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We present a two-stage centralized algorithm for tracking multiple targets using spatially distributed bearings-only sensors that report the observations asynchronously. The sensors are assumed to be passive, i.e., they detect the energy emitted by the targets of interest to measure the bearing. The number of targets in the surveillance region is unknown a priori and the targets can enter or leave the surveillance region at any time. The measurement origin is also unknown since a detection can be due to the target being tracked, from a new target, or from clutter. In the first stage (the initialization stage) the proposed algorithm forms local bearings-only (mono) tracks for each sensor and combines these tracks to generate complete kinematic (stereo) tracks in the Cartesian coordinate frame. Once stereo tracks are formed, in the second stage, which is called the stereo tracking stage, bearing measurements are directly used to update the stereo tracks. This separation of the initialization and maintenance of the stereo tracks is lacking in many existing algorithms and results in improved performance. In this work we used the assignment-based technique to solve various data association problems that arise due to measurement origin uncertainty. Through extensive simulations we show that the proposed algorithm achieves better tracking accuracy while being computationally simpler than existing algorithms.