This paper considers vital signs (VS) such as respiration movement detection of human subjects using an impulse ultra-wideband (UWB) through-wall radar with an improved sensing algorithm for random-noise de-noising and clutter elimination. One filter is used to improve the signal-to-noise ratio (SNR) of these VS signals. Using the wavelet packet decomposition, the standard deviation based spectral kurtosis is employed to analyze the signal characteristics to provide the distance estimate between the radar and human subject. The data size is reduced based on a defined region of interest (ROI), and this improves the system efficiency. The respiration frequency is estimated using a multiple time window selection algorithm. Experimental results are presented which illustrate the efficacy and reliability of this method. The proposed method is shown to provide better VS estimation than existing techniques in the literature.