Estimating the velocity of a moving object submerged in an ocean waveguide with active sonar

Abstract

Standard active sonar and radar systems are often used to estimate the velocity of a moving target in free space by resolving the Doppler shift of the scattered waveform. In an ocean waveguide, multimodal propagation and dispersion make the Doppler effects far more complicated than in free space. In a waveguide, multiple frequency components are typically present in the field scattered from a moving object even if the active source of radiation is harmonic. Applying a free space Doppler correction to the field scattered from a moving object in a waveguide is insufficient to account for the Doppler distortion of the signal in typical ocean waveguides and active sonar scenarios. Spectral and modal formulations for the Doppler-shifted field scattered from a horizontally moving target in a horizontally stratified medium have been developed by Lai and Makris [J. Acoust. Soc. Am. 110, 2724 (2001)]. These formulations are used with the maximum likelihood method to estimate the velocity of the moving target by modeling the multiply Doppler distorted scattered signal measured with noise in a shallow water waveguide. The performance of the maximum likelihood estimate is evaluated by asymptotic analysis of its bias and mean-square error as a function of signal-to-noise ratio.

Estimating the instantaneous velocity of randomly moving target swarms in a stratified ocean waveguide by Doppler analysis

“…10log 10 of the expected square magnitude of the ambiguity function, based on evaluating Eqs. (14)(15) and (6) is also shown (gray line) and is found to be in good agreement with the Monte-Carlo result. The variance of the ambiguity function dominates the total intensity and the magnitude squared of the ambiguity function's expected value is negligible.…”

“…For active sensing of a single deterministic target in a waveguide where N 2 Doppler shifts occur, it has been shown that a relatively accurate estimate of the target velocity can be obtained from the Dopplershifted spectrum of its scattered field. 14,15 Here, we show that, for a group of random targets within a resolution cell, accurate simultaneous estimates can be obtained for the instantaneous velocity and position means of the group, as well as their standard deviations through the Moment Method. In Sec.…”