Rigid body localization (RBL) is to simultaneously estimate the position and attitude of a rigid target. In this paper, we focus on the RBL problem using a single base station (BS) and direction of arrival (DoA) measurements. Several wireless sensors are mounted on the rigid body of interest, and their topology information is known a priori. The single BS measures the DoAs of wireless sensor signals and fuses them with the sensor topology information to estimate the position and orientation of the rigid body and achieve RBL. We propose two RBL methods, namely, the observation matching (OM) algorithm and topology matching (TM) algorithm with refinement. The emerging participatory searching algorithm (PSA) is adopted in both methods to solve the nonlinear matching problems. Simulations show that, compared with the existing approach, the OM method can achieve better RBL accuracy under high DoA noise levels, while the performance of the TM algorithm with refinement is closer to the constrained Cramér–Rao bound (CCRB) under low DoA noise levels.