Algorithm 2. TOA estimation.

Find the index of the maximum variation column in slow time: $$n_{\max \_var}=argma{x}_{n\_fixed}\left|variation\left\{W_{mn}\left(:,n\_fixed\right)\right\}\right|$$ (4) $W_{mn}$ is the gesture matrix, and the “m” represents the slow time length, whereas the “n” represents the fast time length of the matrix. Extract the $siz{e}_{fast}$ data around $n_{\max \_var}$ from one slow time scan data (the x axis is fast time, and the y axis is magnitude), and apply the Hilbert transform to obtain the envelope of these data. $$r_{hilbert}=abs[hilbert\{y\left(n_{\max \_var}-\frac{siz{e}_{fast}}{2}:n_{\max \_var}+\frac{siz{e}_{fast}}{2}\right)\}]$$ (5) $y$ represents the background-subtracted signal after the loopback filter in Section 2.1. $siz{e}_{fast}$ is basically determined by the length of Gaussian-modulated pulses transmitted and received and adds margins taking into account the slight length changes in Gaussian-modulated pulses that occur during reflection from the main target. Find the center of fast time index $n_{\mathrm{center}\_mass}$ using $r_{hilbert}$ and Equation (6). The equation below is similar to the center of mass concept: $$n_{\mathrm{center}\_mass}=\frac{{\sum }_{n=n_{\max \_var}-\frac{siz{e}_{fast}}{2}}^{n_{\max \_var}+\frac{siz{e}_{fast}}{2}}{r}_{hilbert}\left(n\right)*n}{{\sum }_{n=n_{\max \_var}-\frac{siz{e}_{fast}}{2}}^{n_{\max \_var}+\frac{siz{e}_{fast}}{2}}{r}_{hilbert}\left(n\right)}$$ (6) Find $n_{\mathrm{center}\_mass}$ using the method in Step 3 for each slow time. Find the TOA variance using $n_{\mathrm{center}\_mass}$ data in Step 4: $$\mathrm{TOA}\mathrm{variance}=variance\left\{n_{\mathrm{center}\_mass}\left(1:\mathrm{m}\right)\right\}$$ (7)

The symbol “m” represents the slow time length.