Cooperative Multi-Rigid-Body Localization in Wireless Sensor Networks Using Range and Doppler Measurements

This article addresses multirigid-body localization problems in 3-D wireless sensor networks for both stationary and moving cases using range and Doppler measurements. The challenge of stationary (moving) rigid bodies localization is that not only the position (velocity) but also the rotation angles (angular velocity) need to be estimated, resulting in a nonlinear optimization problem with nonlinear constraints. Existing methods are limited to the localization of a single rigid body in a regular network and are difficult to extend to cooperative multirigid-body localization scenarios. For the stationary case, we first reformulate the cooperative localization problem as a nonconvex and smooth optimization problem with respect to two uncoupled blocks of unknown parameters and auxiliary variables. Next we propose an alternating minimization (AM)-based algorithm, which achieves localization in the absence of accurate prior information by setting the value of one block to be a minimizer of the objective with respect to the chosen block alternately. Subsequently, we propose an online updating algorithm that achieves precise localization by solving the maximum likelihood estimation problem with nonlinear constraints using the Gauss–Newton method on the orthogonal group. Both range and Doppler measurements are used to solve the localization problem in the moving case. Simulation results show that the proposed algorithms achieve better estimation accuracy and anti-noise performance than existing methods for both the stationary and moving cases, and they are suitable for both regular and irregular networks.