Time, Clocks, Day

IN NO VA TION

10 12 or better. But over the long tern1 , its fre­ quency can drift by several parts in 10 11 per Time, Clocks, day. In order to keep two clocks using quartz crystal oscillators synchronized to l microsec­ and GPS ond . you wou ld have to reset them at least every few hours. The resonators used in atomic clocks have Richard B. Langley surpassed considerably the accuracy and sta­ bility of quartz resonators. University of New Brunswick

ATOMIC RESONATORS An atomic clock contains an oscillator whose oscillati ons are governed by a particular erating the satellite's signals. But just what atomic process. According to the quantum pic­ is an atomic clock? Before we answer ture of matter. atoms and molecules exist in thi s question, let"s examine so me of the well-defined energy states. An atom that bas ic concepts associated with clocks and fa lls from a higher to a lower energy state timekeeping. emits radiation in the form of light or radio waves with a frequency that is directly pro­ THE QUARTZ CRYSTAL RESONATOR portional to the change in energy of the All clocks contai n an oscillator, which in atom. Conversely. an atom that jumps from turn contains a frequency-determining ele­ a lower energy state to a higher one absorbs ment called a resonator. A resonator is any radiat ion of exactly the same frequency. The "Innovation" is a regular column in GPS device that vibrates or osc illates with a well­ existence of such quantum jumps means that World featuring discussions on recent defin ed frequency when excited. such as gui­ atoms can be used as resonators to govern advances in CPS rec/mology and irs tar and viol in strings, pendulums. and quartz clocks precisely. given a way to tap their reso­ appl icatiom as well as on the fundamentals crystals. Once excited, the oscillations of a nance. Scient ists found such a way in the of GPS posirioning . In this issue 1ve present resonator slowly die out due to energy loss. late 1940s, using the ammonia molecule as a Tutorial 011 one of the underlying principles A perfect resonator has no energy loss and a resonator. However. although the ammoni a of GPS: the precise measurement of time. wi ll osci llate forever. molec ule was a very good resonator com­ This column is coordinared by Richard To be usefu l in an osc ill ator, a resonator pared to what had been prev iously used in Langley and Alfred Kleusberg of the must be sti mulated or energized repeated ly. clocks, certain problems resulted in the reso­ Deparrmenr of Sur veving Engineering at the This process is accomplished in a quartz crys­ nant frequency being somewhat unstable. So Universi(\· of New Brunswick. We welcome tal osciJlator by taking advantage of the piezo­ sc ient ists turned to the cesium atom and by your comments and suggestions of topics for electric effect: An extern al voltage applied the mid- 1950s had built the first ces iu m fi.aure columns. across opposite faces of a piece of quartz crys­ clocks. tal cut in a prescribed way causes the crystal The cesium atom, in its naturally occur­ Time is of the essence. This tatement. used to expand or contract depending on the po­ ri ng form. Cs 133. consists of a nucleus primaril y to characterize the clauses in cer­ larity of the voltage. The inverse is also true: containing 55 protons and 78 neutrons sur­ tain legal documents. also nicely describes forcibly deforming the crystal causes a small rounded by a swarm of electrons. The outer­ the nature of the Global Positioning System. electrical potential to develop. A crystal con­ most electron is in a shell of its own. Both The basic measurement a GPS receiver nected to an alternating voltage source wi ll vi­ the nucleus and this outer electron spi n on makes is of the ti me required for a ignal to brate. The vibrat ions. in turn. will generate their axes and, being charged. generate mag­ propagate from a particu lar satellite to the re­ an alternat ing voltage. These generated sig­ netic dipoles. ln other words. they act like ceiver. Multiplying this time interval by the nals interact with the applied voltage in such tiny bar magnets. The electron ·s magnetic di­ speed at which the signal propagates - the a way that the vibrations and the resultant cur­ pole is either parallel to the nucleus's dipole speed of light - converts it into a range or rent fl ow are at a maximum at a particular fre­ (both north poles pointing in the same direc­ di stance. Such a one-way ranging technique quency - the resonant freque ncy of the crys­ tion) or antiparallel. These two orientations requires accurate timekeeping in both the sat­ tal. which is determined by the size of the correspond to two energy states of the atom. ellite and the receiver. In this article. we' ll crystal and how it is cut. Frequencies range and transitions between these states form the investigate how this accuracy is achieved and from 10 kHz to well into the VHF range. basis of the cesium clock . examine some of the intricacies of time that Accuracy (how well the oscill ator can be A block diagram of a cesiu m clock is are important in GPS positioning. tuned to a specified frequency) and stability shown in Figure I . Cesium. a soft. silvery The high posit ion ing accuracy of GPS is (how well it stays on freq uency) determine metal . is heated in an oven to a couple of hun­ due. in part. to the use of atomic clocks the quality of an osc illator. The oscillator's dred degrees Celsius. Individual atoms boi l co control the generation of the signals stability is measured in terms of the relative off and pass through a magnetic state selec­ transmitted by the satellites. For redundancy, change in its frequen cy over a certain period tor, which defl ects atoms in the higher en­ each Navstar GPS Block II satell ite contains of time. A high-quality quartz crystal oscil­ ergy state. allowing only atoms in the lower four atom ic clocks, one of which is selected lator kept at a constant temperature by a min­ energy state to enter a microwave resonance by the spacecraft controllers to prov ide the iature oven has short-term stability (over pe­ cavity. Whi le in this cavi ty, which operates frequency and timing requirements for gen- riods shorter than about an hour) of a part in on the same principle as the home micro-

