# Coordinate Reference Systems and Positioning

## Introduction

This book is intended to develop content for a new chapter on Coordinate Reference Systems and GNSS Surveying for the Spatial Data Infrastructure Cookbook developed through the Global Spatial Data Infrastructure (GSDI) initiative. The purpose of the chapter is to provide high level information for a basic understanding of global coordinate reference systems (e.g., WGS 84, ITRFxx/GRS80) and case studies from different regions and countries of the world about the challenges of tying their datums to global coordinate reference systems. As the final product will be incorporated in a Portable Document Format (PDF) document, it is important that sufficient information be extracted from open sources so that the user does not have to jump from article to article to get high level information about Global Coordinate Reference Systems and Positioning. Content will be condensed into a chapter covering 15-20 pages.

The Wikibooks approach is being used to foster international collaboration and to quickly develop content. Anyone can contribute and change existing content, and one does not need to register. If, however, you want attribution for your contribution, you are encouraged to register. If you decide to contribute, it is recommended that you familiarize yourself with Wiki markup. The Wikibooks approach is not for people who do not want their masterpiece altered!

As of 2005-01-26, our wish list for contributions is as follows:

1. Extraction of information from open sources for inclusion in this chapter
2. Graphics and figures
3. Case studies from various regions and countries of the world for tying into global coordinate reference systems such as WGS 84 and ITRFxx/GRS80
4. Anything marked as TBSL (To Be Supplied Later)

## Context and rationale

Consistent with the SDI Cookbook, this section establishes the background, context, and rationale for the subject suitable as general orientation for all readers, but targeted for managers and end-users.

### Geodetic datum

#### Ellipsoid

In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the true figure of the Earth or geoid. It is used as the surface on which geodetic network computations are performed and [geographic] point co-ordinates calculated.

Mathematically, the reference ellipsoid is an oblate (flattened) ellipsoid of revolution with two different axes, an equatorial semi-major axis ${\displaystyle a}$ and a polar semi-minor axis ${\displaystyle b}$. The ellipsoid of revolution is obtained by rotating the ellipse about the semi-minor axis ${\displaystyle b}$ (refer to Reference ellipsoid)

The flattening ${\displaystyle f}$ is defined as

${\displaystyle f={\frac {a-b}{a}}}$

- from Reference ellipsoid

GRS80 was adopted by the International Union of Geodesy and Geophysics (IUGG) at its XVII General Assembly in Canberra, Australia, December 1979.

For GRS80, ${\displaystyle a}$ = 6 378 137 m and ${\displaystyle f}$ = 0.003 352 810 681 18

### Geoid

A geoid is a close representation of the shape of the Earth. According to C.F. Gauss, it is the "mathematical figure of the Earth", in fact, of the Earth's gravity field. The geoid is that equipotential surface which coincides on average with mean sea level. - adapted from Geoid

The geoid has an irregular surface and unlike the ellipsoid, cannot be expressed by a mathematical formula.

### Height

In geodesy, height is the distance of a point (usually on the terrain surface, such as a mountain top) vertically above or below a reference surface - adapted from Height

An ellipsoidal height uses the reference ellipsoid as its reference surface. A geodetic height uses the geoid as its reference surface.

### Coordinate systems

#### Cartesian coordinate systems

Cartesian coordinates

### Global Coordinate Reference Systems

#### International Terrestrial Reference System(ITRS)

International Terrestrial Reference System (ITRS)

##### International Terrestrial Reference Frame(ITRF)

The International Terrestrial Reference Frame - The International Terrestrial Reference Frame (ITRF) is a set of points with their 3-dimensional Cartesian coordinates which realize an ideal reference system, the International Terrestrial Reference System (ITRS)

#### World Geodetic System of 1984 (WGS 84)

NIMA Technical Report TR8350.2, "Department of Defense World Geodetic System 1984, Its Definition and Relationships With Local Geodetic Systems"

Plate tectonics

### Global Navigational Satellite Systems (GNSS)

#### Concepts

##### How positions are determined

GNSS determine positions on the earth through trilateration.

## Organizational issues

Consistent with the SDI Cookbook, this section addresses the design architecture of organisations, roles, and software systems that are intended to interact.

This section will provide case studies on how various regions and countries of the world are tying into Global Spatial Reference Systems.

### Regional reference frames

IAG Subcommission 1.3: Regional Reference Frames

### National datums

#### Australia

Geocentric Datum of Australia
Reference Frame: ITRF92(International Terrestrial Reference Frame 1992), Epoch 1994.0, Ellipsoid: GRS80

#### New Zealand

New Zealand Geodetic Datum 2000 (NZGD2000)
Reference Frame: ITRF96 (International Terrestrial Reference Frame 1996), Epoch 2000.0, Ellipsoid: GRS80

New Zealand lies along the boundary of the Australian Plate and Pacific Plate and therefore, is a geophysically active area. The effects of slow crustal deformation (plate tectonics) amount to about 5 cm per year. These changes will be managed through the use of a velocity model to generate NZGD2000 coordinates from observations made at times other than the datum reference epoch. This will allow specialised users to generate coordinates for times other than the reference epoch.

#### United Kingdom

OSGB36 (Ordnance Survey Great Britain 1936)
Reference Frame: OSGB36, Ellipsoid: Airy 1830