Positioning in Wireless Communications Systems

Chapter 5Position Tracking

The approaches presented in the previous chapter consider a static solution of the position estimation. It was assumed that the MT did not move during the estimation process, and therefore, the MT position was treated as a deterministic parameter. In reality, the MT positions are usually correlated over time. For instance, considering a pedestrian user or a moving car, certain information about the position can be derived using the history of past estimates and suitable movement or mobility models. This includes restricted movements of the MT. For instance, a pedestrian cannot ‘jump’ from one position to another in limited time or a car usually can change its direction only ‘smoothly’. This behavior can be used as side information for position tracking algorithms.

For the derivation of the algorithms (also see Arulampalam et al. 2002; Krach 2010; Mensing 2013; Ristic et al. 2004), we assume that the time axis is divided in to discrete time intervals. Further, we presume a causal system, that is, future states (such as position or velocity) cannot impact current and past estimates. However, since the past states can impact the current and future states, this property has to be reflected in the chosen model. A commonly used model in this position tracking context is a first order hidden Markov model.

Figure 5.1 depicts such a Markov model, for example, (Krach et al. 2008), with unknown states that have to be estimated in each time-step . It is a hidden ...