Introduction
GPS is a Global Positioning System based on satellite technology. The fundamental technique of GPS is to measure the ranges between the receiver and a few simultaneously observed satellites. The positions of the satellites are forecasted and broadcasted along with the GPS signal to the user. Through several known positions (of the satellites) and the measured distances between the receiver and the satellites, the position of the receiver can be determined. The position change, which can be also determined, is then the velocity of the receiver. The most important applications of the GPS are positioning and navigating.
Through the developments of a few decades, GPS is now even known by school children. GPS has been very widely applied in several areas, such as air, sea and land navigation, low earth orbit (LEO) satellite orbit determination, static and kinematic positioning, flight-state monitoring, as well as surveying, etc. GPS has become a necessity for daily life, industry, research and education.
If some one is jogging with a GPS watch and wants to know where he is located, what he needs to do is very simple; pressing a key will be enough. However, the principle of such an application is a complex one. It includes knowledge of electronics, orbital mechanics, atmosphere science, geodesy, relativity theory, mathematics, adjustment and filtering as well as software engineering. Many scientists and engineers have been devoted to making GPS theory easier to understand and its applications more precise.
Galileo is an EU Global Positioning System and GLONASS is a Russian one. The positioning and navigating principle is nearly the same compared with that of the US GPS system. The GPS theory and algorithms can be directly used for the Galileo and GLONASS systems with only a few exceptions. A global navigation satellite system of the future is a combined GNSS system by using the GPS, GLONASS and Galileo systems together.
In order to describe the distance measurement using a mathematical model, coordinate and time systems, orbital motion of the satellite and GPS observations have to be discussed (Chap. 2-4). The physical influences on GPS measurement such as ionospheric and tropospheric effects, etc. also have to be dealt with (Chap. 5). Then the linearised observation equations can be formed with various methods such as data combination and differentiation as well as the equivalent technique (Chap. 6). The equation system may be a full rank or a rank deficient one and may need to be solved in a post-processing or a quasi real time way, so the various adjustment and filtering methods shall be discussed (Chap. 7). For precise GPS applications, phase observations must be used; therefore, the ambiguity problem has to be dealt with (Chap. 8). And then the algorithms of parameterisation and the equivalence theorem as well as standard algorithms of GPS data processing can be discussed (Chap. 9). Sequentially, applications of the GPS theory and algorithms to GPS/Galileo software development are outlined, and a concept of precise kinematic positioning and flight-state monitoring from practical experience is given (Chap. 10). The theory of dynamic GPS applications for perturbed orbit determination has to be based on the above-discussed theory and can be described (Chap. 11). Discussions and comments are given at the last topic. The contents and structure of this topic are organised with such a logical sequence.
Contents of this topic covered kinematic, static and dynamic GPS theory and algorithms. Most of the contents are refined theory, which has been applied to the independently developed scientific GPS software KSGsoft (Kinematic and Static GPS Software) and MFGsoft (Multi-Functional GPS/Galileo Software) and which was obtained from extensive research on individual problems. Because of the strong research and application background, the theories are conformably described with complexity and self-confidence. A brief summary of the contents is given in the preface.
The Global Positioning System was designed and built, and is operated and maintained by the U.S. Department of Defence (c.f., e.g., Parkinson and Spilker 1996). The first GPS satellite was launched in 1978, and the system was fully operational in the mid-1990s. The GPS constellation consists of 24 satellites in six orbital planes with four satellites in each plane. The ascending nodes of the orbital planes are equally spaced by 60 degrees. The orbital planes are inclined 55 degrees. Each GPS satellite is in a nearly circular orbit with a semi-major axis of 26 578 km and a period of about twelve hours. The satellites continuously orient themselves to ensure that their solar panels stay pointed towards the Sun, and their antennas point toward the Earth. Each satellite carries four atomic clocks, is the size of a car and weighs about 1 000 kg. The long-term frequency stability of the clocks reaches better than a few parts of 10-13 over a day (cf. Scherrer 1985). The atomic clocks aboard the satellite produce the fundamental L-band frequency, 10.23 MHz.
The GPS satellites are monitored by five base stations. The main base station is in Colorado Springs, Colorado and the other four are located on Ascension Island (Atlantic Ocean), Diego Garcia (Indian Ocean), Kwajalein and Hawaii (both Pacific Ocean). All stations are equipped with precise cesium clocks and receivers to determine the broadcast ephemerides and to model the satellite clocks. Transmitted to the satellites are ephemerides and clock adjustments. The satellites in turn use these updates in the signals that they send to GPS receivers.
Each GPS satellite transmits data on three frequencies: L1 (1575.42 MHz), L2 (1227.60 MHz) and L5 (1176.45 MHz). The L1, L2 and L5 carrier frequencies are generated by multiplying the fundamental frequency by 154, 120 and 115, respectively. Pseudorandom noise (PRN) codes, along with satellite ephemerides, ionospheric model, and satellite clock corrections are superimposed onto the carrier frequencies L1, L2 and L5. The measured transmitting times of the signals that travel from the satellites to the receivers are used to compute the pseudoranges. The Course-Acquisition (C/A) code, sometimes called the Standard Positioning Service (SPS), is a pseudorandom noise code that is modulated onto the L1 carrier. The precision (P) code, sometimes called the Precise Positioning Service (PPS), is modulated onto the L1, L2 and L5 carriers allowing for the removal of the effects of the ionosphere.
The Global Positioning System (GPS) was conceived as a ranging system from known positions of satellites in space to unknown positions on land and sea, as well as in air and space. The orbits of the GPS satellites are available by broadcast or by the International Geodetic Service (IGS). IGS orbits are precise ephemerides after postprocessing or quasi-real time processing. All GPS receivers have an almanac programmed into their computer, which tells them where each satellite is at any given moment. The almanac is a data file that contains information of orbits and clock corrections of all satellites. It is transmitted by a GPS satellite to a GPS receiver, where it facilitates rapid satellite vehicle acquisition within GPS receivers. The GPS receivers detect, decode and process the signals received from the satellites to create the data of code, phase and Doppler observables. The data may be available in real time or saved for downloading. The receiver internal software is usually used to process the real time data with the single point positioning method and to output the information to the user. Because of the limitation of the receiver software, precise positioning and navigating are usually carried out by an external computer with more powerful software. The basic contributions of the GPS are to tell the user where he is, how he moves, and what the timing is.
Applications for GPS already have become almost limitless since the GPS technology moved into the civilian sector. Understanding GPS has become a necessity.
