 at time tl. If the user clock and changes systematically in time along with the GPS system time are synchronous, then, as we random components. stated previously, the range to the satellite can With this model then, we can express time be determined directly by simply measuring the error accumulation, T(t), in the form time it takes the satellite signal to reach the user. However, in the general case, there will be some unknown offset, t, between system time and user time. Thus, what is measured is not the where c(t) is the random component, 0 is a coef- range, but what is called the "pseudo-range," ficient which defines the systematic frequency which contains a term expressing the error due to drift, and Ro is the initial frequency offset (9). clock offset. For the coordinates defined above, An expression of this type, coupled with the the pseudo-range, rl, to S1 is: pseudo-range measurements, provides enough information to solve for the user's position and initial clock offset. As a practical matter, however, clock errors accumulated between measurements may be small where c is signal speed. enough to ignore, when compared to other error Suppose now the pseudo-range to S2 is measured sources. The receiver described in this paper at time t2, later than tl. Since no clocks are requires at most 10 minutes to "acquire" a GPS perfect, the clock offset will change by an amount, signal and measure the pseudo-range to 4 GPS At, over the interval t2- tl, so that the pseudo- satellites. If we assume that the frequency range r2 to S2 is offset, Ro, and systematic frequency drift, 0, are known, then the only term of concern is e(t); the random component. With typical commercial frequency standards available today (both rubidium and crystal), the amount of accumulated error for a More generally, the pseudo-range, rn, to the period of 10 minutes is less than a nanosecond, nth satellite is considerably under the uncorrected ionospheric and tropospheric errors. If careful corrections are made for these effects, then clock error accumulation will have a magnitude which is comparable to the corrected atmospheric delay effects as discus- where P = 1.2.3, n-1 represent the sed earlier. clock offset change between successive measure- As we pointed out, the system was primarily ments. If the Ati are unknowns, then there are designed for common-mode time transfer between fixed locations. Thus, the emphasis was on re- meter) and GDOP is 4, then the 1 u radial error in ceiver stability and not on absolute receiver three-dimensional space is 1 meter x 4 = 4 meters. delay. However, with measurements to four satel- The degree to which the user will want to lites where only a position fix is required, it is correct for the various sources of error will not necessary to know absolute receiver delay. depend upon the position fix accuracy required. Receiver delay represents a common bias for all Let's consider what might be termed a "worst case" measurements, so that the term (ct) in equation 1 example. Normally, if satellites below 10 degrees could be rewritten in the form, c(t + tR),where, elevation are not observed, ionospheric delay will as before, t is clock offset and tRis receiver not exceed 90 ns and tropospheric delay will be delay. Now, when the equations relating the four under 80 ns. Assuming 0 db antenna gain and a measurements are simultaneously solved, the quan- 1 Hz loop bandwidth, the signal instability is tities obtained are x, y, z, and c(t + tR). Of about 30 ns, as we stated earlier. We must also course, if one wants to know clock offset t, it is consider the error due to the Sagnac effect. As necessary to know tR. With the present system, it we saw in the previous discussion, it depends upon is estimated that tRis of the the order of 30 ns the geometry of the user and the array of satel- and can be measured with a precision of t5 ns. lites he is observing. Further, the correction In many position location problems, it may may be negative or positive for a particular not be practical to use a tracking antenna of the satellite. For the sake of our illustration, we kind we envisioned for the time transfer applica- will assume that the error due to the Sagnac tion. First, the user may not know his position effect for all the observations produces a compos- well enough to point the antenna to the satellite, ite error of 100 ns. The total error due to all of and second, such an antenna may be unwieldy for these sources is 300 ns or about 100 meters. If mobile applications. If we assume an omni- we assume a "worst case" GOOP of 4, then the directional, 0 db gain antenna, then the signal position fix error in three-dimensional space is stability will be degraded from 2 ns to about approximately 400 meters. Considering the nominal 30 ns, which is of the same order of delay error cost of the equipment, this is quite a satisfactory introduced by the tropospheric and ionospheric result and is adequate for many applications. delay. Taking the Sagnac effect into account and with When the satellites are used in the time even rather crude modeling of the ionospheric and transfer mode, range error translates directly tropospheric delays, the position fix can probably into time transfer error, while in the navigational be improved by at least a factor of 3. Of course, mode, the geometric arrangement of the satellites at a fixed location, it is possible to average and the user must be taken into account. The many measurements over a long period of time, so impact of geometry on position fix accuracy has that modeling errors become the 1 imiti ng factor-- been studied extensively (see Ref. 10 for a good not signal instability. summary) and is usually referred to as "geometric In the discussion so far, we have assumed dilution of precision" (GDOP). The position fix that the user is fixed in space--which may or may error can be expressed as the product of GDOP and not be the case. If the user movement is small the satellite range error (assuming it is the same over the observation time compared with the posi- to all satellites). Small values of GOOP indicate tion fix accuracy required, then the movement can a good geometrical arrangement of the satellites, be ignored, just as we ignored accumulating clock while large values fndicate poor geometrical error over sufficiently short observation periods. arrangements. Most users, after all 18 satellites However, if the motion cannot be ignored within have been launched, should be able to select four the required position fix accuracy, then extra satellites such that the GDOP never exceeds 4. information is required to make the observations Thus, if the rms time error is 3 ns (about 1 spatially coherent, just as we needed a model for

