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In this paper, we present an extended Kalman filter (EKF)-based solution for the estimation of the angular motion using a gyro-free inertial measurement unit (GF-IMU) built of twelve separate mono-axial accelerometers. Using such a GF-IMU produces a vector, which we call the angular information vector (AIV) that consists of 3D angular acceleration terms and six quadratic terms of angular velocities. We consider the multiple distributed orthogonal triads of accelerometers that consist of three nonplanar distributed triads equally spaced from a central triad as a specific case to solve. During research for the possible filter schemes, we derived equality constraints. Hence we incorporate the constraints in the filter to improve the accuracy of the angular motion estimation, which in turn improves the attitude accuracy (direction cosine matrix (DCM) or quaternion vector).