Instrument noise calibration with arbitrary sensor orientations

Instrument noise calibration is indispensable for laboratory and field testing with applications in disciplines such as seismology and structural health monitoring, establishing the basic information for the quality of data. Different methods exist assuming different kinds of information, among which the 'three-channel method' developed by Sleeman and co-workers allows one to calibrate the power spectral density (PSD) of instrument noise without prior information. The method makes use of the sample cross-covariance of three data channels assumed to measure the same input motion. In reality, the input motions of the three channels are never identical due to sensor alignment error and spatial incoherence of the input motion. This leads to bias in the estimated noise PSD, which turns out to also increase with the signal-to-noise ratio. In this paper, the noise calibration problem is investigated analytically to yield explicit formulas that account for the bias due to alignment error and spatial incoherence. Leveraging on fundamental understanding of the bias, a method is proposed which can overcome the bottleneck stemming from alignment error. The proposed method is still based on three collocated sensors but now it makes use of multi-dimensional (biaxial or triaxial) motion data. The latter is the key for the method to be applicable (unbiased) for arbitrary sensor orientations, which significantly enhances the robustness and accuracy of 'huddle test'. Numerical studies with simulated data and a series of specially designed experiments based on servo-accelerometers are presented to verify the analytical findings, to provide a critical appraisal of the proposed method and to demonstrate practical applications.