Observing Relative Motion With Three Accelerometer Triads

A gyroscope-free inertial measurement unit (GF-IMU) detects the relative motion of a body based on acceleration measurements only. It consists of multiple transducers attached at distinct locations within the body that together form an accelerometer array. In this paper, we employ only three accelerometer triads in order to completely capture the transversal and angular acceleration as well as the angular velocity. By modeling the GF-IMU as a nonlinear control system, we are able to conduct an observability analysis, which shows that this approach is capable of capturing an arbitrary spatial motion. We also show that additional triads only provide redundant information. Based on the control system formulation, we derive the models required to employ a nonlinear Kalman filter as a state observer. As the system description is of a general form they are suitable for any accelerometer array regardless of the number and placement of the transducers. Hence, the presented Kalman filter approach is applicable to all observable GF-IMU configurations. The measurements taken with a prototype on a 3-D rotation table confirm the observability analysis. The evaluations also show that the approach using three accelerometer triads achieves an estimation accuracy comparable with that of arrays employing a higher number of triads.