38 GPS WORLD No

sium or rubidium clocks because they gener­ ally are more costly and less rugged. A ma­ Feedback ser has been employed in a sub-orbital rocket flight , but one has yet to be fl own in a satel­ lite. Plans to modify the Block II satellite qualification model for an Advanced Clock/ Ranging Experiment include a hydrogen ma­ Detector ser clock as one of the four clocks in the satel lite.

JUST A SECOND - Before 1956. the fundamental unit of time Cesium Resonance cavity was the mean solar day. which is based on oven the rotation of the earth on its axis. But it Magnetic Magnetic was known for some time that the earth· s ro­ state selector state selector tation speed. and hence the length of the day. was not constant due to the action of ocean tides, atmospheric winds, and even mo­ Figure 1. Basic operation of a cesium atomic clock tions in the earth ·score. Although the larger wave oven. the cesium atoms are subjected form of a very low pressure gas. are con­ variations cou ld be measured and time scales to a radio signal synthesized from the output tained in a glass cell situated inside a micro­ corrected to account for them. it became nec­ of a quartz crystal oscillator. The frequency wave resonance cavity. A microwave signal essary to define a new fundamental unit of of this signal is very close to that of the en­ whose frequency is tuned by a feedback loop time. In 1956. the second. defined in terms ergy difference between the two states of the induces transitions. The short-term stability of the period of the earth· s orbit around the cesium atom described above. A certain num­ of rubidium clocks is almost as good as that sun. became the new standard. But this stan­ ber of atoms absorb this radiation and change of cesium clocks. In fact. over one-day av­ dard. known as the ephemeris second. was their state. eraging periods. the rubidium clocks in some short-lived. When the atoms leave the cavi ty, they of the Block I satellites had stabilities of 1.6 Because the frequency of the cesium reso­ again go through a magnetic gate . wh ich di­ parts in 10 13 or better. However. the fre­ nator is so stable, the development of the ce­ rects atoms in the higher energy state toward quency of rubidium clocks tends to wander sium clock made it poss ible to define the sec­ a detector. The detector produces an electri­ over longer periods. resulting in poorer per­ ond such that it cou ld be accurately realized cal signal whose intensity is related to the formance. Each Block II satelli te contains in a laboratory without resorting to a long se­ number of atoms it intercepts. This signal is two rubidium clocks in addition to the two ce­ ries of astronomica l observations. In 1967, fed back to the quartz crystal osci ll ator and sium clocks. is used to control the oscillator's frequ ency The third and most stable of the atomic and. hence. that of the synthesized radio clocks is the hydrogen maser. The word ma­ signal. Through this feedback process. the ser is an acronym for microwave amplifica­ frequency is automatically adjusted to maxi­ tion by stimulated emission of radiation , mize the number of atoms reaching the de­ and. as the name suggests. its operating prin­ tector. which means that the radio frequency ciple is simi lar to that of the laser. Accord­ exactl y equals the cesium atom's resonance ing to the ru les of quantum mechan ics. an Cesium clocks are frequency. The frequency of the oscillator's atom in an energy-emitting state wi lL even­ output signal can be electronically di vided tually. emit radiation of its own accord. Hy­ well known for down to produce, for example, a one-pulse­ drogen masers magnetically select hydrogen their excellent long­ per-second signal to drive a display that tells atoms in an energy-emitting state to enter a the time. quartz storage bulb. If enough atoms are term stability. Each GPS Block II satell ite contains two present in the bulb. one of them will emit cesium clocks, with typical stabilities of I to spontaneously a packet of radiation - a pho­ 2 parts in 10 13 over a one-day period. These ton - at the resonant frequency. A photon clock stabilities contribute from 2.6 to 5.2 me­ that strikes another atom in the energy-emit­ ters to the pseudorange error budget. Over ting state may stimulate that atom to emit an averaging period of 10 days . the stability radiation at exactly the same frequ ency and of the cesium clocks improves to about 4 exactly in phase with the incident radiation. the atomic second formally replaced the parts in 10 14, decreasing only slight ly for pe­ This process continues with other atoms, and ephemeris second as the fund amental unit of riods as long as I00 days or more. Cesium self-oscillation starts very rapidly in the reso­ time in the International System of Scientific clocks are well known for their excellent nance cavity surrounding the bu lb. A detec­ Units. The atomic second was defined as ex­ long-term stability. tor picks up the resu lting microwave signal actl y 9. 192.631.770 cycles of the unper­ Atomic clocks also have been developed and uses it to phase lock a crystal osc illator. turbed microwave transition between the two based on two other resonators. The rubidi um Hydrogen masers have been built with sta­ energy levels of Cesium 133 used in the ce­ clock is based on a part icular resonant fre­ bil ities on the order of a few parts in 10 15 . si um clock. a number chosen to agree quency of rubidium atoms. The atoms. in the However. masers are not as common as ce- closely with the ephemeris second over the pe-

