Compact radar sensors for Internet of Things applications can be used to analyze indoor human gait characteristics. Conventional human gait analysis methods typically involve generating two-dimensional (2D) high-resolution time-frequency images and employing image-processing techniques to estimate gait parameters of a walking human. However, these computations can be resource-intensive for the compact radar sensors. To address this problem, we propose a new scheme for estimating gait parameters. Our method has four significant contributions: 1) utilization of one-dimensional phase modulation in a radar echo for efficient gait-parameters estimation, as opposed to relying on 2D time-frequency images; 2) decomposition of micro phase modulations corresponding to the torso or pelvis and lower body parts (e.g., knee, tibia, and ankle) using dedicated filtering techniques to mitigate the interference between body components; 3) compensation for effects of nonlinear macro phase modulation caused by whole-body movements; and 4) robust estimation of gait parameters including time-varying radial velocity, gait rate, step length, and the height of the lower body. In experiments performed using a 5.8 GHz continuous-wave Doppler radar, we observed that the proposed scheme can perform efficient and robust gait parameter estimation of an indoor human walking.