Stochastic calculus analysis of optical time-of-flight range imaging and estimation of radial motion

Time-of-flight range imaging is analyzed using stochastic calculus. Through a series of interpretations and simplifications, the stochastic model leads to two methods for estimating linear radial velocity: maximum likelihood estimation on the transition probability distribution between measurements, and a new method based on analyzing the measured correlation waveform and its first derivative. The methods are tested in a simulated motion experiment from (-40)-(+40)  m/s, with data from a camera imaging an object on a translation stage. In tests maximum likelihood is slow and unreliable, but when it works it estimates the linear velocity with standard deviation of 1 m/s or better. In comparison the new method is fast and reliable but works in a reduced velocity range of (-20)-(+20)  m/s with standard deviation ranging from 3.5 m/s to 10 m/s.