Optimized estimator for real-time dynamic displacement measurement using accelerometers

This paper presents a method for optimizing the performance of a real-time, long term, and accurate accelerometer based displacement measurement technique, with no physical reference point. The technique was applied in a system for measuring machine frame displacement.

The optimizer has three objectives with the aim to minimize phase delay, gain error and sensor noise. A multi-objective genetic algorithm was used to find Pareto optimal estimator parameters.

The estimator is a combination of a high pass filter and a double integrator. In order to reduce the gain and phase errors two approaches have been used: zero placement and pole-zero placement. These approaches were analysed based on noise measurement at 0g-motion and compared. Only the pole-zero placement approach met the requirements for phase delay, gain error, and sensor noise.

Two validation experiments were carried out with a Pareto optimal estimator. First, long term measurements at 0g-motion with the experimental setup were carried out, which showed displacement error of 27.6 ± 2.3 nm. Second, comparisons between the estimated and laser interferometer displacement measurements of the vibrating frame were conducted. The results showed a discrepancy lower than 2 dB at the required bandwidth.