The problem of localization involves estimating the position of a user from a number of noisy sensor measurements. In a practical wireless network, these sensor measurements cannot be collected instantaneously and arrive after a certain delay. In a dynamic scenario where the users move around, this delay will render some measurements out-dated and, if not taken into account, have a negative effect on the localization performance. This paper consists of two parts, in the first part we investigate the effect of user movement on the measurement models for ranging. In the second part we use these models to analyze the impact of movement on the accuracy of the position estimate by means of the Cramer-Rao lower bound (CRLB) which bounds the performance of the estimation.