Optimal Gyro-Free IMU Geometry

A Gyro-Free Inertial Measurement Unit (GF-IMU) uses a configuration of accelerometers only to measure the three accelerations and the attitude of a rigid body in 3-D space. Theoretically, almost any configuration of six distributed accelerometers yields sucient measurements to solve for the translational and angular acceleration. In reality, however, sensor noise corrupts the measurements and good sensor geometry is necessary to obtain an accurate estimate of the translational and angular accelerations. This paper investigates the use of symmetry and the Platonic solids as a basis for the design of GF-IMU configurations in order to obtain the best possible observability, given noisy accelerometer measurements. This same theory can then be applied to the design of optimal configurations using accelerometer triads as found in conventional IMUs.