Doppler-warping transform and its application to estimating acoustic target velocity

Abstract

When there appears the relative motion between the sound source and the receiver, the received tonal signal will produce Doppler shift, and the Doppler information is relevant to the motion parameters of the target. According to the acoustic Doppler shift frequency, we propose the Doppler-warping transformation. The phase linearization of the Doppler signal can be realized by using the transformation. Then, we deduce the warping operator and propose an algorithm for estimating the target motion parameters by using the proposed transformation. Firstly, the Doppler-warping operator under different motion parameters is constructed. Secondly, the time resampling of the received time-domain signal is performed by using the operator. Then, the spectral function of the transformed signal is calculated. Finally, the spectral function entropy is minimized to estimate the objective parameter. The simulation results show the effectiveness of the proposed method. For a low signal-to-noise ratio of sea trial data, where the real speed of a fishing boat is 4.5 m/s, the result from the traditional minimum mean square error (MMSE) velocity estimation method is 5.2 m/s, and the estimation error is 15.56%. The proposed Doppler-warping transform method can estimate the target velocity more accurately, specifically, it is 4.7 m/s and its corresponding estimation error is 4.44%.

Estimation of Target Motion Parameters from the Tonal Signals with a Single Hydrophone

“…The basic idea of the warping transformation is to take the inverse function of the instantaneous phase of the signal as the time domain warping operator and then use the warping operator to resample the signal so that the nonlinear phase of the signal becomes a linear phase. According to Equation (15), the Doppler-warping operator can be set as shown in Equation (18), which contains the parameters , , , and [ 30 ]. …”

“…This can estimate the motion parameters of near-field targets according to the least squares method. In 2021, the Doppler-warping transformation was proposed by Gao, which uses the Doppler frequency shift of the tonal signals, which can be used to estimate the speed of the sound source under the premise of a known distance [ 30 ]. However, in the case of a small Doppler frequency shift or low signal-to-noise ratio, there is a serious parameter coupling problem between v and , so that it is impossible to accurately estimate the two parameters.…”

An Underwater Localization Algorithm for Airborne Moving Sound Sources Using Doppler Warping Transform

“…In the work by Gao Deyang et al [19], the Doppler warping transform operator is employed to linearize the instantaneous frequency of the line spectrum in a received signal originating from a uniformly moving linear source in a free field, as observed at a stationary receiver.…”

“…The warping transform operates by resampling a complex non-stationary signal according to a functional relationship in either the time or frequency domain. Gao Deyang [19] introduced the Doppler warping transform and employed it in estimating the motion parameters of sound sources exhibiting uniform linear motion in the infinite free field. The Doppler warping transform serves as a valuable tool for addressing the nonlinear instantaneous phase problem associated with the Doppler shift.…”