Constrained Angular Motion Estimation in a Gyro-Free IMU EZZALDEEN EDWAN, Member, IEEE STEFAN KNEDLIK, Member, IEEE OTMAR LOFFELD, Senior Member, IEEE ZESS Germany 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). Manuscript received July 8, 2008; revised June 5, 2009; released for publication October 10, 2009. IEEE Log No. T-AES/47/1/940050. Refereeing of this contribution was handled by D. Gebre-Egziabher. This work was partially supported by the German Research Foundation (DFG) under Grant KN 876/1-2. Authors’ address: Center for Sensorsystems (ZESS), University of Siegen, Paul-Bonatz Str. 9-11, Siegen 57068, Germany, E-mail: (edwan@ipp.zess.uni-siegen.de). 0018-9251/11/$26.00 c ° 2011 IEEE I. INTRODUCTION A conventional inertial measurement unit (IMU) consists of three gyros for measuring rotational motion and three accelerometers for measuring linear acceleration. In contrast to a conventional IMU, a gyro-free IMU (GF-IMU) uses a configuration of accelerometers only to measure acceleration and rotational motion of a rigid body in 3D space. In principle it benefits from an effect known as lever-arm effect. To have this effect, the accelerometers must be distributed in distance over the body. In order to distinguish it from a conventional gyro IMU, researchers use other names interchangeably to describe its functionality. The most commonly used names are GF-IMU [1—3], nongyroscopic inertial measurement unit (NGIMU) [4, 5], accelerometer based IMU, and all-accelerometer IMU [6—8]. There exists a variety of reasons for using distributed accelerometers to estimate the angular velocity vector. Most of the GF-IMU publications list some of the justifications [1, 3, 4, 6, 8—13]. In short, the gyroscope typically has the disadvantage of complicated manufacturing techniques, high cost, high power consumption, large weight, large volume, and limited dynamic range [11]. In addition, low-cost micro-electro mechanical system (MEMS) gyroscopes have more inherent physical complexities than accelerometers [1]. On the other hand, accelerometers are smaller, less costly, and less power consuming than comparable gyros. Using certain configurations of twelve separate mono-axial accelerometers produces an angular information vector (AIV) that consists of a 3D angular acceleration vector and six quadratic terms of angular velocities, as is shown later. Unfortunately the angular velocity vector is not expressed explicitly in the AIV. The motivation for this research is that little attention has been given to the sensor fusion of the AIV. The approach of using a double integration of the angular acceleration as described in [14] to achieve the orientation has been proven to be theoretically feasible, but it has a faster error growth rate compared with a conventional inertial navigation system (INS). The advantage of only using the angular acceleration vector has a little value compared with the need for a double integrator. Another problem with such an approach is the need to initialize the angular velocity to be able to integrate the angular acceleration. Continuous research efforts have been conducted to benefit from the other components in the AIV. Recently Park [1] aided the angular acceleration vector by three cross-quadratic terms of angular velocity using an extended Kalman filter (EKF), but his scheme is not using all possible quadratic angular velocity terms as it is possible to get three more quadratic terms. Furthermore, such a scheme suffers from an observability problem if one of the 596 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011