  Source localization techniques incorporating hybrid measurements improve the
reliability and accuracy of the location estimate. Given a set of hybrid
sensors that can collect combined time of arrival (TOA), received signal
strength (RSS) and angle of arrival (AOA) measurements, the localization
accuracy can be enhanced further by optimally designing the placements of the
hybrid sensors. In this paper, we present an optimal sensor placement
methodology, which is based on the principle of majorization-minimization (MM),
for hybrid localization technique. We first derive the Cramer-Rao lower bound
(CRLB) of the hybrid measurement model, and formulate the design problem using
the A-optimal criterion. Next, we introduce an auxiliary variable to
reformulate the design problem into an equivalent saddle-point problem, and
then construct simple surrogate functions (having closed form solutions) over
both primal and dual variables. The application of MM in this paper is distinct
from the conventional MM (that is usually developed only over the primal
variable), and we believe that the MM framework developed in this paper can be
employed to solve many optimization problems. The main advantage of our method
over most of the existing state-of-the-art algorithms (which are mostly
analytical in nature) is its ability to work for both uncorrelated and
correlated noise in the measurements. We also discuss the extension of the
proposed algorithm for the optimal placement designs based on D and E optimal
criteria. Finally, the performance of the proposed method is studied under
different noise conditions and different design parameters.