November/December 1991 GPS WO~lD 39 INNOVATION

riod 1956 to 1965 to avoid discont inu ities in (noon). is arbitrary. In fact. the custom up un­ which then had 86.40 I seconds. The inser­ a tronomical records. ti l the late 1800s was for each vi llage , town. tion of that leap econd put UTC exactly 26 The time scale based on the atomic second or city to define it own local mean time. econds beh ind TA l. The provision also ex­ is known as Internat ional Atomic Time or Noon was when the "mean" sun crossed the ists for remov ing leap seconds from UTC TAl. the French acronym. However. not local meridian. But with the introduction of should UTI's rate of change reverse sign. as even an atomic clock keeps perfect time. So. standard time zones. everyone in a zone ap­ it did in the last century. rather than re ly on just one clock to provide prox imately 15 degrees of longitude wide UTI traditionally was deri ved from visual atomic time. TAl is computed from an ensem­ kept the same time. an integral number of and photographic observat ions of the passage ble of atomic clocks throughout the world. hours different from time at the Greenwich of stars acros an obse rva tory's meridian. An international body called the Bureau In­ meridian - Greenwich Mean Time (GMT) with responsibility for definit ively determ in­ ternational des Poids et Mesures (BIPM) or Uni versal Time (UT). as it has come to be ing UT I given. by in ternational agreement. based in Sevres just outside Paris performs called . Howeve r. a few exceptions to thi s to the Bureau International de I' Heure (BIH ) this computation. Through a va riety of clock- rule exist. For example. standard ti me in the at the Pari s Observatory. As the years Canadian prov ince of Newfoundland is three passed. the BIH refined the red uct ion pro­ and a half hours behind UT. cess and incorporated ob ervat ions from new Although corrected for the non un ifonnity techn iques that became available. Eve ntu­ of the sun· s apparent mot ion. mean solar ally. the more accurate space geodetic tech­ time. and hence UT. is st ill irregular due to niques of very long ba eline interferometry variation. in the ea rth 's pin on it axis. as and satellite and lun ar laser ranging sup­ mentioned earl ier. A slight shi fting of the ro­ planted conventional techniq ues. In 1987. tat ion axis with respect to the earth's crust. the activities of the BI H were reorganized. Not even an atomic a phenomenon known as polar morion. and the new Internat ional Earth Rotation Ser­ clock keeps pe1ject causes further complicat ion. An observa­ vice (IERS ). whose Central Bureau remained tory's determ ination of Universal Time from at the Paris Observatory. took over responsi­ measurements of the passage of stars across bility for determining UT I and polar mot ion its meridi an. known as UTO (UT zero). em­ in 1988 . The IERS works closely wi th the bodies the effects of both po lar motion and BIPM to determi ne when UTC leap seconds variations in the earth 's spi n. Polar motion's will occur. contribut ion to UTO is a function of the ob­ servatory's position on the earth. and only if GPS TIME a number of observatories around the world The signals transm itted by GPS satellites are comparison techniques. including Loran-C ra­ each detennine UTO can the magnitude of po­ referenced to CPS (System ) Tim e. which un­ dionavigation signals. television signals. and lar motion be determined and the UTO mea­ til June 1990 wa the time kept by a single GPS. the Bureau compares