Optimal Receiver Placement for Collaborative Mapping of Signals of Opportunity

Mapping an unknown terrestrial signal of opportunity (SOP) via multiple collaborating receivers is considered. The receivers are assumed to have knowledge about their own states, make pseudorange observations on an unknown SOP, and fuse these pseudoranges through a central estimator. Two problems are considered. The first problem assumes N 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 estimate quality of the SOP’s states is addressed. Three optimization problems are compared: minimizing the geometric dilution of precision (GDOP), maximizing the determinant of the GDOP matrix, and maximizing the area of the polygon inscribed in the unit circle whose vertices are the unit line of sight vectors from the SOP to the receivers. It is demonstrated that the three optimization problems are comparable and it is shown that the area maximization problem is piecewise-concave with a simple analytical solution. The second problem addresses the optimal estimation performance as a function of time and number of receivers in the environment. It is demonstrated that such optimal performance assessment could be generated offline without knowledge of the receivers’ initial states and trajectories or the receivers’ estimates of the SOP.