Optimal Sensor Placement for Full-Set TDOA Localization Accounting for Sensor Location Errors

The positioning accuracy of a signal source is influenced by where the sensors are deployed. Studies in the literature for the optimal sensor placement (OSP) of localization often ignore the presence of sensor position errors. In practice, however, it is impossible to place the sensors precisely at the desired locations. This work designs OSP by accounting for the presence of Gaussian sensor position errors that are independent and identically distributed (IID), with the full set of Time Difference of Arrival measurements corrupted by Gaussian IID noise. The criterion is the A-optimality equal to the trace of the source position Cramer-Rao Bound (CRB). We show that the presence of sensor position errors introduces a multiplication factor to the same criterion for the case without sensor position errors. The latter factor is dependent on the ratio of the sensor position error power to the range difference noise power but independent of the sensor positions, implying that the A-optimality OSP in the presence of sensor position errors is the same as in the absence. To our knowledge, this is the first time such results have been derived. Simulation studies validate the derived OSP, show the minimal OSP performance gap with sensor positioning error and without, and illustrate the better source localization accuracy by OSP.