9 clock error (Eq. 2) to provide time coherence when if desired). Two prototypes are being built at the observations are not sufficiently close in the National Bureau of Standards to test these time. If the user's motion is constrained to the ideas. If these prototypes work as planned, the surface of the earth (boats, etc.). then local above approach would provide a very cost-effective heading and speed provide the necessary informa- navigation approach available also to the civilian tion. Of course, if the user is moving in three- sector. dimensional space, an extra "dimension" of information is needed. As a final point and as we REFERENCES stated earlier, there has been some discussion that the C/A signal-to-noise might be degraded. 1. Spilker, James J., "Global Positioning System: As in the time transfer case, this presents no Signal Structure and Performance Characteris- problem for determining the location of fixed tics," Stanford Telecommunications, Inc. positions. However, for moving vehicles, this Report, 1 June 1978, $TI-TM-8802. could be a serious problem, since there would not 2. Putkovick, K., "Initial Test Results of USNO be sufficient time to average the signal to obtain GPS The Transfer Unit," Proceedings of Fre- the desired position fix accuracy. quency Control Symposium. Philadelphia, PA, 28-30 May 1980. CONCLUSIONS 3. Besson. J. (1970), "Comparison of National Time Standards by Simple Overflight," IEEE In conclusion, we have shown that one-way Trans. on Instrumentation and Measurement satellite transmission from a GPS satellite in IM-19(4), 227-232. common-view at two sites allows one to do accurate 4. MacDoran, Peter F., (1979). "Satellite Emis- time transfer to 10 ns or better. This accuracy sion Radio Interferometric Earth Surveying, is achieved because of common-mode cancellations SERIES - GPS Geodetlc System," Bulletin of several contributing errors in the system. The Geodes ique. system furthermore has the potential to achieve 5. Private Communication, Albert Bierman, Aero- accurate time transfer of the order of a nano- space Corp. second. The estimated stability of the receiver 6. Klobuchar, J. A. (1978), "Ionospheric effects delays and all contributing error delays should on Satellite Navigation and Air Traffic yield stabilities of the order of 1 ns, which Control Systems," NATO AGAR0 proceedings, means that on a 24 hour basis, frequency transfer Lecture Series No. 93, Recent Advances in can occur with an accuracy of the order of a part Radio and Optical Propagation for Modem in 10". Communication, Navigation, and Detection We have also shown how the receiver for time Sys tems . transfer could be used for position fixing. Even 7, Martin, E. H. (1978), "GPS User Equipment with "worse case" geometry and no corrections for Error Models ,'I Navigation 25: 2, 201-210 ionospheric, tropospheric, and receiver delay, it Sunmer (1978). appears as though the three-dimensional error 8, Ashby, Neil and Allan. David W., Practical would not exceed 400 m. With crude modeling. it Implications of Relativity for Global Coordin- should be possible to reduce the error to about ate Time Scale," Radio Science 14:2, 649-669 100 m. With averaging at a flxed location, even July-August 1979. better accuracy can be obtained. The present 9. Hellwig, Helmut, "Microwave Time and Frequency receiver is software controlled and there is Standards." Radio Science 2:2. 561-572 sufficient unused memory to incorporate the neces- July-August 1979. sary mathematical steps to solve for the user's location (and clock offset from GPS system time,

10 .

10. Milliken, R. J. and Zoller, C. J., "Principle 2 m radial corresponding to of Operation of NAVSTAR and System Character 41.23 ns nns (square root of the istics," Navigation g:2,95-106 Summer 1978. sum of the squares divided by the speed of lfght). The even-numbered

