ABSTRACT
Signals returned from an object containing fast-moving parts have Doppler frequency modulations, called micro-Doppler effects, which produce time-varying spectral contents. Motion analysis, which involves parameter estimation of the target micro-Doppler signatures, is important in urban sensing. One of the goals in urban radar is the classification of 284different types of human gait. It is equally important to separate multiple micro-Doppler components induced by rigid bodies. Time–frequency representation has been shown to be a powerful tool in the analysis of such signals. However, the information rendered by time–frequency analysis can be impacted, if not compromised or distorted, when dealing with data from random sampling or significantly reduced sampling frequency. These changes in the sampling patterns can be attributed to changes in the pulse repetition periods to avoid range or Doppler ambiguities or can be a result of deliberately discarding samples highly contaminated by disturbances. Nevertheless, the problems can be observed within the concept of compressive sensing theory and practice. After a short review of the basic compressive sensing methods, various approaches for the analysis and separation of fast-varying signal components are presented. Several methods are considered. First, we discuss direct applications of the compressive sensing algorithms to the ambiguity domain for the purpose of achieving high-resolution time–frequency representations. Next, in dealing with missing samples, we consider sparse signal reconstructions when operating on both the data and the local autocorrelation function. The latter can result from bilinear products or from performing higher-order estimations. The presented methods are illustrated using simulated and real data, demonstrating effectiveness of the compressive sensing based time–frequency approaches in the analysis of radar signals with micro-Doppler effects.
