GPS çalışmalarında en uygun uydu konumlarının belirlenmesi
The Determination of the most adequate satellite constallation in the GPS works
- Tez No: 21748
- Danışmanlar: DOÇ. DR. RASİM DENİZ
- Tez Türü: Yüksek Lisans
- Konular: Jeodezi ve Fotogrametri, Geodesy and Photogrammetry
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 54
Özet
ÖZET Günümüzdeki en büyük uzay programlarından biri olan GPS sistemi, başlangıçta askeri amaçlara yönelik hizmet verecek biçimde planlanmasına ragmen giderek sivil kullanıma açılmaktadır. GPS 'den jeodezik ve navigasyon amaçları dışında kutup hareketinin belirlenmesi, yerin dönme hızındaki değişmeler ve jeodinamik amaçlı çalışmalarda da yararlanılmaktadır. Sistem üç ana bölümden oluşmaktadır. Bunlar; 1) Uzay Bölümü 2) Kontrol Bölümü 3) Kullanıcı (alıcı) Bölümü Bu çalışmada NAVSTAR-GPS (NAVigation Satellite for Time And Range-Global Positioning System) sistemi ve bu sistem ile konum belirlemede en uygun gözlem zamanının bulunması için hesap yolu incelenmiştir. Birinci bölümde genel konular incelenmiş ve ikinci bölümde GPS sisteminin kısaca tanıtımı yapılmış ve genel özelliklerini içeren bilgiler, ölçme ve konum belirleme metodları gösterilmiştir. Yeryüzü ve yeryüzünün uzaydaki hareketine ilişkin genel bilgiler, kutup hareketi, nutasyon ve presesyon gibi bu harekete etkiyen sebepler sonucu yeryüzünün hareketindeki değişmelerin uyduların yörüngelerine olan etkileri, zamana bağlı olarak uyduların yörünge elemanlarına (efemeridlere) ilişkin bilgiler ve bu bilgilere bağlı olarak ölçme değerlerine uygulanacak düzeltmeler hakkında bilgiler verilmiştir, Astronomik almanaklarda ve uydu verilerinde kullanılan tak vimin hesabı gösterilmiştir. Bölüm 3'de efemeridler yardımıyla herhangi bir t anında uyduların konumlarının hesabına ilişkin bilgiler, koordinat dönüşümleri ve konumu belli olan uydu için uydunun bir yeryüzü noktasından görünürlüğü incelenmiştir. En uygun gözlem zamanı için göz önünde bu lundurulması gereken konulara değinilmiştir. Son bölümde atmosferik etkilerin uyduların* görünürlüğüne etkileri gös terilmiştir.
Özet (Çeviri)
SUMMARY THE DETERMINATION OP THE MOST ADEQUATE SATELLITE CONSTALLATÎON ÎN THE GPS WORKS Satellite navigation started with_the commissioning of Transit Doppler (the US Navy Navigation Satellite System) in the mid 1960's, i.e. over 25 \years ago. The first GPS satellite, GPS 14 or NAVSTAR Il-l, -was launched on 14 Februar 1984. The Navstar Global Positioning System (GPS) was conceived in the early 1970' s as a highly accura te sattelite-based Navigation system. GPS has three segments which are; 1) Space segment 2) Control segment 3) User segment Space segment includes satellites. When the system reaches its full configuration, it will consist of 18 sa tellites (and three spares) arranged in six orbital planes of 55° inclination. (in 1995, the configuration will change form1 18 satellites plus 3 spares' to a more effec tive (24 satellites' configuration). This configuration will make it possible to have a minimum of four satellites in view, each transmitting a unique data set for idenbif ication and navigational positioning through two L-band (RF) frequencies L^ and L2 L^ at 157^. 42MHz., equivalent to a wavelenght of approximate lly 19cm L2 at 1227.60MHz., equivalent to a wavelenght of approximate lly 24cm The lii carrier is modulated by two ranging codes, L/A (Coarse/Acquasition) - code and P (Precise) -code. The navigation service provided by C/A-code is referred to as VIthe standart positioning service (SPS). The navigation service provided by the P-code is referred to as the pre cise positioning service (PPS). L2 carrier contains only P-code, however P-code is restricted to unauthorized users by A. S. Department of Defense. Both carriers carry the Broadcast satellite message to inform the user about healty ephemerides, clock parameters, almanac and tropospheric corrections. The control segment consists of five control sta tions, perform the following functions; - Tracking all GPS signals - Predicting the GPS satellite ephemerides, satellite clock corrections and ionospheric corrections - Transmitting the data up to GPS satellites - Replace a dead satellite by a spare The user segment includes receivers and artennas to track GPS signals. GPS receivers contain presently quartz crystal atomic clocks but it is anticipated that rubidium or cesium atomic clocks will be used. Range between receiver and satellite is the basic observable in the GPS system. ideally, one could obtain the position of a navigator from three measured ranges of three satellites. However, these ranges are measured by 'delay time1 which is contaminated by the receiver's clock off-set in relation to the satellite clocks which are (nominally) set in the GPS time frame work. Therefore a minimum of four pseudo-ranges are necessary in order to solve for the three coordinates of the receiver and its unknown 'clock bias'. There are two main GPS observables, pseudo-ranges and carrier frequercy phase measurements. In principle, pseudo ranges (i.e. ranges affected by the receiver's clock bias) are used in navigation and phase measurements for high precision positioning. To compute the position of a point on the earth (or a position difference) from GPS pseudorange or phase obser vations, the 3-d coordinates of the satellites, at every observational epoch are required. In practice, this orbi tal information is expressed as the satellite ephemerides. With exception of the 'codelless' receivers the majority of GPS receivers have access to the broadcast ephemeris contained in the Navigation Message. The orbits of naviga tion satellites have to be determined very precisely. The transit broadcast (predicted) ephemeris, which is computed by the US Navy Astronautics Group, has an estimated orbital positional accuracy of the order of 25m in each direction. By contrast, the precise ephemeris which is determined by the US Defense Mapping Agency, reaches accu racies of the order of 10m. vxiThese orbital accuracies have an almost one-to-one correspondence with the precision of the absolute coordina tes of points determined by using these satellites. In relative positioning, the orbital errors tend to cancel out for short baselines. However, relative positioning accu racies of better than 0.1 parts-per-million (10~^ of the corresponding baseline lenght), can only be achieved if satellite orbits of a corresponding high accuracy are either made available or computed as part of the solution. For the derived observation equations the coordinates of satel lites at the time t should be known in other words epheme- rides of satellites has to be provided. These are two kinds of ephemerides, Broadcast ephemerides and Precise epheme- rides. The Broadcast ephemeris for the global positioning system consists of 15 Keplerian type coefficients, which are revised every hour, but are said to be valid for up to 4 hours. The following is the full list of the broadcast coefficients. t0 reference epoch for the ephemeris M0 mean anomali at t0 An correction to the computed mean motion n0 e eccentricity of orbital ellipse >'a square root of the semi-major axis ft0 right ascension of ascending node at tQ i0 inclination of orbital plane u argument of perigee di rate of change of the inclination with time dt dfl dt rate of change of right ascension with time CUC,CUS amplitude of cos and sin correction terms of the argument of latitude (u) Crc,Crs amplitude of cos and sin correction terms of the geocentric radius (r) ciccis amplitude of cos and sin correction terms to the inclination of the orbital plane (i) The GPS receiver decodes the broadcast ephemeris and proceeds to compute the instantaneous attitude of the or bital ellipse and the position of the satellite on it, for vxnall the epochs of observation, t0+t. This is done by determining the longitude of the ascending node Q, the inclination of the orbital plane i, the argument of latitude of the satellite in the orbital plane U and its geocentric radius r. The Earth-fixed cartezian coordinates X, Y, Z of the satellite at epoch t are obtained from the 'Keplerian' coordinates u, r, i, fi in three stages. First, the car tesian coordinates are obtained in the orbital plane system, Xg/ Yg, Zg. XE = r cos u Ye = r sin u ZE = 0 The plane of the orbital ellipse is then rotated about the Xg axis (through the ascending node) by the inclination angle i, until Zg is coincident with the ter restrial Z axis, resulting in Xrp = Xg Yqi = Yg cos i Zrp = Yg sin i Lastly, the X^ axis (which is in the equatorial plane) is rotated about the Z axis by fi, until it coincides with the terrestrial X axis (which passes through the Greenwich meridian). X = Xt cos -Yt sin ti Y = Xj sin +Yrp cos Q Z = Zt To get the visibility charts of a point on the earth for any satellite, the topocentric coordinats should be known. Therefore the terrestrial coordinats of satellites must be transformed to the topocentric coordinate system. Visibility charts are planes, on which the satellite visi bilities are shown. These charts depends on the station point, on which the observations are made. Convertional GPS processing techniques use the broad cast ephemeris to obtain relative station coordinates. Errors in the broadcast ephemeris can cause baseline errors of the order of 1 ppm. For high order geodetic positioning accuracies, it is therefore necessary to determine precise sattellite orbits. Predicted orbits can be