Positioning in Wireless Communications Systems

Chapter 3Measurements and Parameter Extraction

Wireless positioning is based on the observation of radio signals. Several parameters of a received radio signal depend on the position of the receiver. So, a first step in wireless positioning is the estimation of those signal parameters that depend on location. Such parameters for instance are delay, amplitude, or phase of a signal. These parameters have to be derived from an observed signal. Normally, this signal is represented by noisy signal samples. Here, noise is a kind of signal distortion, which we do not know deterministically. However, we can consider such distortions as stochastic processes where information about the parameters of the stochastic process may be known or can be estimated. A well-known example for stochastic signal distortions is additive white Gaussian noise (AWGN).

3.1 Parameter Estimation

We are interested in obtaining a parameter, which has a continuous range of values, from a received set of signal samples. Subsequently, we will formulate the estimation problem in general. The quality of parameter estimation is of great interest. Parameters are estimated from a received signal, which is corrupted stochastically. Thus, estimates of the parameters itself will be noisy as well. We will consider the variance of estimates as a quality measure. It is obvious to raise the question about the optimum achievable estimation performance. The Cramér–Rao inequality provides a lower bound on the variance of an ...