Positioning in Wireless Communications Systems

Chapter 4Position Estimation

In this chapter, we address how to calculate the MT position, given a set of measurements according to Chapter 3 in a static scenario, using the position principles presented in Chapter 2. We assume that the MT is stationary during the position estimation process. Thus, the MT position is deterministic. In Chapter 5, we extend the static position estimation to the dynamic position tracking.

In this chapter, we consider ideal and erroneous measurements. With erroneous measurements, we mean measurements that are noisy or biased, for example, due to thermal noise or unknown MT clock offset for TOA measurements. However, we do not consider in this chapter measurement errors due to multipath and NLOS propagation. For that, we refer the reader to Chapter 7.

In the following section, we present the navigation equations for the positioning principles in Chapter 2. To allow a simple visualization, we restrict ourselves to a two-dimensional planar space. By default, we assume Cartesian coordinates. Where appropriate, we will extend our considerations to three-dimensional space.

The BSs are located at

and the MT is located at

The distance between -th BS and the ...