Two calibration procedures for a gyroscope-free inertial measurement system based on a double-pendulum apparatus

This paper presents a novel calibration algorithm to be used with a gyro-free inertial measurement unit (GF-IMU) based on the use of linear accelerometers (AC). The analytical approach can be implemented in two calibration procedures. The first procedure (P-I) is articulated in the conduction of a static trial, to compute the sensitivity and the direction of the sensing axis of each AC, followed by a dynamic trial, to determine the AC locations. By contrast, the latter procedure (P-II) consists in the calculation of the previously indicated calibration parameters by means of a dynamic trial only. The feasibility of the two calibration procedures has been investigated by testing two GF-IMUs, equipped with ten and six bi-axial linear ACs, with an ad hoc instrumented double-pendulum apparatus. P-I and P-II were compared to a calibration procedure used as a reference (P-REF), which incorporates the AC positions measured with an optoelectronic system. The experimental results we present in this paper demonstrate that (i) P-I is able to determine the calibration parameters of the AC array with a higher accuracy than P-II; (ii) consequently, the errors associated with translational (a₀ - g) and rotational () acceleration components for the two GF-IMUs are significantly greater using P-II than P-I and (iii) the errors in (a₀ - g) and obtained with P-I are comparable with the ones obtainable by using P-REF. Thus, the proposed novel algorithm used in P-I, in conjunction with the double-pendulum apparatus, can be globally considered a viable tool in GF-IMU calibration.