Instantaneous Linear Dimensionality Reduction of Multichannel Time-Series Signal for Array Signal Processing

Abstract

Linear dimensionality reduction of signals observed by a sensor array is often useful in balancing the accuracy and speed of post-stage processing, especially in real-time systems with limited computational resources. However, for multichannel time-series signals having time-invariant intertemporal and interchannel correlations, the direct application of frequency-wise linear dimensionality reduction method requires a large number of digital filters with large filter lengths, which is still unpreferable in the viewpoint of computational cost. We propose a frequency-independent, i.e., instantaneous, linear dimensionality reduction method that achieves low computational cost and latency and high restoration accuracy. We also show several results of numerical experiments to compare the proposed method with other instantaneous linear dimensionality reduction methods, i.e., the principal component analysis and element selection method, and demonstrate the effectiveness of the proposed method.