Performance Analysis of Relative Localization with Unknown Clock and Orientation

High-accuracy position information is essential for emerging applications in cooperative networks. Compared with absolute coordinates, relative positions of nodes are more perti-nent for tasks like autonomous driving. In this paper, we establish a theoretical analysis framework for relative localization with unknown clock and orientation parameters. First, we specify three scenarios for relative localization in cooperative networks. The relative position estimation is proved to be a constrained optimization and the relative Cramér-Rao lower bound (CRLB) is derived as the constrained CRLB. Then we prove that the equivalent Fisher information matrix (EFIM) retains the information for relative localization of the concerned nodes. Moreover, we derive the Fisher information matrix for three scenarios and give the corresponding nullspace. Finally, the relative CRLB is proved to be the pseudo-inverse of the EFIM.