This paper investigates the performance of a likelihood ratio test in combination with a polynomial subspace projection approach to detect weak transient signals in broadband array data. Based on previous empirical evidence that a likelihood ratio test is advantageously applied in a lower-dimensional subspace, we present analysis that highlights how the polynomial subspace projection whitens a crucial part of the signals, enabling a detector to operate with a shortened temporal window. This reduction in temporal correlation, together with a spatial compaction of the data, also leads to both computational and numerical advantages over a likelihood ratio test that is directly applied to the array data. The results of our analysis are illustrated by examples and simulations.

翻译：本文研究了似然比检验结合多项式子空间投影方法在宽带阵列数据中检测微弱瞬态信号的性能。基于先前经验证据表明似然比检验在低维子空间中具有应用优势，我们通过分析揭示了多项式子空间投影如何对信号的关键部分进行白化处理，从而使检测器能够在缩短的时间窗口内运行。这种时间相关性的降低，结合数据的空间压缩，相较于直接应用于阵列数据的似然比检验，带来了计算与数值上的双重优势。我们的分析结果通过示例与仿真实验进行了验证。