A Bayesian approach to respiration rate estimation via pulse-based ultra-wideband signals

In this paper, theoretical limits on estimation of respiration rates via pulse-based ultra-wideband (UWB) signals are studied in the presence of prior information about respiration related signal parameters. First, a generalized Cramer-Rao lower bound (G-CRLB) expression is derived, and then simplified versions of the bound are obtained for sinusoidal displacement functions. In addition to the derivation of the theoretical limits, a two-step suboptimal estimator based on matched filter (correlation) processing and maximum a posteriori probability (MAP) estimation is proposed. It is shown that the proposed estimator performs very closely to the theoretical limits under certain conditions. Simulation results are presented to investigate the theoretical results.