Self-Calibration of Accelerometer Arrays

A gyroscope-free inertial measurement unit employs solely accelerometers to capture the motion of a body in the form of its linear and angular acceleration as well as its angular velocity. For that, multiple transducers are fixed at distinct locations of the body that together 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. Current state-of-the-art calibration methods are able to reconstruct the geometrical sensor configuration based on a set of motion data and corresponding acceleration measurements. However, to impose a reference motion on the sensor array and to capture that motion with the necessary accuracy requires sophisticated laboratory equipment. In this paper, we present a method to estimate the transducer poses using only their own measurements without depending on reference motion data. 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 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. We compare our method to the conventional calibration using reference data in terms of its estimation accuracy. Furthermore, we analyze the convergence properties of our method by evaluating its tolerance to initial pose deviations. For both, we use synthetic and experimental data recorded on a 3-D rotation table.