Self-Calibration of Accelerometer Arrays (SCARS)
Final Report Abstract
A conventional inertial measurement unit (IMU) infers the motion of a body in the form of its linear acceleration and its angular velocity. To capture a spacial motion the devices incorporate accelerometers and gyroscopes. In contrast to this, a gyroscope-free inertial measurement unit (GF-IMU) uses only accelerometers in order to capture the linear as well as the angular motion. The sensors are mounted at distinct locations of the body, which are assumed to be constant. Thus, together they form an accelerometer array. To accurately estimate the motion, the poses of the sensors, i.e., their positions and orientations, must be known precisely. Unfortunately, these parameters are typically hard to assess. Conventional calibration methods are able to reconstruct the geometrical sensor poses based on a set of motion data and corresponding acceleration measurements. In practice, the main challenge of these methods is to provide accurate reference data of the motion. Either a mechanical manipulator imposes a known motion on the array or the motion must be captured by a reference measurement system. Both options require expensive laboratory instrumentation. We consider this as one of the main hurdles to employ a GF-IMU. In this project we addressed this issue by introducing a self-calibration for accelerometer arrays, i.e., the poses of the array are estimated using only their own measurements without the requirement of any external reference. It is based on an iterative graph optimization that considers both the sensor poses and the motion as target variables. Initially, this results in infinitely many solutions. We were able to reduce the solutions to only one global optimum by explicitly modeling the used triple-axis accelerometers as sensor triads and furthermore taking the temporal dependence of the acceleration samples into account. Not all possible motions incorporate the required information to successfully execute a self-calibration of the accelerometer poses. To identify the requirement for a suitable motion we formulate the self-calibration problem as a state-space system and analyze its observability depending on the imposed motion. Based on the results we derived criteria for the recorded measurement data that allow to test whether they originate from a suitable motion and rate its quality. We developed an online algorithm that constructs a set of measurements with a bounded size by selecting segments of incoming measurements based in the derived criteria. The algorithm and the criteria are computationally efficient and can be processed in real-time alongside the sampling process.
Publications
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“Self-calibration of accelerometer arrays,” IEEE Trans. Instrum. Meas., vol. 65, no. 8, pp. 1913–1925, Aug. 2016
P. Schopp, H. Graf, W. Burgard, and Y. Manoli
