Physics-Informed Signal Processing for Time Series Data From Accelerating Sensors

Abstract

Detecting and processing electromagnetic (EM) waves in modern applications involves obtaining time series data from EM sensors and applying standard methods such as the fast Fourier transform to obtain frequency and amplitude information. Often, however, EM sensors are accelerating through physical space, which results in modulated frequencies in the time series obtained by the sensor. In this work, we evaluate the effect of receiver acceleration on observed signals in the context of wireless communications and introduce methods to reconstruct the transmitted signal. We analyze the effect of constant acceleration and uniform circular motion which result in sensor time series that are distorted by quadratic and sinusoidal phase changes, creating physical linear and angular chirps, respectively. In a homogeneous medium, the time sampling of the received signal can be transformed to a nonuniform grid to account for the phase modulations induced by acceleration along 3-D trajectories in space. The nonuniform fast Fourier transform can then be applied to recover the spectrum of the transmitted signal. For general EM wave fields, new signal processing techniques need to be developed. We introduce a physics-informed randomized algorithm to analyze and reconstruct transmitted sparse EM signals propagating in inhomogeneous, stratified media using time series data of the electric field obtained from sensors moving along arbitrary trajectories in space. Our work goes beyond conventional Doppler analysis and includes general nonlinear phases and directionality effects.