  Source localization plays a key role in many applications including radar,
wireless and underwater communications. Among various localization methods, the
most popular ones are Time-Of-Arrival (TOA), Time-Difference-Of-Arrival (TDOA),
and Received Signal Strength (RSS) based. Since the Cram\'{e}r-Rao lower bounds
(CRLB) of these methods depend on the sensor geometry explicitly, sensor
placement becomes a crucial issue in source localization applications. In this
paper, we consider finding the optimal sensor placements for the TOA, TDOA and
RSS based localization scenarios. We first unify the three localization models
by a generalized problem formulation based on the CRLB-related metric. Then a
unified optimization framework for optimal sensor placement (UTMOST) is
developed through the combination of the alternating direction method of
multipliers (ADMM) and majorization-minimization (MM) techniques. Unlike the
majority of the state-of-the-art works, the proposed UTMOST neither
approximates the design criterion nor considers only uncorrelated noise in the
measurements. It can readily adapt to to different design criteria (i.e. A, D
and E-optimality) with slight modifications within the framework and yield the
optimal sensor placements correspondingly. Extensive numerical experiments are
performed to exhibit the efficacy and flexibility of the proposed framework.
