GPS tracking solutions - the basic science behind GPS

Fundamentals of satellite-based positioning

To understand the true value and cost of the positioning capabilities of the GPS, it is important for the user to have a basic understanding of the science behind positioning, and the types of components and techniques that may be used to calculate accurate positions. The basic science behind GPS; the different unassisted and assisted position calculation techniques that may be used, depending upon the needs of the specific application; and the hardware and software components necessary for calculating a position.

The basic science of global positioning

The design of the electronic tracking devices makes it an all-weather system whereby users are not limited by cloud cover or inclement weather. Broadcasting on two frequencies, the GPS provides sufficient information for users to determine their position, velocity and time with a high degree of accuracy and reliability. As mentioned previously, frequency L1 is generally regarded as the civilian frequency while frequency L2 is primarily used for military applications. Applications and positioning techniques in this chapter will focus on GPS receiver technology capable of tracking L1 only, as cost and security issues typically preclude most users from taking full advantage of both GPS frequencies. Without a complete knowledge of the encrypted L2 frequency, only mathematical exercises enable high accuracy applications of GPS such as surveying to take advantage of any information provided by L2.

Position calculation

The fundamental technique for determining position with the GPS is based on a basic range measurement made between the user and each GPS satellite observed. These ranges are actually measured as the GPS signal time of travel from the satellite to the observer’s position. These time measurements may be converted to ranges simply by multiplying each measurement by the speed of light; however, since most GPS tracker internal clocks are incapable of keeping time with sufficient accuracy to allow accurate ranging, the mathematical PVT solution must solve for errors in the receiver clock at the time each observation of a satellite is made. Satellite ranges are commonly called pseudoranges to include this receiver clock error and a variety of other errors inherent in using GPS. These receiver clock errors are included as one component in a least squares calculation, which is used to solve for position using a technique called trilateration.

Coordinate systems

The coordinate frame used by the GPS to map a satellite’s position, and thus a receiver’s position, is based on the World Geodetic System 1984 (WGS 84). This coordinate reference frame is an Earth-centred, Earth-fixed (ECEF) Cartesian coordinate system, for which curvilinear coordinates (latitude, longitude, height above a reference surface) have also been defined, based on a reference ellipsoid, to allow easier plotting of a user’s position on a traditional map. This coordinate frame, or datum, is the standard reference used for calculating position with the GPS. However, many regional and local maps based on datums developed from different ground based surveys are also in use today, whose coordinates may differ substantially from WGS 84. Simple mathematical transformations can be used to convert calculated positions between WGS 84 and these regional datums, provided they meet certain minimum criteria for the mapping of their longitude, latitude and local horizontal and vertical references. At last count, more than 100 regional or local geodetic datums were in use for positioning applications in addition to WGS 84.

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