GPS has a master clock. It is not a “physical” clock but rather a “paper” clock. It consists of calculations and measurements made by the Control Segment (CS) of the system. Up to this point the clocks in our linear model at points A and B, we have assumed to be in synchronism. We will now allow them to have a small error with respect to each other.
Figure1.6shows the new system. It is identical to the two-clock system we just covered except we have added a master clock. The camera still records the state of the two replica clocks and the receiver reference clock @ snapshot instant for use in
1.12 A Master Clock 15
CLOCKAT POINTA
LIGHT REC. A
DIRECTION OFTRAVEL DADB DA + DB =46,000KILOMETERS CISTHESPEEDOFLIGHT
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LIGHT TRANSMITTER LIGHT REC.PATHDELAYPATHDELAY NOTE:1)ALLCLOCKDIALSROTATECLOCKWISE. 2)CAMERARECORDSTHREECARCLOCKS ATSAMEINSTANT,"SNAP_SHOT"
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00.977uSEC Tbiashasbeen"CorrectedOut"on receiverreferenceclock.Itnowreads thesametimeasclocksatAandB.
c DKD INSTRUMENTS c DKD INSTRUMENTS
Fig.1.5Carclockhaserror(Tbias)correctedoutusingmeasureddistanceandtimesfromclocksAandB16 1 Fundamental Concepts of Distance Measurement Using Synchronized Clocks
CLOCKAT POINTA
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00.977uSEC t=Trec-Tbias-TsentAAA t=Trec-Tbias-TsentBBB
LET:R=D AD B+ R=tAtB+[]*C
tADA=*CtBD B=*C TerrBTerrA
+
+
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MASTERCLOCK NOTE:SMALLERROR ONCLOCKA WRTMASTERCLOCK
NOTESMALLERROR ONCLOCKB WRTMASTERCLOCK TrecA +TrecB -TsentA -TsentB
__ c
[] 2Tbias=
TerrB
TerrA ++
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-c DKD INSTRUMENTS c DKD INSTRUMENTS
Fig.1.6ClocksatAandBhavesmallerrorwithrespecttoeachother;eachclocksendsreceiveritserrortermwithrespecttomasterclock1.12 A Master Clock 17
the calculations of Tbias and the distance to A or B. There is a difference: note that Clocks A and B are not synchronized below the 1 ms level. Inspection of the dials in Fig.1.6reveals this. The error is less than a millisecond. The receiver reference clock is shown synchronized with the master clock. How can the receiver reference clock be synchronized to our new master clock? The “trick” is that the clocks at points A and B “know” their respective errors as compared to the master clock. In the GPS the CS sends each SV its error with respect to the master clock. In our linear model the transmitters at A and B send their error terms (as part of the data stream) to the receiver. These terms tell the receiver how much the clocks at A and B they are “off” from “master” time. We can include these terms in our correction terms for the receiver’s reference clock as shown in Fig.1.6. The error terms must also be applied to receiver’s replica clocks. In addition, if weaddedthe path delay associated with each replica clock, the replica clocks would be in synchronism with the master clock. The receiver would still need to solve for its Tbias as before, but now displayed time it is referenced to the master clock time.
In this fashion the receiver’s reference and replica clocks are adjusted so that the entire system is now referenced to the master clock. The reasons for using this method lie in the complexities associated with synchronizing multiple SV clocks. It is easier to allow a small error to exist and have the SV send the error information to the user receiver.
A final note on the master clock. As shown in Fig. 1.6it has 20 tics on the 0.977 ms dial. In the GPS master clock this resolution is much higher. For all practical purposes this dial becomes an analog dial (infinite number of tics) and its precision is so high.