Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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has seemed to consider the use of Doppler positioningin weak signal conditions. The great benefit of the Doppler positioning is that the Doppler measurements can be received even when the standard positioningfails. The Doppler measurements can be used to solve the receiver position even without demodulatingthe navigation message. This requires that the satellite orbital parameters and the current time are known from some other source. Thus, this thesis belongs to the field of assisted GPS. The discussion of the GPS Doppler positioningis started with the physical background of the Doppler effect in Chapter 2. The chapter also enlightens the applications of the Doppler effect in satellite positioningand other fields. Chapter 3 introduces the Global PositioningSystem, its standard positioningalgorithm and its limitations. Chapter 4 begins by discussing the feasibility of GPS Doppler positioning. Later in the chapter, the new Doppler positioning algorithm is presented. Chapter 5 turns the attention to the important issue of positioning accuracy. Possible error sources are discussed. In addition, a theory for estimatingDoppler positioningaccuracy is developed. The possible applications of the theory are also covered. Chapter 6 begins with a numerical analysis of the properties of the measurement noise. Later, the new theory is compared with the numerical results. Furthermore, positioningresults with real measurement data are illustrated. Finally, Chapter 7 ends the thesis with conclusions. 2
Chapter 2 The Doppler Effect In this chapter we will shortly discuss the Doppler effect as a physical phenomenon and introduce some of its applications in modern technology. In addition, the history of exploitingthe Doppler effect in satellite navigation is considered. 2.1 Physical Background and Applications The Doppler effect was first noticed by the Austrian physicist C.J. Doppler (1803- 1853). The phenomenon was first noticed in sound, but it applies to every kind of wave propagation. The Doppler effect is caused by a transmitter that is in relative motion with respect to a receiver. When the transmitter approaches the receiver, the transmitted signal is squeezed. This produces a rise in the frequency of the transmitted signal. As explained in [Alonso & Finn, p. 706] and [Giancoli, p. 321], the frequency experienced by the receiver can be modelled as ω ′ = 1 − vrel cos θ ω (2.1) vprop where ω ′ is the received frequency, ω is the transmitted frequency, vrel is the magnitude of relative velocity of the transmitter with respect to the receiver, vprop is the propagation speed of the wave and θ is the angle between the relative velocity and the wave propagation direction. The equation 2.1 is a valid approximation when vrel ≪ vprop. Figure 2.1 illustrates the squeezing of the signal when the transmitter located at the point x is at motion with speed v. The Doppler effect is still mostly known from acoustics. An example from everyday life is the shift in the tone of a car when it passes the listener. The Doppler effect in acoustics is widely exploited in military applications. Assume that a noisy object (eg. a helicopter) is travellingalonga straight line with a constant velocity. Then a stationary sensor receives a frequency that varies with time as 3
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: Chapter 1 Introduction Satellite po
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 and 28: in weak signal conditions. The key
Page 29 and 30: navigation message. Here, however,
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
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Chapter 7 Conclusions This thesis d
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The positioningalgorithm was develo
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[Hill] Hill, Jonathan. The Principl
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Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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