Optimal Collaborative Mapping of Terrestrial Transmitters: Receiver Placement and Performance Characterization

Mapping multiple unknown terrestrial signals of opportunity (SOP) transmitters via multiple collaborating receivers is considered. The receivers are assumed to have knowledge about their own states, make pseudorange observations on multiple unknown SOPs, and fuse these pseudoranges through a central estimator. Two problems are considered. The first problem assumes multiple receivers with random initial states to pre-exist in the environment. The question of where to optimally place an additional receiver so to maximize the quality of the estimate of the SOPs' states is addressed. A novel, computationally efficient optimization criterion that is based on area-maximization is proposed. It is shown that the proposed optimization criterion yields a convex program, the solution of which is comparable to two classical criteria: minimization of the geometric dilution of precision (GDOP) and maximization of the determinant of the inverse of the GDOP matrix. The second problem addresses the optimal mapping performance as a function of time and number of receivers in the environment. It is demonstrated that such optimal performance assessment could be generated off-line without knowledge of the receivers' trajectories or the receivers' estimates of the SOP. Experimental results are presented demonstrating collaborative mapping of an unknown terrestrial SOP emanating from a cellular tower for various receiver trajectories versus the optimal mapping performance.