the readings of surements corrected. UTO corrected fo r lhe ef­ atomjc clock at one of the mon itor stations. atom ic clocks from more than 50 laborato­ fect of polar motion is known as UTI . UTI However. GPS Time now deri ves from a com­ ries around the world. The definiti ve TAT is represents the actual orientat ion of the earth posite or "paper" clock consisting of all op­ determined from those readi ngs. in space and is the time needed . for exam­ erational monitor station and sate llite clocks. As an aside. we note that -ince 1983 the ple. by sai lors and others to navigate by the GPS Time i steered over the long run to meter also is defin ed in terms of the atomic stars. keep it wi thin about I microsecond of UTC. second. By fixi ng the speed of light at Bu t UTI is still a nonuniform time scale. ignoring leap seconds. So unlike UTC. GPS 299.729.458 meters per second. the 17th Gen­ In add it ion to irregu lar short-term and sea­ Ti me has no leap second jumps. At the inte­ eral Conference on Weights and Measures de­ sonal variations. UTI drifts with respect to ger second level, GPS Time equalled UTC fined the meter as the di stance travelled by atomic time in the long tenn. At present this in 1980. but present ly. due to the leap sec­ li ght in a vacuum during 1/299.729.458 of a drift amoun ts to several mi lliseconds per onds that have been inserted into UTC. it is second. or a li ttle over 3 nanoseconds. day. Over the span of a year these mi II isec­ ahead of UTC by 7 seconds plus a fraction onds can add up to a fu ll second . Civ il ti me­ of a microsecond that varies day to day. UNIVERSAL TIME keeping required a time scale that had the A particular epoch is ident ified in GPS Al thoug h an imperfect timekeeper. the un iformity of atomic ti me but was not too Time as the number of seconds that have earth· rota t ion wi lh respect to the sun has different from UTI . Such a time scale. elapsed since the previou Saturday/Sunday governed human affairs since time immemo­ called Coordinated Universal Time or UTC. midnight. Such a time measure is. of course, rial. True solar time. the time kept by a sun­ was introduced in 196 1. Originally UTC was ambiguous. so one must also indicate in dial. is nonun iform due to the earth 's va ry­ kept close to UTI by periodically adjusting which week the epoch is. GPS week tart ing speed in it orbit and because the earth · s its rate and by adding or subtract ing step of with week 0 on January 6. 1980. and are num­ equator i not parallel but inclined to its or­ a fraction of a second. However. since 1972 bered consecutively. Figure 2 (a screen shot bit by about 23.5°. However. a mean time the UTC rate has been et equal to that of of a Macintosh Computer HyperCard stack) cale can be derived by calculating the vari­ TAl and leap seconds have been introduced shows the GPS week and seco nds of the ations in true solar time. which can amount into the UTC time cale to prevent UTC wee k correspondi ng to the UTC epoch of to as much as 16 minutes. and remov ing from deviating from UT I by more than 0.9 12:00:00. November l. 199 1: the correspond­ them from true time. The origin of such a seconds. The last leap second (as of this writ­ ing Jul ian Date (JD). wh ich represents the time scale. that is. the instan t when the time ing) was inserted into UTC just before mid­ number of days and fractional days elapsed is zero hou r (midni ght ) or twe lve hours night on the last day of December 1990. si nce noon UT on January I. 47 13 B.c.; and

