Hexagon (Switzerland)

Inertial sensor drift is usually corrected on a single-sensor unit level. When multiple sensor units are used, mutual information from different units can be exploited for drift correction. This study introduces a method for a drift-reduced estimation of three dimensional (3-D) segment orientations and joint angles for motion capture of highly dynamic movements as present in many sports. 3-D acceleration measured on two adjacent segments is mapped to the connecting joint. Drift is estimated and reduced based on the mapped accelerations' vector orientation differences in the global frame. Algorithm validity is assessed on the example of alpine ski racing. Shank, thigh, and trunk inclination as well as knee and hip flexion were compared to a multicamera-based reference system. For specific leg angles and trunk segment inclination mean accuracy and precision were below 3.9° and 6.0°, respectively. The errors were similar to errors reported in other studies for lower dynamic movements. Drift increased axis misalignment and mainly affected joint and segment angles of highly flexed joints such as the knee or hip during a ski turn.

3D imaging and sensing modules for smart and IoT devices pose demanding requirements on form factor, robustness and performance. Enabling technologies include wafer-level packaging, micro-optic, time-of-flight sensors, software and connectivity solutions. Article not available.

The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and for any frequency based on the use of the GMD, AMD, and AMSD. Since partial inductance of single wires cannot be measured, the errors of the analytical approximations are computed with the help of exact computations of the six-dimensional integral defining induction. These are obtained by means of a coordinate transformation that reduces the six-dimensional integral to a three-dimensional one, which is then solved numerically. We give examples of an application of our analytical formulae to the calculation of the inductance of short-circuited two-wire lines. The new formulae show a substantial improvement in accuracy for short wires.

Differential carrier-phase GPS-based attitude determination represents an attractive alternative to expensive and complex inertial measurement units (IMUs) and attitude heading reference systems (AHRS), for aeronautical, marine and machine-guidance applications. Previous work in GPS-based attitude systems, using ultra-short baselines (less than a couple of metres) between three/four antennas, have been shown to provide high accuracies, most of the time to the sub-degree level in yaw, pitch and roll.

Replication technology enables Diffractive Optical Elements (DOEs) to be mass produced at low cost and is a major factor in their use in consumer products. They can also provide superior performance, size and weight compared with classical optical elements. New design approaches and fabrication technologies have led to a rapid increase in the acceptance of these optical elements in commercial products. The paper will discuss the advantages of replicated DOEs and give examples of applications in products currently on the market.