Cooperative Multiple Rigid Body Localization via Semidefinite Relaxation Using Range Measurements

This paper investigates the multiple rigid body localization (MRBL) problem using range measurements. To address the MRBL problem, we propose the cooperative approach by availing of not only the sensor-anchor but also the sensor-sensor measurements. The performance of cooperative MRBL is proven to be better than that of the noncooperative MRBL approach, in which only sensor-anchor measurement is used to locate the rigid bodies. Considering two different cases of 2-D and 3-D, we also propose a cooperative semidefinite programming (CSDP) solution to determine the rotation matrices and positions of multiple rigid bodies. At low noise levels, the performance of the CSDP solution is proven to sufficiently approach the Cramér-Rao Lower Bound (CRLB) accuracy due to its tight CSDP form. In addition, a set of determinant constraints is developed and included in the CSDP to improve the performance of the moderate noise levels. The simulated results show that the cooperative CSDP has significantly improved performance compared with the noncooperative approach. At moderate noise levels, the CSDP performs better than the CSDP-NDet, which does not include the determinant constraints. In the simulations, we also verify the conditions of the tight CSDP form. Besides, we also demonstrate that the CSDP solution outperforms the existing methods at varying noise levels.