1549-7747 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCSII.2019.2928476, IEEE Transactions on Circuits and Systems II: Express Briefs > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract — In this work, a new custom circuit is proposed to make the acquisitions of low-power tri-axial accelerometers independent from the spatial orientation of the sensors. For the purpose, a new vector rotation algorithm has been developed in order to reduce the overall computational effort and the complexity of the resulting circuit. The modularity of the computational scheme and the specific design choices have limited the area occupancy and the power dissipation of the circuit to negligible values with respect to the circuitry embedded in typical low-power accelerometers. The design has been prototyped with a Xilinx Artix-7 FPGA, where it achieves a maximum throughput of 81.2 kHz. Synthesis using a 65 nm CMOS standard cells library provides a maximum throughput of 223 kHz and an occupied area of 0.024 mm 2 . By setting the sample rate of the sensor to 25 Hz used as reference in many motion sensing applications, the standard cells power dissipation is about 1 μW. Comparisons with the state-of-the-art in the literature show a maximum area and power reduction of 40% and 55%, respectively. Index Terms— Inertial sensors; smart sensors; low-power; wearable systems; FPGA. I. I NTRODUCTION OR some time, accelerometers have been the inertial sensors of choice for low-power embedded applications thanks to their compactness and energy efficiency. Nevertheless, they are becoming even more attractive for more complex applications enabled by all-accelerometers or heterogeneous inertial measurement units [1]-[3]. For several applications, such as human activity recognition and fall prediction, assisted hand-held microsurgical devices, position and orientation estimation, the capability to use a common reference system for different measurements is mandatory, as well as the elimination of noise deriving from the lack of a fixed sensor orientation [3]-[8]. In this paper, a new custom circuit is proposed, which makes the acquisitions of a tri-axial accelerometer independent from the orientation of the sensor. This is achieved by implementing a new “hardware friendly” algorithm, specifically derived from the Rodrigues’ rotation formula [9]. The algorithm is capable to rotate each sample from a tri-axial accelerometer from an arbitrary coordinate system to a reference one in real-time. Namely, three components of a measured acceleration vector are rotated before the arrival of the next ones in sensor sampling order. This feature has been obtained by minimizing the number of arithmetic operations and eliminating the trigonometric ones that, instead, are necessary within alternative approaches presented in the next section. Moreover, the proposed calculation scheme is favorably composed by a pattern repetition of arithmetic operators. Therefore, the derived circuit is implemented by a very reduced sub-set of arithmetic modules, which iteratively process raw data from the accelerometer. The reduced dimensions and the specific design choices for the arithmetic circuits limit the power dissipation to negligible values compared to tens μW, typically required by the low-power always-on accelerometers currently on the market [10], and triggers the opportunity to integrate the proposed circuit as part of the sensor circuitry. The design has been implemented on a Xilinx Artix-7 FPGA, where it achieves a maximum throughput of 175.6 kHz. Synthesis using a 65 nm CMOS standard cells library provides a maximum throughput of 223 kHz and an occupied area of 0.024 mm 2 . By setting, for example, the sample rate of the sensor to 25 Hz required by a human motion sensing application, the standard cells power dissipation is about 1 μW. Comparisons with alternative HW solutions built on processing cores taken from the state-of-the-art in the literature, show maximum area and power reductions of about 40% and 55%, respectively. In addition, the accuracy has been kept high by using a 24-bit fixed-point coding for the intermediate results, which limits the error to ± 1 LSB. II. RELATED WORKS Four approaches are mainly used in the literature for vector orientation recalculation [11], [12]: the Euler angles, which express the rotation of a vector in the space as three consecutive rotations around coordinate axes; the rotation matrix, which is calculated from the Euler angles but it is often preferred to them because of singularities, as happens in [13] for attitude estimation; the Rodrigues’ rotation formula Antonio De Vita, Student Member, IEEE, Gian Domenico Licciardo, Senior Member, IEEE, Aldo Femia, Student Member, IEEE, Luigi Di Benedetto, Member, IEEE, Alfredo Rubino, Member, IEEE and Danilo Pau, Fellow, IEEE Embeddable Circuit for Orientation Independent Processing in Ultra Low-Power Tri-axial Inertial Sensors F A. De Vita. G.D Licciardo, A. Femia, L. Di Benedetto, A. Rubino are with Department of Industrial Engineering of the University of Salerno, 84084 Fisciano (SA), Italy (e-mails: andevita@unisa.it; gdlicciardo@unisa.it, aldo.femia@gmail.com, ldibenedetto@unisa.it). D. Pau is with System Research and Applications, STMicroelectronics, 20864, Agrate Brianza (MB), Italy (e-mail: danilo.pau@st.com).