Multistatic Localization of Multiple Moving Objects Without Transmitter Position and Synchronization

We are interested in the localization of multiple moving objects that are present simultaneously using the delay times and Doppler frequency shifts (DFSs), in a multistatic scenario with a covert transmitter at an unknown position not synchronized with the receivers. The crucial component toward solving this challenging problem is to associate the measurements with each object, and we apply the minimum measurement solutions (MMSs), clustering, and optimization to do so. Specifically, we derive the MMSs of the object velocity candidates from the DFS measurements and develop an efficient clustering algorithm based on the K-nearest neighbors (KNN) to cluster the paired object position and velocity MMS candidates. Afterward, the MMS candidates within each cluster are averaged to obtain preliminary estimates of the object location parameters. Data association in terms of the permutation matrices of the measurements to the objects is deduced from the preliminary estimates by solving a second-order cone programming problem. Finally, from the estimated data association, we create a weighted least squares problem with constraints to jointly improve the preliminary estimates of all objects and arrive at their final location estimations, where the solution of the constrained WLS problem is found using the semidefinite relaxation approach. Theoretical analysis is conducted for the proposed method to show its optimal performance, when the data model noise is Gaussian. Simulation results confirm the performance of the proposed method.