Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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Recently, a project similar to the GPS has also been launched in the Europe. The project is called Galileo. The Galileo satellite system is planned to be perfectly compatible to the GPS. This is a benefit, because the same receivers can use either or both of the systems. The main difference between Galileo and GPS is that Galileo has not been planned to be used by the military. Galileo is a completely civil project, which is funded by the European Union and various European companies. The Galileo system is expected to be operational in 2008 [ESA]. 3.2 The Basic Concepts 3.2.1 Reference Coordinate Systems In every kind of navigation one needs some reference coordinate system. In GPS this is an important issue, since the natural coordinate systems for the satellites’ positions and for the receiver’s position are different. The Earth-centred inertial (ECI)coordinate system is particularly suitable for determiningthe orbits of the satellites [Kaplan, p. 23]. The origin of the ECI system is at the centre of mass of the Earth. The equations of motion of the GPS satellites can be modelled as if the ECI system were unaccelerated. For the purposes of computingthe position of a GPS receiver, it is more convenient to use a coordinate system that rotates with the Earth. This coordinate system is called Earth-centred Earth-fixed (ECEF)system. A stationary receiver on the surface of the Earth is stationary also in the ECEF coordinate system. Thus, the natural coordinate system for the satellites is ECI and that for the receiver is ECEF. The normal procedure is to compute the satellite orbits in the ECI system and then transform them to the ECEF system. Thereafter, the receiver position is computed in the ECEF system. In this thesis, unless otherwise specified, all the given coordinates will be in the ECEF coordinate system. 3.2.2 Range Positioning GPS has been designed to be a time-of-arrival positioningsystem. This means that the receiver’s position is determined by measuringthe time that the GPS signal uses to travel from the satellite to the receiver. With the knowledge that the signal travels with the speed of light c, the satellite-to-receiver range can be computed. When range measurements are simultaneously performed with 8
sufficiently many satellites, the receiver’s position can be solved. An example in two dimensions is shown in Figure 3.1. Satellite 1 Receiver Satellite 3 Satellite 2 Figure 3.1: Principle of Range Positioning When the user knows the positions of the satellites and the satellite-to-receiver distances, he can draw a picture similar to Figure 3.1. In three dimensions the circles around the satellites are naturally spheres. The radii of the spheres are the distances to the satellites measured by the receiver. The receiver position can be found from the intersection of the spheres. 3.2.3 GPS Signal Structure The GPS satellites transmit two different signals. Coarse/acquisition (C/A) signal is transmitted at the frequency L1 (1575.42 MHz). The C/A signal is open to be used by everyone. The precision (P(Y)) signal is transmitted at the frequency L2 (1227.6 MHz). The P(Y) signal is encrypted and can be used only by the U.S. military. The GPS receivers are totally passive in the sense that they need not transmit anything. In order to conclude its position, the receiver only needs to listen to the frequency L1. The satellite carrier signals are binary phase shift key modulated with pseudorandom noise (PRN) codes. The modulation frequency is 1.023 MHz. The code repeats once in a millisecond. The PRN codes are binary sequences that appear to be noise but are actually deterministic. Determinism is naturally necessary because the receiver needs to demodulate the signal. The noise-like characteristic 9
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: Chapter 3 The Global Positioning Sy
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

Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

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