Estimating the position of a mobile node by linear sensor fusion of ranging, speed, and orientation measurements has the potentiality to achieve high localization accuracy. Nevertheless, the design of these sensor fusion algorithms is uncertain if their fundamental limitations are unknown. Despite the substantial research focus on these sensor fusion methods, the characterization of the Cramér Rao Lower Bound (CRLB) has not yet been satisfactorily addressed. In this paper, the existence and derivation of the posterior CRLB for the linear sensor fusion of ranging, speed, and orientation measurements is investigated. The major difficulty in the analysis is that ranging and orientation are not linearly related to the position, which makes it hard to derive the posterior CRLB. This difficulty is overcome by introducing the concept of posterior CRLB in the Cauchy principal value sense and deriving explicit upper and lower bounds to the posteriori Fisher information matrix. Numerical simulation results are provided for both the parametric CRLB and the posterior CRLB, comparing some widely-used methods from the literature to the derived bound. It is shown that many existing methods based on Kalman filtering may be far from the the fundamental limitations given by the CRLB.