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# Global positioning systems

Institute for Environmental and Spatial Analysis...University of North Georgia

## 1   How is a global positioning system (GPS) used in civil applications?

Land, sea, air, and space navigation

Intelligent Vehicle Highway System (IVHS)

Search and rescue

Mapping and GIS

Recreation

Surveying

## 2   Three main components of GPS

Space segment: GPS satellites

Control segment: Ground controls and monitoring stations

### 2.1   Space segment

Constellation of 24 operational satellites

Run by the Department of Defense

• U.S. Air Force Space Command (AFSPC)

First satellite launched in 1978

### 3.2   System of equations

\begin{align*} (x-X_1)^2+(y-Y_1)^2+(z-Z_1)^2&=D(\hat{T}_1,e)^2\\ (x-X_2)^2+(y-Y_2)^2+(z-Z_2)^2&=D(\hat{T}_2,e)^2\\ (x-X_3)^2+(y-Y_3)^2+(z-Z_3)^2&=D(\hat{T}_3,e)^2\\ (x-X_4)^2+(y-Y_4)^2+(z-Z_4)^2&=D(\hat{T}_4,e)^2 \end{align*}

### 3.3   Why do we need four satellites again?

Why does GPS positioning require four satellites? Four unknown variables!