An experimental investigation of people detection in Industry 4.0 environments, using impulse radio ultra-wideband signals, is described in this paper. Given the specific characteristics of the considered indoor environment and signals of interest, we first address clutter reduction, and then propose a two-paths signal processing architecture for constant false alarm rate (CFAR) detection of moving and stationary people, using matched filtering and Doppler focusing, respectively. A statistical study of the residual clutter and noise is carried out, and optimal threshold values are derived for these two use cases. The performance of the two CFAR detectors is then assessed using simulated data for different signal-to-noise ratios (SNR) and false alarm probabilities. Finally, their detection capabilities are explored using real data, measured in a heavily cluttered Industry 4.0 indoor environment, for a specially designed scenario with a person alternating between stop and motion phases.