Accurate Localization Of A Stationary Rigid Body In The Presence Of Anchors Uncertainties

Source localization has been the focus of research because of its effectiveness in various applications.With the development of wireless sensor technology,source localization based on wireless sensor network can be used in more practical scenarios.Traditionally,the source localization method based on wireless sensor network regards the object of interest as a point source.However,many localization applications consider the target as a rigid body in which deformation is zero or so small it can be neglected,but the distance between any two given points on a rigid body can not be neglected.Sensors with known topologies are mounted on the rigid body,and some known observation points are distributed around the rigid body.These observation points are called anchors in this paper.Using the range or time measurements between the sensors and the anchors identifies the orientation and the position of the rigid body jointly.The localization scenario has been called rigid body localization in this paper.A previous study shows that a stationary rigid body can be localized accurately using the time measurements between the sensors on the rigid body and a few landmarks outside(called anchors in this paper).The previous studies are performed under the condition where the exact positions of the sensors and the anchors are known.This paper extends the previous work to a more practical scenario where the exact positions of the anchors are not known exactly.The accuracy of a rigid body location estimate is very sensitive to the accurate knowledge of anchor positions.By modeling the anchor position errors as additive Gaussian noise,the amount of reduction in rigid body localization accuracy due to anchor position errors is derived through Cramér Rao lower bound(CRLB)analysis.With the presence of anchor position noise,we derive the Maximum Likelihood Estimator(MLE)as a benchmark for rigid body localization performance evaluation.A closed-form enhanced divide and conquer(e DAC)estimator is then developed by accounting for the anchor position errors and it is proved analytically to reach the CRLB accuracy when the anchor position errors are small relative to the range between the anchors and the rigid body sensors.The proposed e DAC estimator is non-iterative and have three steps: intermediate variables,preliminary solution and the refinement.Another proposed enhanced semidefinite programming(e SDP)method generates an initial estimate based on the semidefinite relaxation technique,and applies orthogonalization to obtain the final SDP solution.The iterative nature of SDP results in the high computational complexity.Simulations show that both the proposed e DAC and e SDP estimators can approach the CRLB performance and the MLE performance under Gaussian noise over the small error region.Simulations also validate the better performance of the proposed e SDP method than the e DAC method when the anchor position noise level increases to a high level.Simulations also show that the proposed e DAC and e SDP methods are more effective to reduce the probability of large estimation error solutions compared with the previous works when the anchor position uncertainties are very large.Taking into account the computational complexity,it is more appropriate to employ the proposed e DAC method when the anchor position errors are Gaussian and in the small error power region,and it is more appropriate to employ the proposed e SDP method under large noise power level if high computational complexity is tolerable.