We consider the ability of a mobile sensor to locate its own geographical location, the so-called self-localization problem. The need to locate people and objects has inspired the development of many systems for automatic localization. Most systems are based on location information and measured radio propagation characteristics for received signals from sensors in the proximity of the mobile sensor. It is of fundamental importance that such systems also works in critical situations such as loss of observability or the presence of multipath. The present paper suggest a framework to assess the performance of localization algorithms in mobile and critical situations. This is done by exploring the performance of various filtering techniques for self-localization of a mobile sensor in a field of sensors. More specifically, we model the mobility of the sensor such that the velocity varies according to an autoregressive model. Measurement uncertainty is assumed to follow a Gaussian distribution and the probability for detecting a distance to a given sensor is assumed to fall off exponentially with squared distance. The combined model is formulated as a nonlinear state space model and Bayesian inference is performed with the extended Kalman filter (EKF) and a particle filtering method. Precision of the position estimate is evaluated by the root mean square error (RMSE). A lower bound on the RMSE of the estimate is derived, thus providing important information on the best achievable precision for any algorithm. We report a number of simulation experiments which validate our proposed algorithms and theoretical results. We conclude that the performance of the EKF and particle filtering methods are comparable and that the derived lower bound is a useful lower limit on the RMSE.