Hilbert transform based analyses on ship-rocking signals

The ship-rocking is a crucial factor which affects the accuracy of the ocean-based flight vehicle measurement. Here we have analyzed four groups of ship-rocking time series in horizontal and vertical directions utilizing a Hilbert based method from statistical physics. Our method gives a way to construct an analytic signal on the two-dimensional plane from a one-dimensional time series. The analytic signal share the complete property of the original time series. From the analytic signal of a time series, we have found some information of the original time series which are often hidden from the view of the conventional methods. The analytic signals of interest usually evolve very smoothly on the complex plane. In addition, the phase of the analytic signal is usually moves linearly in time. From the auto-correlation and cross-correlation functions of the original signals as well as the instantaneous amplitudes and phase increments of the analytic signals we have found that the ship-rocking in horizontal direction drives the ship-rocking in vertical direction when the ship navigates freely. And when the ship keeps a fixed navigation direction such relation disappears. Based on these resultswe could predict certain amount of future values of the ship-rocking time series based on the current and the previous values. Our predictions are as accurate as the conventional methods from stochastic processes and provide a much wider prediction time range.