Dynamic reconstruction and data reconstruction for subsampled or irregularly sampled data

Abstract

The Nyquist-Shannon criterion indicates the sample rate necessary to identify information with particular frequency content from a dynamical system. However, in experimental applications such as the interrogation of a ow eld using Particle Image Velocimetry (PIV), it may be impracticable or expensive to obtain data at the desired temporal resolution. To address this problem, we propose a new approach to identify temporal information from undersampled data, using ideas from modal decomposition algorithms such as Dynamic Mode Decomposition (DMD) and Optimal Mode Decomposition (OMD). The novel method takes a vector-valued signal, such as an ensemble of PIV snapshots, sampled at random time instances (but at Sub-Nyquist rate) and projects onto a low-order subspace. Subsequently, dynamical characteristics, such as frequencies and growth rates, are approximated by iteratively approximating the ow evolution by a low order model and solving a certain convex optimization problem. The methodology is demonstrated on three dynamical systems, a synthetic sinusoid, the cylinder wake at Re = 60 and turbulent ow past the axisymmetric bullet-shaped body. In all cases the algorithm correctly identies the characteristic frequencies and oscillatory structures present in the ow.

Comparative Efficiency Analysis of Data Fusion Methods for Vehicle Trajectory Reconstruction

“…Interpolation is used in vehicle trajectory reconstruction from detector to visualize vehicle movements, which help understand traffic system efficiency and calculate pollution emission [7]. The research [6] presented the fusion process with localization errors but did not mention missing data caused by non-detection of object.…”