generated by numerically integrating a model of the forces acting on the satellite. The cartesian position of a GPS satellite, in its orbit, can be predicted by using a model which represents all the IXknown forces acting upon the space craft. The acceleration vector of the satellite obtained from this force model can be numerically integrated from initial position and velocity (state) vectors, once to obtain velocity and twice to give position, with respect to time. The forces acting upon the GPS satillites can be divided into the gravitational forces and the surface forces. The gravitational forces include the gravitational attrac tions of the earth, moon, sun, the planets and the effects of the solid earth and ocean tides. The principle surface force acting upon the satellites is due to the solar radiation pressure. This force is one of the most difficult to model due to the complex shape, of the. GPS satellites. Other surface forces are air drag and infra-red radiation. As described previously the broadcast ephemeris may not be of sufficient accuracy for a number of GPS applications, such as regional crustal dynamics studies. Furthermore some 'codeless' receivers are not able to decode the broadcast ephemeris and so must use an externally produced post-com puted ephemeris. There are several ways of improving the accuracy with which the satellite coordinates are known. The first is the use of 'The Precise Ephemeris', which is calculated by the US Naval Surface Weapons Centre (NSWC). Using tracking data from the 5 monitor stations and "several other DMA sites around the world, the orbits of the GPS satellites are calculated and made available to bona fide users several days after the observation period. This Precise Ephemeris is purported to be accurate at 5 metre level. There are also research establishments and commer cial companies in the USA which produce a precise ephemeris (e.g. the University of Texas, Litton Aero Services Ltd). Since most geodetic space techniques basically involve a direct or differential distance observation, obtained by a 'time of flight' type measurement, they require an accurate estimation of the error induced in the distance measurement by the atmosphere. Any light or microwave signal, whether incoming (e.g. from a quasar or GPS satellite) or outgoing (e.g. from an SLR laser) passes through the Earth's atmosp here, which not only bends the ray, but also slows it. With regard to the transmission of light waves or microwaves, the atmosphere may conveniently be regarded as the ionosphere and the troposphere. The ionosphere is the upper of the two layers, -extending from about 50km up to approximately 500km. The troposphere is the region below this, extending from ground level up to the base of the ionosphere. It is therefore the troposphere in which most of the common climatic variations occur. xWith in the ionosphere, the different characteristics of a radio wave are affected in different ways. In addition, the dispersive nature of the ionosphere at radio frequencies means that these effects vary with the frequency of the radio wave. The basic form of the relation ship between the refractive index, n, and the frequency is given by n =1± f2 where } Ai is a sample combination of a number of physical constants (=40.3) Ne is the free electron density in the ionosphere (units of 1016 el/m2) f is the frequency of the signal (GHz) The± depends on whether the refractive index for the velocity of the code envelope (the group refractive index) or for the phase of the signal (the phase refractive index) is being determined. Apart from the frequency of the signal, the other contributing factor to the variation of the refractive index is the free electron density within the layer. The ioniza tion which produces the free electrons is caused by ultra violet and X-ray radiation from the sun and is consequently governed by the activity of the sun. Accordingly, a number of well known periodicities are evident in the state of the ionosphere, including the 11-year sun spot cycle, a seaso nal cycle and a diurnal cycle. During a solar maximum, the vertical ionospheric error may reach as much as 10m (at GPS frequencies) during the day, this value reducing to 1 or 2m at night. The integral of electron density with respect to distance along the line of sight is commonly expressed as the Total Electron Content (TEC), which typically varies from 0.5*1017el/m3 at night to 5.0*1017 el/m3 during the day. Thus, the excess path length is given by A]_*TEC A, s ~ o f2 and the delay (in seconds) is given by As Ai * TEC At = _ _ = C c*f2 where ; c is the velocity of light t is the ionospheric group delay xi
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