FIGURE CAPTIONS figures use error values projected ~ for 1985: 7 m in-track, 3 m Figure 1. Four methods of time transfer and cross-track, and 0.6 m radial their approximate accuracies corresponding to 25.46 ns rms. The using GPS: satellite direction is always Upper left, using data from the northerly in the ''a'' figures and Satellite to find GPS time and southerly in the "b" figures. The comparing a local clock with ground station locations are marked the GPS time scale. with an "x". The contours in a Upper right, using one satellite to given1 figure are spaced for equal decode GPS time at two differ- error values with error increasing ent locations and times to as one goes from dotted to dashed compare both clocks with the to solid to dotted lines. Figures GPS time scale and hence with 3a, 3b, 4a, and 4b are examples of each other. all four combinations; the odd Lower left, measuring the time of numbered "all figures and the even arrival of a common signal numbered "b" are deleted thereafter from a satellite at two loca- because their contour may be infer- tions to compare the computed red from studying Figures 3a, 3b, time of transmission according 4a, and 4b along with the station to the two clocks and thus combination of interest. compare the clocks. Lower right, recording signals from four satellites at two stations to determine locations and time differences. Figure 2. lime transfer via a satellite in common view of two ground stations indicating that fairly large errors (100 m = 333 ns radial error or 10 m = 33 ns in-track or cross- track error) in satellite ephemeris can cancel to a few ns time transfer error. Figures 3-18. Contour graphs of the error in common-view time transfer for various choices of ground stations, satellite direction, and ephemeris error. The odd-numbered figures use current ephemeris error estimates: 10 m in-track, 7 m cross-track, and

11 * . .. ..- -.. .

TIME AND TIME TRANSFER ala GPS.

GPS Time Clock Fly-over (-100 nr) (-50 a)

Differential VLBl Techniques Common.ui.w ova; short bse liner (Si0 nr) (SYSit', - ...

Figure 1.

12 NAVSTAR

A = USNO - B = NBS 8 = 9.2O

4.2 earth radii *=> 4 ns sync errc

for 100 m Sr or 10m 8+

Figure 2.

13 .

NBS-BIH Time Transfer Erro;--- from rms ephemerts error - 4 I. 23 ns .. uoits-nanoseconds, direct io?-nwth c.nn /L/ ns between contours t

e Lc?~Lt ude Figure 3a. --

14 NBS-BIH Time Transfer Error from rms ephemepts error - 41.23 ns un its-nanoseconds, d bectLon-sc uth A85 ns between contours t

Lonqttude Figure 3b.

15 NBS-BIH TimeTransfer Error from rms ephemeris error - 25.45 FIS units-nuncseconds, dtrectton-narth

16 .

Lmq It de Figure 4b.

17 NBS-NRC Ti" Transfer Error . from rms ephemerts error - 41.23 ns units-namseconds, btrectton-sc uth

0 3

4, 0' M

Lmqhude Figure 5b.

18 NEE-PTB Tlme Transfer Error. from rms ephemeris error - 4L23 ns un ks-nanoseconds; d ;.rest Lon-sc uth 609 ns between contours

3 -2 3 0 3

Q, 0 )3

LonqLt ude Figure 7b.

19 NBS-NRC Time Transfer Eva- from rms ephemerts error - 25.46 ns unLts-nmoseconds, direct:Lorl-noPth

167 ns&- between- .--e.._ . . contours t

Lonqltude figure 6a.

20 Lonq Ltuds Figure 8a.

21 . .

0784 ns between contours C

Lorlqltude Ffgure 9b.

22 un Lts-nanoseconds, dlrecttan-north- 0561 ns between contours t

3 -2 3

Figure loa.

23 NBS-USNO Time Transfer Error from rms ephemerts error - 41.23 ns units-nonoseconds, dtrectton-south

LanqLtude Figure llb. . .

Lorlqtt ude Figure 12a.

25 .

umts-nanoseconds, dlrecti,o-=south .lo2 ns between contours

Lmqtt ude Figure 13b. NBS-Vmdenber Time Transfer Error fromD- pms epa emerls error - 25.46 ns un Lts-nanoseconds, d trect ton-no&G- .091 ns between contours

e c 0' M _.-

0 3

.Lonqttude Figure 14a.

27 c

Lcnqltuje Ffgure 1%.

28 c

29 ac, 3 3 -J 3 0 3

30 USNO-BIH Time Transfer Error- . from rms ephernerts error - 25.46 ns mhs-nanoseconds, dlre&,on-nort,h

e Loqq tt ude Figure 18a.

31 . a

IONOSPHERIC TIME DELAY (8ENT MOOEL) (NANOSECONDS AT 1.6 CHr) OOh UT, MARCH 1968

8 Worldrido averrge vrrticrl lonorphrric time delay at 1.6 GHt for 00 hours uaiverrrl tis* Watch, 1968, rn avorage rolar marisua yoar. 0-1 d

WW0091 1V SON033SONVN

P .-C -3 L. cri v) 9 i 5 af I: f zbJ&

L W J W J 0a

wf >

‘ 33 Fig. 2 1 Corrections due to unh roution for one-way satellite tr.nsmiUioas. such u in be GPS system [Schuchmun ond Spike, 1977; Euirson et a/., 1977).