40 GPS WORlD November/ December 1991 INNO VA TION

the Modifi ed Julian Date (MID). which equals JD min us 2400000.5. JD and MJD are frequently used by astronomers. naviga­ tors. and others for compactly and unambi­ When? guously identifying a pa rticular epoc h in GPS Time : I 12.00 07 Fndcy, November 1, 199 1 ti me. Atom ic clocks perform best with a min i­ GPS Time- UTC : [2] seconds mum of adj ustments. So to avoid continuous - ® UTC O GPSTime- adj ustment, the clocks in the GPS satell ites GPS Week ~ Year [IQ [ill Hours are on ly approximately sy nchronized to GPS GPS Seconds 1475207 1 Time. The GPS Operational Control System and the United States Naval Observatory Month [ill §] Minutes Q Day of t he Year l 3o5 l (USNO) carefully monitor the offsets of the Day [I] §] Seconds satell ite clocks from GPS Time. wh ich can Julian Date 12448562 be a mill isecond or so. They then determine (Now) Modified Julian Date 14856 1 5 an offset at an init ial epoch . a linear drift L______~ term. and. for rubidium clocks. a drift rate of chan ge term for each sate llite cloc k. ~ ~ ( Clear) ( Set Mac clock offset) (Do conversion) (L) These parameters are upl oaded to the corre­ sponding satell ite and subsequently included in its nav igation message . A GPS recei ver uses the satellite clock data to convert the Figure 2. Computer screen display illustrating the conversion of an arbitrary UTC measured pseudoranges from the satell ite epoch to GPS Time time scale to GPS Time. The satell ite mes­ sage also includes the offset of GPS Time oped sophisticated techniques for using GPS with respect to UTC. to synchronize clocks to a precision of I0 When a GPS receiver init ially acquires sig­ nanoseconds or better even when the clocks Satellite time nals. its clock. in general. wi ll have a large are on differen t continents. unknown offset with respect to GPS Time. I GPS Time ; This offse t. however. will contribute the RELATIVISTIC EFFECTS i same timing bias to all pseudorange measure­ The atomic clocks in the GPS satellites have I I !Receiver ti me ments made at any particular epoch and can a 10.23-MH z frequency output. This funda­ be solved for along with the receiver coordi­ menta l frequency corresponds to the chip­ l nates. Once determined. the bias can be used ping rate of the pseudorandom noise P-code pic i to sy nchronize the receiver clock to GPS and , when divided by 10. gives the rate of Time. GPS Time or UTC then can be dis­ the CIA-code. Multiplying the fundamental played by the receiver or used to time-t ag re­ frequency by 154 produces the L I carrier fre­ Figure 3. Relationships among GPS corded data or to generate a one-pul se-per­ quency and by 120 produces the L2 carrier Time and satellite and receiver time second electrical signal for controll ing other freq uency . Actually. in order to account for scales equipment. Figure 3 shows schematically the the effects of relati vity. the fundamental fre­ relationships among the satellite. rece iver. quency of the satellite clocks is set at slightly and system time scales and pseudorange mea­ less than 10.23 MHz. responds to a relative frequency offset of its surements. The receiver makes a raw measure­ Einstei n showed in his Special Theory of oscillator of 4.45 x I0- 10. In order to com­ ment of the time interval. d-r. wh ich when Relativity published in 1905 that a clock mov­ pensate for this offse t. the fu ndamental fre­ multiplied by the speed of light. c, gives the ing with a constant speed relati ve to another quency of the sateLlite clocks is reduced by measured pseudorange. p. Correcting this clock will appear to run more slowly. Accord­ 0.00455 Hz to 10.22999999545 MHz. measurement for satelli te clock. dt, and re­ ingly, a clock in a satell ite traveli ng in a cir­ Lf GPS satellites were in circular orbits. ceiver clock. dT. offsets wi th respect to GPS cular orbit around the earth would appear to their signals would req ui re no further com­ Time gives the true geometric range. p. ig­ lose time compared to one on the ground . pensations for relativity to ach ieve ranging noring propagat ion delays and other potential But II years later in his Genera l Theory of accuracies at the meter level. However, the biases . Relativity, Einstein deduced that clocks in dif­ orbi tal eccentricity of a GPS satellite can Several manufacturers offer GPS receivers ferent gravitat ional potentials also will ap­ range up to 0.02. which means that both its specifically designed for use as sources of pre­ pear to run at different rates. Due to the dif­ speed and the gravi tational potential it expe­ cise time information. Such rece ivers gener­ te rence in gravitational potential. a clock in riences change with time. The result is an ally are operated from fix ed sites and, once a satell ite will appear to run faste r than one oscillating time offset that is proportional to their locations are accurately determined. pro­ on the ground . The net effect on a satell ite eccentricity and va ries sinusoidally with the vide synchronized time signals even when clock is the combinat ion of the two effects. positi on of the satelli te in its orbit. The magn i­ on ly one satell ite is in view . These receivers A clock in a GPS satellite in a circular orbit tude of this effect can range up to 45.8 readi ly achieve accuracies to withi n about with a nom inal radi us of 26.560 ki lometers nanoseconds, which corresponds to a ranging I00 nanoseconds. gains 38.4 microseconds per day compared error of 13.7 meters. A GPS receiver must The USNO. BfPM , and others have deve l- to one on the ground. This time difference cor- correct its measured pseudoranges fo r this

