Frequency Estimation From Limited Samples: Nonlinearizing Time-of-Flight Radial Velocity Estimation

Radial motion in indirect time-of-flight range imaging causes instantaneous frequency shifts in the data. Instantaneous frequency estimation is a well studied topic, but existing methods are either computationally inefficient, or require a minimum of several tens of samples to be accurate. Time-of-flight range imaging satisfies neither of these conditions, necessitating a new technique. Through differentiation, a differential equation of the instantaneous frequency is derived, transformed to a nonstationary ordinary differential equation, and solved by polynomial solution. Hence, instantaneous frequency is recast as a linear algebraic inversion problem. Semisimulated experimental tests show the proposed method is accurate, with interquartile velocity precision of 1.5-6.3 m/s.