Insomnia, whether situational or chronic, affects over a third of the general population in today’s society. However, given the lack of non-contact and non-inductive quantitative evaluation approaches, most insomniacs are often unrecognized and untreated. Although Polysomnographic (PSG) is considered as one of the assessment methods, it is poorly tolerated and expensive. In this paper, with the recent development of Internet-of-Things devices and edge computing techniques, we propose a detrended fractal dimension (DFD) feature for the analysis of heart-rate signals, which can be easily acquired by many wearables, of good sleepers and insomniacs. This feature was derived by calculating the fractal dimension (FD) of detrended signals. For the trend component removal, we improved the null space pursuit algorithm and proposed an adaptive trend extraction algorithm. The experimental results demonstrated the efficacy of the proposed DFD index through numerical statistics and significance testing for healthy and insomnia groups, which renders it a potential biomarker for insomnia assessment and management.