  We present a variational message passing (VMP) approach to detect the
presence of a person based on their respiratory chest motion using multistatic
ultra-wideband (UWB) radar. In the process, the respiratory motion is estimated
for contact-free vital sign monitoring. The received signal is modeled by a
backscatter channel and the respiratory motion and propagation channels are
estimated using VMP. We use the evidence lower bound (ELBO) to approximate the
model evidence for the detection. Numerical analyses and measurements
demonstrate that the proposed method leads to a significant improvement in the
detection performance compared to a fast Fourier transform (FFT)-based detector
or an estimator-correlator, since the multipath components (MPCs) are better
incorporated into the detection procedure. Specifically, the proposed method
has a detection probability of 0.95 at -20 dB signal-to-noise ratio (SNR),
while the estimator-correlator and FFT-based detector have 0.32 and 0.05,
respectively.
