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Navigation and Pose Estimation Theory

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Basic Theory In the previous chapter, we introduce about the indoor positioning system techniques and the research directions. In this chapter we will describe the basic theory related with the navigation and pose estimation systems for example, the coordinate system, the dead-reckoning method, the characteristic of Wi-Fi radio signal propagation etc. For all of the basic ideas are very important thing to understanding the configuration of our research as follow;

2.1 The Local Coordinate system The coordinate system was used to defined in local-area environment name is the Cartesian coordinate system refer to [55]. It can be referenced by placing the origin to the local point consist with 3 reference axis, there are axis is directed to the vertical, axis is pointed to the north and axis is directed to the east, see in figure 1. Figure 1 The Cartesian coordinate system.

The plane is the horizontal plane and the vertical plane is defined perpendicular to the ellipsoid such a coordinate system is also called a local horizontal coordinate system. From figure 1. can be described, the projection point whose coordinates in global and local coordinate system are and respectively, one has relation of as follow: (2.1)
Where the is the azimuth angle measure from the north clockwise, is the zenith distance that mean the angle the vertical and the radian and r is the radian of the in the local system.

2.1.1 Transformation Matrix in Cartesian coordinate

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