Measuring motion with kinematically redundant accelerometer arrays: Theory, simulation and implementation

• A sensor fusion algorithm for an array of n triple-axis accelerometers.
• Algorithm provides angular velocity, angular and linear acceleration and orientation.
• Two methods are contrasted in simulation studies: combinatorial and pseudoinverse.
• The error vs redundancy relationship is validated through empirical studies.

This work presents two schemes of measuring the linear and angular kinematics of a rigid body using a kinematically redundant array of triple-axis accelerometers with potential applications in biomechanics. A novel angular velocity estimation algorithm is proposed and evaluated that can compensate for angular velocity errors using measurements of the direction of gravity. Analysis and discussion of optimal sensor array characteristics are provided. A damped 2 axis pendulum was used to excite all 6 DoF of the a suspended accelerometer array through determined complex motion and is the basis of both simulation and experimental studies. The relationship between accuracy and sensor redundancy is investigated for arrays of up to 100 triple axis (300 accelerometer axes) accelerometers in simulation and 10 equivalent sensors (30 accelerometer axes) in the laboratory test rig. The paper also reports on the sensor calibration techniques and hardware implementation.