Algorithm 1: Flow of extracting vital signal ${\tau }_v\left(t\right)$.

Input: Filtered echo matrix $s(t_i,{\tau }_j)$, $1\le i\le L$, $1\le i\le K$.

Output: Chirp signal $g\left(t_i\right)$ containing the vital signal ${\tau }_v\left(t_i\right)$, $1\le i\le L$.

1: Along the ridgeline of $s(t_i,{\tau }_j)$, save the amplitudes in to a vector $s_a\left(t_i\right)$, $1\le i\le L$;

2: Along the ridgeline of $s(t_i,{\tau }_j)$, save the fast time delay in to a vector ${\tau }_a\left(t_i\right)$, $1\le i\le L$;

3: Find the maximum in $s(t_i,{\tau }_j)$, note the amplitude as $s_m$, and save the fast time delay as ${\tau }_m$;

4: Obtain the relative fast-time delay ${\tau }_d\left(t_i\right)$ as $max\left({\tau }_a\left(t_i\right)\right)-{\tau }_0\left(t_i\right)$ by solving Equation (10);

5: Compensate large body movements as Equation (11);

6: return $g\left(t_i\right)$;