Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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Chapter 4 Doppler Positioning with the GPS In this chapter, the possibility of usingthe Doppler measurements in GPS will be discussed. The theory for positioningbased on simultaneous Doppler measurements will be developed. In addition, an iterative algorithm suitable for the positioningis presented. 4.1 Need for Doppler Positioning The Global Positioning System was developed for pseudorange positioning. There is no doubt that usingthe pseudorange measurements is the most accurate way to find a position estimate for the receiver. However, the end of the preceding chapter gave a glimpse of the difficulties that frequently arise in pseudorange positioning. Very often it happens, that there are several attenuated GPS satellite signals available. The signals are so noisy that the demodulation of the navigation message is impossible. Thus, the pseudorange measurements cannot be performed. However, the signals are sufficiently good so that the signals can be recognised accordingto the PRN codes. In addition, the received signal frequencies can be measured. The frequency differences are mainly caused by the Doppler effect. In this chapter it will be shown that the frequency shifts can be used for positioning without knowledge of the pseudoranges. This kind of positioning will be referred to as GPS Doppler positioning. In pseudorange positioning the user needs to know the satellite positions. In GPS Doppler positioningthe same applies, but the user also needs to know the satellite velocities. The usual way to achieve this information is to demodulate the 16
navigation message. Here, however, we assumed that the signals are so attenuated that this is impossible. The solution is the assisted GPS. We will assume that the satellite orbital parameters and the current time is received from somewhere out of the GPS system. Typically this means that the receiver is connected to a cellular network. It is evident that the ability to perform the positioningusingonly Doppler measurements would be of great use in many situations. Even if the positioning estimate would not be as accurate as in pseudorange positioning, the Doppler positioningwould still make sense. As was written above, the pseudorange positioningis not always possible. More good news is that carryingout the Doppler measurements does not require any hardware modifications to the receiver. Actually, the state of the art receivers are doingthe Doppler measurements all the time as a by-product of satellite tracking. 4.2 Comparison between GPS and Transit In Chapter 2 the basic principles of the historical Transit Doppler positioning satellite system were enlightened. The Chapter 3, by contrast, introduced the modern GPS pseudorange positioning. There is no doubt that GPS pseudorange positioningis much more accurate than the Transit Doppler positioning. But let us now assume that the GPS is used in Doppler positioningmode. Naturally, before going on to designing algorithms for GPS Doppler positioning, it is desirable to know if the positioninghas any chances to succeed. We know that the Transit positioningwas possible with about 500 meters accuracy. Let us now compare Transit and GPS Doppler positioningto see if the GPS can be expected to beat the Transit. Let us first consider the bad sides of the GPS when compared to the Transit. First of all, the GPS only has one available civil frequency. In Transit there were two separate frequencies. This is a bigbenefit allowingthe user to eliminate all the first order errors in measurements. Thus, most of the atmospheric and receiver measurement errors can be eliminated in the Transit. In addition, the Transit satellites were at lower orbits and travelled at a higher velocity. This produces benefits in Doppler positioning, because the Doppler shifts are larger. Furthermore, the positioninggeometry is better when the satellites are at lower orbits. In other words, the positioningerror for the same Doppler measurement error is smaller for low orbit satellites [Hill]. However, there are also good things in the GPS when compared to the Transit. The biggest advantage of using the GPS for Doppler positioning in stead of the Transit is the satellite availability. There are much more satellites in the GPS. In 17
Page 1 and 2: TAMPERE UNIVERSITY OF TECHNOLOGY De
Page 3 and 4: Contents Abstract v Tiivistelmä vi
Page 5 and 6: 5.2.3 Applications of the Doppler D
Page 7 and 8: Tiivistelmä TAMPEREEN TEKNILLINEN
Page 9 and 10: Abbreviations and Acronyms C/A coar
Page 11 and 12: σ2 variance, covariance a vector i
Page 13 and 14: Chapter 1 Introduction Satellite po
Page 15 and 16: Chapter 2 The Doppler Effect In thi
Page 17 and 18: in Figure 2.2. The shape of the so
Page 19 and 20: Chapter 3 The Global Positioning Sy
Page 21 and 22: sufficiently many satellites, the r
Page 23 and 24: The satellite signal is very accura
Page 25 and 26: The estimated position and time vec
Page 27: in weak signal conditions. The key
Page 31 and 32: where wi is the satellite velocity,
Page 33 and 34: the receiver clock is runningfast a
Page 35 and 36: Let us now turn into our main goal,
Page 37 and 38: Definition 3. Delta range residuals
Page 39 and 40: method [Fletcher, p. 110], [Kaleva1
Page 41 and 42: product formula a × (b × c) =(a
Page 43 and 44: Chapter 5 Positioning Performance I
Page 45 and 46: eplaced by vi −△wu. Let us rewr
Page 47 and 48: Thus, the time bias effect to the p
Page 49 and 50: Let us first calculate the expected
Page 51 and 52: • Doppler drift dilution of preci
Page 53 and 54: Let us now make the even stronger a
Page 55 and 56: Chapter 6 Numerical Results In Chap
Page 57 and 58: 6.2.2 Numerical Testing of Normalit
Page 59 and 60: 6.2.4 Magnitude of Errors The actua
Page 61 and 62: Histogram of positioning errors wit
Page 63 and 64: used for testinghow the algorithm b
Page 65 and 66: Chapter 7 Conclusions This thesis d
Page 67 and 68: The positioningalgorithm was develo
Page 69 and 70: [Hill] Hill, Jonathan. The Principl

Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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