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to get the position error The GPS system has been designed to keep the PDOP factor less than 6 most of the time (Langley, 1991c) The GPS constellation consists of 24 satellites in six near-circular orbits, at an altitude of approximately 20,000 km (Daly, 1993) The ascending nodes of the orbits are separated by 60 , and the inclination of each orbit is 55 The four satellites in each orbit are irregularly spaced to keep the PDOP factor within the limits referred to earlier Time enters into the position determination in two ways First, the ephemerides must be associated with a particular time or epoch (as described in Chap 2) The standard timekeeper is an atomic standard, maintained at the US Naval Observatory, and the resulting time is known as GPS time Each satellite carries its own atomic clock.

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The time broadcasts from the satellites are monitored by the control station, which transmits back to the satellites any errors detected in timing relative to GPS time No attempt is made to correct the clocks aboard the satellites; rather, the error information is rebroadcast to the user stations, where corrections can be implemented in the calculations It can be assumed, therefore, that the satellite position relative to the ECEF coordinate system (the geocentric-equatorial coordinate system, Sec 296), is accurately known The coordinates for satellite n will be denoted by (xn, yn, zn) Second, time markers are needed to show when transmissions leave the satellites so that, by measuring propagation times and knowing the speed of propagation, the ranges can be calculated Therein lies a problem, since the user stations have no direct way of telling when a transmission from a satellite commenced.

12.1.1 12.1.2 12.1.3 12.1.4 12.1.5 12.1.6 12.1.7 12.1.8 The Algorithm The Main Program Creating a Cluttered Room Facing the Beacon Moving Toward the Beacon Going Around an Obstacle Determining If the Beacon Is Found A Potential Problem

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The problem is overcome by having the satellite transmit a continuous-wave carrier, which is modulated by a pseudo-random code, timing for the carrier and the code being derived from the atomic clock aboard the satellite At a user station, the receiver generates a replica of the modulated signal from its own (nonatomic) clock, which is correlated with the received signal in a correlator A delay is introduced into the replica signal path and is adjusted until the two signals show maximum correlation If the receiver clock started at exactly the same time as the satellite clock, the delay in the replica path would be equal to the propagation delay As it is there will be some unknown difference in the start times Let tn be the true propagation time from satellite n to the observer, and let tdn be the delay time as measured by the correlator.

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Let t be the unknown difference between the clock start times then tn tdn t ( t can be + or ) The satellite clocks are synchronized to the master atomic clock, so t will be the same for all satellites The range to the satellite n is therefore.

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(17.2)

where c is the speed of light. Substituting this in Eq. (17.1) gives: O (xn x0 )2 (yn y0)2 (zn z0)2 c2(tdn t)2 (17.3)

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