The timed up and go (TUG) test is a simple, valid, and reliable clinical tool that is widely used to assess mobility in elderly people. Several research studies have been conducted to automate the TUG test using wearable sensors or motion-tracking systems. Despite their promising results, the adopted technological systems present inconveniences in terms of acceptability and privacy protection. In this work, we propose to overcome these problems by using a Doppler radar system set into the backrest of a chair in order to automate the TUG test and extract additional information from its phases (i.e., transfer, walk, and turn). We intend to segment its phases and extract spatiotemporal gait parameters automatically. Our methodology is mainly based on a multiresolution analysis of radar signals. We proposed a segmentation technique based on the extraction of limbs oscillations signals through a semisupervised machine learning approach, on the one hand, and the application of the DARC algorithm on the other hand. Once the speed signals of torso and limbs oscillations were detected, we suggested estimating 14 gait parameters. All our approaches were validated by comparing outcomes to those obtained from a reference Vicon system. High correlation coefficients were obtained by comparing the speed signals of the torso (ρ=0.8), the speed signals of limbs oscillations (ρ=0.91), the initial and final indices of TUG phases (ρ=0.95), and the extracted parameters (percentage error < 4.8) obtained after radar signal processing to those obtained from the Vicon system.