Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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Signal magnitude Frequency shift for a moving transmitter x Position v Figure 2.1: Doppler effect Frequency versus time for a passing single-pitch object Frequency Time Figure 2.2: Doppler curve 4
in Figure 2.2. The shape of the so called Doppler curve in Figure 2.2 can be used to estimate the distance to the tracked object as well as its velocity. Numerically this can be done with least squares curve fitting. The applications of the Doppler effect are by no means limited to acoustics. Perhaps the most used application of the Doppler effect is radar. The principle of Doppler radar is explained in [Janza et al., p. 410]. In addition to radars, the Doppler effect is also important in lidars (light detection and ranging). The workingprinciple of a lidar closely resembles that of a radar, but the lidar is used at optical frequencies [Post & Cupp]. Doppler lidars are mainly used in atmospheric measurements of small particles. Another important application is the laser Doppler anemometry. The use of laser Doppler anemometry (LDA) in fluid velocity field measurement is explained in [Tropea]. The method is also sometimes called laser Doppler velocimetry [Wang& Snyder]. Furthermore, Doppler ultrasound measurements are widely used in medicine. Blood flow velocity, for example, is an important measurable that can be measured with Doppler ultrasound [Bascom & Cobbold]. 2.2 History of Doppler Navigation The precedingsection showed that there are numerous applications in different fields that take advantage of the Doppler effect. The Doppler effect, by its nature, is ideally suited for velocity measurement. However, it has already for longbeen used in navigation. In this section, we will enlighten the history of satellite Doppler navigation. The idea of a satellite Doppler navigation system comes from Applied Physics Laboratory of the John Hopkins University, United States. The invention was made in 1958 and was publicised in 1960. The early development of the project and a proof of feasibility of satellite Doppler navigation was presented in [Guier & Weiffenbach]. The U.S. Navy Navigation Satellite System, alsoknown as Transit, was designed based on this idea. The system became operational in 1964. Details of the system were released in 1967 by the U.S. government. This was done in order to permit commercial manufacture and use of Transit navigation equipment. The Transit system provided intermittent position fix updates rather than continuous navigation information [Laurila, p. 463]. It consisted of satellites in circular, polar orbits about 1075 kilometres high. The receiver only needed to track one satellite to produce a navigation fix. In order to produce an accurate estimate, 5
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: Chapter 2 The Doppler Effect In thi
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
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
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Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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