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

Doppler analysis has been extensively used in active radar and sonar sensing to estimate the speed and direction of a single target within an imaging system resolution cell following deterministic theory. For target swarms, such as fish and plankton in the ocean, and raindrops, birds and bats in the atmosphere, multiple randomly moving targets typically occupy a single resolution cell, making single-target theory inadequate. Here, a method is developed for simultaneously estimating the instantaneous mean velocity and position of a group of randomly moving targets within a resolution cell, as well as the respective standard deviations across the group by Doppler analysis in free-space and in a stratified ocean waveguide. While the variance of the field scattered from the swarm is shown to typically dominate over the mean in the range-velocity ambiguity function, cross-spectral coherence remains and maintains high Doppler velocity and position resolution even for coherent signal processing algorithms such as the matched filter. For pseudo-random signals, the mean and variance of the swarms' velocity and position can be expressed in terms of the first two moments of the measured range-velocity ambiguity function. This is shown analytically for free-space and with Monte-Carlo simulations for an ocean waveguide.