November/December 1991 GPS WOIILD 41 INNOVA T ION

bi t informat ion in the navigat ion message. DoD man ipulates or dithers the sate ll ite 400 clock frequency. Thi dithering. referred to Vi' 300 as the o-process. introduces errors in the mea­ '0 c: sured pseudoranges and carrier-phase measure­ 0 (,) 200 Q) ments. Together wi th orbit errors. dithering Ul 0 can limit the accuracy of horizontal position c: 100 .s<0 by up to 100 meters. 95 percent of the time. Q) Excursion up to 300 meters may be ex­ (,) c: Q) pected the re mai ning 5 percent of the ti me. ~ 100 Velocity accuracy is also degraded . i5 -<> SA also comprom ises the accuracy with E- 2oo PAN 3 PAN 14 which GPS Time or UTC can be determined f= 300 from pseudorange measurements. Figu re 4 shows the effect of SA on ti ming measure­ - 4 00~---~---+---~---~---4----+---~ ments made at the Paris Observatory in Ju ly 7-23-90 7·28-90 8·2·90 8·7·90 8·1 2·90 8-17-90 8·22·90 8·27·90 and August 1990. The differences between daily determinat ions of GPS Time from two Figure 4. Discrepancies remaining in individual daily determinations of GPS Time individual satell ites (PRN 3. a Block I satel­ at the Paris Observatory after removal of a smoothed estimate based on data from lite; and PRN 14. a Block n satell ite) and a all Block I satellites best determ ination of GPS Time obtai ned by moothing the data from all Block 1 satell ites variation using the satellite orbit description graded when select ive avai labi lity (S A) is in are plotted. The turning off of SA on about contained in the navigation message. effect. SA is one of the method used by the August 10, 1990. can be seen clearly. Depart ment of Defense (DoD) to deny the Authorized users of GPS can recover from SELECTIVE AVAILABILITY fu ll acc uracy capabil ity of GPS to ··non­ SA errors using information encrypted in the The norma lly excellent behav ior of atomic authorized users." meaning most civilians. In navigat ion message. Nonauthorized use rs clocks in GPS satell ites is intentionally de- add ition to purposely degradi ng satellite or- must either endure SA or find ways of mini ­ ------, mizing its effect. For example. by using dif­ ferential GPS techniques. in which a pair of receivers sim ultaneously observe the same set of satell ites. the effect of clock dithering can be differenced away (see ''The Issue of Select ive Avai labi lity ." GPS World. Septem­ ber/October 1990).

CONCLUSION In th is artic le we have looked at the very important role that time plays in the Global Position ing System. Thanks to mi nute energy changes in individual atoms of ce­ sium and rubidium . humankind possesses the abi lity to synchronize clocks anywhere in the world to better than I0 nanoseconds. Bu t given this amazing abili ty to measure time. we still don't know what time actually is. What St. Augustine said at the end of the fourth century st ill ho lds: "What. then, is time ? If no one asks me, I know what it is. If 1 wish to explain it to him who asks. I do not know." •

42 GPS WOFILD November/ December 1991