Alan Oxley
Bahrain Polytechnic
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Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter covers the rudiments of what the NAVSTAR Global Positioning System (GPS) is. Users come into contact with GPS by using a receiver. They are aware that problems that can arise (have arisen) by a receiver inaccurately calculating a location. Technically speaking, GPS is a satellite-based radio-positioning system. However, it can also be used to accurately find out the time. GPS is financed by the US Department of Defense. They are also responsible for its design, deployment, and operation. The chapter also highlights the significant benefit that GPS has made to civilian community who are using GPS in a large and expanding number of applications.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
Using GPS alone may not give the desired positioning accuracy. Some applications require high accuracy, such as when an aircraft is landing. This chapter describes some ways of using additional information, that is, augmenting GPS, so as to produce a better result. One way is to have a receiver that uses signals from two GNSSs—such as GPS and GLONASS. There are potential problems with integrating two GNSSs though, as the systems have different characteristics. Another approach is to supplement GPS with a Satellite-Based Augmentation System, where geostationary satellite(s) are used to supply the additional information. Several other approaches exist, such as Network RTK and Assisted GNSS.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter is about the use of GPS for something other than positioning. It is the use of GPS for time and frequency measurement. In metrology laboratories, usage is made of GPSDOs which is a special type of GPS receiver. This chapter explains how a GPSDO works. A description of GPSDO performance is also given. Knowing the advantages and disadvantages of GPSDOs, when a laboratory is about to purchase a time and frequency standard it is able to choose whether to purchase a GPSDO or opt for a rubidium or a cesium clock. It is advantageous for the reader to gain some exposure to GPS activities in metrology laboratories because of the very fine detail to which their work is carried out.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter includes a number of topics. One of these looks at the planned accuracy and precision, of positioning, with which Global Positioning System (GPS) was designed to work. Another topic is the natural effects that GPS signals are subjected to, such as relativity. Mention is also made of some abnormal natural effects that can occur, such as a solar maximum. When a solar maximum occurs it results in ionospheric scintillation and this adversely affects the signal to noise ratio. Differential GPS, which is a means of improving position accuracy by using additional data, is discussed. The chapter also shows how the Earth is modeled.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter discusses positioning and navigation. The chapter looks at the characteristics of positioning systems as a whole. The reader is able to see how the satellite positioning techniques used in the Global Positioning System, which is a Global Navigation Satellite System (GNSS), compare to those techniques used in terrestrial positioning systems. Positioning and navigation systems exist for land, sea, and air applications and different technologies suit different applications. Some of the error modeling carried out on terrestrial positioning systems contributes to GNSS error modeling. Algorithms for improved positioning are a subject of active research. As research progresses, users will be able to move between positioning technologies seamlessly.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter describes the structure of Global Positioning System signals. On each of two frequencies, there is a carrier signal, and this is modulated by ranging code(s), as well as data. The two ranging codes are coarse/acquisition (C/A) and P(Y) codes. These are PRN bit sequences. Each satellite uses a different C/A code and a different P(Y) code so that a receiver can identify which satellite a signal is being transmitted from. The coarse/acquisition code is used for the Standard Positioning Service whereas the P(Y) code is used for the Precise Positioning Service. The data is used for navigation. It is referred to as the navigation message. It is made of several items of data, including satellite ephemeris.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter describes how a receiver position can be calculated accurately given the exact position of at least four satellites and the exact pseudodistances. Example data is given from which a receiver must calculate its location. The complete calculation is carried out for example data where there are five satellites. Details are given of a competition that was run to elicit solutions to a GPS positioning problem. Data was given on five satellite positions and the pseudodistances to the receiver. For simplicity, some of the natural and other effects that cause errors in positioning calculations were ignored. Two challenges were posed. This chapter tackles the first of these.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
This chapter describes an example problem in which the errors are distributed for two items of data—the satellites’ locations, and the pseudodistances. Probability distributions for these two items are given. Possible methods of solution are described. One method is described in fine detail and the result that it produces is explained. The solution gives a 3D description of the probability of the receiver’s position. For practical use, positioning often requires a solution to be given in 2D, that is, on the surface of the Earth. In view of this, it is shown how the 3D solution of the example problem can be further processed to produce a 2D solution.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
The ranging codes for the Global Positioning System’s (GPS’s) legacy signals are C/A and L1 P(Y) (both broadcast on the L1 frequency) and L2 P(Y), broadcast on the L2 frequency. GPS is undergoing a process of modernization. This includes the addition of new ranging codes. Detailed characteristics of the legacy and new codes are given. Satellites launched more recently have different characteristics to older satellites. An explanation is given of how a receiver is able to process signals from multiple satellites. The technique employed is code division multiple access. The steps that a receiver takes in acquiring a signal and tracking it are described.
Uncertainties in GPS Positioning#R##N#A Mathematical Discourse | 2017
Alan Oxley
In reality, the problem is that a receiver cannot calculate its position exactly; it can only do so to a certain degree of accuracy. This chapter explains why a satellite’s position cannot be found exactly. One of the reasons for this is that a pseudo-distance is not known exactly. This and other sources of inaccuracy are explained. The positioning calculation and subordinate calculations are dependent on these various factors. In addition to this, GPS has its vulnerabilities. GPS signals can be deliberately interfered with; physical equipment can degrade, and so on. An explanation of what is meant by accuracy is given.