This paper presents a method for determining 3D angular motion of a rigid body using linear acceleration data obtained from a set of randomly oriented accelerometers arranged in a plane. The angular accelerations are treated as design variables and are determined using an optimization methodology which minimizes the cumulative error at each time step between the measured linear accelerations and computed linear accelerations. It has been shown in the past that the six-accelerometer array becomes unstable in the presence of small inaccuracies in the measured accelerations when closed form methods are used for finding the solution. The current methodology uses an optimization technique instead of a closed form method to determine the angular accelerations and can be used with the six-accelerometer array without any instability. As a validation of the method, known angular kinematics obtained from the nine accelerometer array data are used. In-plane accelerometer subsets are used to obtain the linear acceleration data and the optimization methodology is applied to these subsets. The angular kinematics obtained with these subsets compare well with the originally known angular kinematics. Further studies are conducted with this methodology on mouthpiece accelerometers and issues like accuracy improvement and effect of cross-axis error are studied.