The nine accelerometer array sensor package is used extensively in injury biomechanics research to obtain the rotational acceleration time histories of a rigid body. It has been shown in the past to remain computationally stable while the alternative, the six accelerometer array, becomes unstable in the presence of small inaccuracies in the individually measured accelerations. The nine accelerometer array process achieves its stability by requiring the measurement of three rotational accelerations, thus eliminating the six accelerometer array’s dependency on having knowledge of the rigid body’s three rotational velocities at each instant in time. The nine accelerometer array’s additional three measurements also provide other important benefits:​ 1. Identifying whether or not any one of the nine translational acceleration measurements is inconsistent with rigid body motion, 2. If an incorrect acceleration is found, determining what the actual time history should be for that case, 3. Use of optimization methodology to obtain the best possible solution for the rigid body motion. This paper presents the derivation of an additional set of constraint equations that a given set of nine linear accelerations must satisfy to be consistent with rigid body motion, demonstrates how an inconsistent acceleration input is discovered, and describes the process by which the true time history of the acceleration is recovered. In addition, optimization methodology is introduced to obtain the best possible solution for a randomly distributed in-plane accelerometer system when errors in measurements are artificially introduced.