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

Abstract

Time-of-flight range imaging is analysed 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 analysing 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.

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

“…This problem has drawn significant attention over many years, leading to fast solutions like autoregression based methods [1], [2] that require a substantial number of samples, to slower methods that work on limited samples, such as multiple signal classification (MUSIC) [3], [4]. Statistical estimators improve accuracy but, again, often at the cost of computation time and power [5]. Iterative schemes [5], [6] are also performant and flexible but, at the same costs as statistical techniques.…”

“…Statistical estimators improve accuracy but, again, often at the cost of computation time and power [5]. Iterative schemes [5], [6] are also performant and flexible but, at the same costs as statistical techniques.…”

“…Time-of-flight (ToF) range imaging is a multiframe full-field imaging method, which is vulnerable to motion error but provides the opportunity to measure radial velocity as well [5], [7]. The very large scale integration of pixels into ToF image sensor arrays causes significant limitations on the number of samples per pixel that may be acquired, transmitted, and processed in the short amount of time required to obtain full-frame rate range imaging.…”

“…In other previous work, radial velocity estimation computes a single pooled estimate over the raw frames, providing an estimate of linear velocity [5], [7]. The matrix pencil method has garnered attention in recent years in ToF (see, e.g., [11] and [13]), and much earlier in communications applications, e.g., [14].…”

Classifying Transverse Motion in Time-of-Flight Range Imaging

“…Taking inspiration from stochastic modelling of ToF imaging [3], we investigate the financial modelling method of the stochastic oscillator [4], as well as auto correlation, to normalize unwanted parameters from the ToF data.…”