Time delay velocity estimation from a superposition of localized and uncorrelated pulses
This study investigates a novel method for estimating two-dimensional velocities using coarse-grained imaging data, which is particularly relevant for applications in plasma diagnostics. The method utilizes measurements from three non-collinear points and is derived from a stochastic model that describes the propagation of uncorrelated pulses through two-dimensional space. We demonstrate that the method provides exact time delay estimates when applied to a superposition of Gaussian structures and remains accurate for various other pulse functions. Through extensive numerical simulations, we evaluate the method's performance under variations in signal duration, pulse overlap, spatial and temporal resolution, and the presence of additive noise. Additionally, we investigate the impact of temporal pulse evolution due to linear damping and explore the so-called barberpole effect, which occurs with elongated and tilted structures. Although the method is susceptible to the barberpole effect, we analytically demonstrate that this effect does not occur when the elongated structures propagate parallel to one of their axes, and we establish bounds for the associated errors. We propose a series of safeguards to anticipate the applicability of the velocity estimation method, considering factors such as signal length, number of pulses, temporal and spatial resolution, signal-to-noise ratio, and pulse size. However, these safeguards do not ensure applicability in cases involving the barberpole effect or correlations between amplitudes and velocities. Overall, our findings provide a comprehensive and robust framework for accurate two-dimensional velocity estimation, enhancing the capabilities of fusion plasma diagnostics and potentially benefiting other fields requiring precise motion analysis.