Study On Algorithms About Rigid Body Localization Based On The Semidefinite Programming

As an application of wireless sensor networks(WSN),target positioning plays an important role in social production,life and military.In some applications,such as robotics,spacecraft,and so on,we need to obtain additional location information of the object when it is viewed as a rigid body.Localization of a rigid body consists of not only the position,but also the orientation.If the body is moving,additional parameters of translation and angular velocities are also desired.The challenge is that the rotation matrix and position vector are nonlinearly related to the measurements and they are strongly coupled with each other.Moreover,the elements of the rotation matrix must satisfy a few nonlinear constraints.As a result,rigid body localization is a difficult nonlinear optimization problem.The main research results for the rigid body localization problem are as follows:(1)For the stationary rigid body localization,we propose two semidefinite programming(SDP)methods.The first method is based on the range measurement model and semidefinite relaxation(SDR)is applied to the maximum likelihood estimator(MLE)problem to obtain a SDP problem.In the second method,we start from transforming the measurement model and formulate a constrained weighed least-squares(CWLS)problem.SDR is then applied to obtain a SDP problem.Two methods all need orthogonalization and refinement procedure.The simulations show that the proposed methods achieve better accuracy than the previously developed methods and can reach the Cramér-Rao lower bound(CRLB)accuracy when the noise level is not significant.(2)For the moving rigid body localization,the second solution to stationary rigid body localization can also be applied when we add the Doppler measurements.We can also formulate a CWLS problem and then obtain a SDP problem.Meanwhile,a new refinement procedure is followed to improve the accuracy of the estimation.The simulations show that the proposed method performs better than the previously developed methods and can reach the CRLB accuracy when the noise level is not significant.