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Angular Accelerometers (AA) directly measure angular accelerations, in contrast to the traditional approach which requires calculating the angular accelerations by differentiating the angular rates from rate gyroscopes. Whereas very accurate and robust, AA are physical measuring devices, which means that they could have construction and alignment imperfections that affect their outputs. In this paper, AA sensor's output was verified in order to meet a standard reference, achieved by means of an off-line calibration method. To begin with, a laboratory measurement with a customized input sequence was conducted using a high precision calibration table as a reference. The angular acceleration reference signal, however, was not measured directly by the calibration table, but instead calculated from a position reference using a second order differentiator. Inherently, the noise in the position measurements was significantly amplified, leading to an angular acceleration reference that cannot be used directly. A non-linear extended state observer was developed to estimate a more accurate acceleration reference. Subsequently, a calibration model covering the entire domain was identified based on a least-squares approach. This paper improves calibration table angular acceleration data and provides a method to calibrate the new type of angular acceleration sensor.

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The calibration of Angular Accelerometers requires a controlled test with a known acceleration profile. However, current turntables have been designed primarily for generating a constant rotational velocity. To generate a profile with varying angular acceleration we propose using constant rotational velocity on the two axes of a 2-axes motion simulator. The proposed sequence was developed to obtain the required rotational acceleration signal quality using only rotational velocity input. The identified pattern is applied to an envelope of test conditions, resulting in test matrix. This method provides an alternative means to generate inputs that can be used to calibrate angular accelerometers using calibration hardware that is not primarily designed to provide accurate acceleration inputs. Nomenclature AA Angular accelerometer DAS Data Acquisition System IMU Inertial Measurement Units PSD Power Spectral Density Subscripts i Inner-axis o Outer-axis Symbols α Angular acceleration, deg/s 2 i Unit vector in X-axis j Unit vector in Y-axis k Unit vector in Z-axis ω Angular velocity, deg/s ψ Inner-axis rotation angle, deg ω Associated angular velocity, deg/s r Radius of a circle, m SXY Z Coordinate System t Time, s