Time Series Modeling and Tracking Method of Vessel Shaft-Rate Electromagnetic Field

This article presents a novel time series simulation and tracking method of shaft-rate electromagnetic (EM) field for moving vessels. Two approaches, superimposed from the frequency and time domain, respectively, are proposed to synthesize shaft-rate EM time series without a Fourier transform. The modeling method can simulate the shaft-rate EM time series of vessels with arbitrary frequency, horizontal position, draft, electric moment, and initial phase. To obtain shaft-rate EM field amplitude and phase for vessel tracking, the amplitude spectrum analysis is used to identify the shaft-rate fundamental frequency. The short-time Fourier transform and linear least-squares method are combined to estimate the Fourier coefficients of the shaft-rate time series. The response characteristic analysis of multivessel shows that the initial phase does not affect the received EM field amplitudes, but it could cause an unfixed overall shift in the phase of the recorded EM components. Since the vessels being tracked are noncooperative targets, whose parameters, including the initial phase, are unknown, the tracking method of multiple vessels using a multiplicative cost function is applied to estimate the moving vessel’s trajectory, electric moment, and initial phase. We design synthetic experiments of both single vessel and two vessels to validate the proposed tracking method. Inversion results of synthetic examples show that the proposed method can obtain accurate trajectories for both single-vessel and multivessel cases. The proposed method has also been applied to an experiment with real-world noise, and the tracking result shows that the trajectory of the vessel can be estimated reliably.