Multiple Order Fourier Linear Combiner: Estimating Phase Shift for Real-Time Vibration Compensation

Real-time (RT) vibration sensing and compensation are essential to maintaining reliable laser positioning on remote platforms, which possesses a rising research interest in recent years. The technical challenge in sensing is that the input signal possesses: 1) multiple and time-variant dominant frequencies, 2) broad bandwidth, 3) delay-induced phase shift, and 4) sensor disturbances, including noise and integration drift. This paper proposes an adaptive filter and a time series forecasting method to obtain an accurate vibration signal from the input, overcoming the mentioned challenges. The adaptive filter, namely the Recursive Least Square (RLS) based filter, is proposed to de-noising and remove drift. The technique achieves adaptive filtering by adapting a regression model using the RLS algorithm to reduce the effect of historical data points. A Fourier Linear Combiner (FLC) based algorithm, namely the Multiple Order-FLC (MOFLC), is applied in a two stages forecasting method to eliminate the phase shift caused by inherent system delay. The MOFLC adapts a Fourier series model using the Least Mean Square (LMS) algorithm referencing both signal and signal derivative simultaneously, which is more reliable in phase shift correction than traditional FLC-based algorithms. Both offline and online experiments are conducted to validate the sensing accuracy and RT compensation performance. The proposed techniques are proved to typically possess over 70% accuracy in compensation.