Methods for linear radial motion estimation in time-of-flight range imaging

Abstract

Motion artefacts in time-of-flight range imaging are treated as a feature to measure. Methods for measuring linear radial velocity from range imaging cameras are developed and tested. With the measurement of velocity, the range to the position of the target object at the start of the data acquisition period is computed, effectively correcting the motion error. A new phase based pseudo-quadrature method designed for low speed measurement measures radial velocity up to ±1.8 m/s with RMSE 0.045 m/s and standard deviation of 0.09-0.33 m/s, and new high-speed Doppler extraction method measures radial velocity up to ±40 m/s with standard deviation better than 1 m/s and RMSE of 3.5 m/s.

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

“…4 demonstrates the success of the proposed instantaneous velocity estimation, but also that it is strongest at low speeds and that error increases with velocity. The standard deviation is smaller than the earlier attempts at linear velocity estimation [5], but larger than the more recent results [7] wherein standard deviations better than 1 m/s were achieved. In that earlier work, however, an average radial velocity was found over the whole phase step set, in contrast here we resolve down to each raw frame.…”

“…where 30 is the target range frame rate of the camera, f mod is the camera modulation frequency [15], c is the speed of light in a vacuum, and as noted in earlier work [5], [7], harmonic interference causes bias in the velocity prediction, which we inspect and correct via the constant C.…”

“…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].…”

Time-of-Flight Range Image Measurement in the Presence of Transverse Motion Using the Kalman Filter

“…Early modeling led to a reduction of that error by appropriate processing [4], and by modification of the raw frame acquisition process [10]. In more recent work radial motion is measured, e.g using heterodyne modulation [11], continuous wave homodyne [9], and analysis of the raw data using principles from quadrature modulation and stochastic calculus [12].…”