In this paper, we present a new algorithm for detection of respiratory movement of a person behind an obstacle by using ultrawideband (UWB) impulse radar. In this scenario, the most significant sign of being alive is the respiratory motions, which is hidden in parameters of the returned signal. This signal, whose statistical characteristics are generally nonstationary, is mixed with both stationary and nonstationary clutters and white and colored noise. In this paper, in an analytical way, the returned signal has been addressed by the Fourier series model with time-varying coefficients, as a fitting model. Then, based on the unconditional orthonormal representation of band-limited signals, a minimum mean square error estimator is introduced to determine the time-varying coefficients of the Fourier series. Using the new representation of the Fourier coefficients, a new approach is suggested that enables us to extract parameters of the respiration in very low signal-to-noise-and-clutter ratio (SNCR) conditions in the presence of both stationary and nonstationary clutters. Getting the most out of the estimator, this approach alleviates the problems associated with clutters and noise, without resorting to match filtering. Hence, a robust and blind respiratory-motion detection (RMD) from stationary or nonstationary received signal is obtained. By experimental data, we demonstrate the applicability of the new approach for the respiratory detection using UWB impulse radar in different aspects.