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This paper discusses the design, calibration, simulation, and experimental validation of a kinematically redundant inertial measurement unit that is based solely on accelerometers. The sensor unit comprises 12 accelerometers, two on each face of a cube. The location and direction of the sensors are determined so as to locally optimize the numerical conditioning of the system of governing kinematic equations. The orientational installation error of each sensor is identified by off-line iterative processing of the gravitational acceleration measurements made at a number of known orientations of the unit, thus allowing subsequent calibration. Furthermore, a novel procedure is developed through which the acceleration measurements can be used to directly determine the body angular velocity; this results in a major accuracy improvement over similar works whereby the angular velocity is obtained via integrating the angular acceleration. Experimental results are presented to validate the methodology, design, and implementation.