Algorithm 1 Resampling Transform Algorithm

1: Input: Original sampling sequence $y_n[m]$, transmit slope $K_n$, reference slope $K_{\mathrm{Ref}}$

2: Output: Range estimate R

3: Calculate resampling factor: ${\alpha }_n=K_{\mathrm{Ref}}/K_n$

4: Define new time variable: $\tilde{t}={\displaystyle \frac{K_n}{K_{\mathrm{Ref}}}}t={\displaystyle \frac{1}{{\alpha }_n}}t$

5: Calculate new time points: ${\tilde{t}}_{\mathrm{req}}={\alpha }_n{t}_k={\alpha }_{n}k{T}_s$

6: Interpolate original sequence: $y_n[k]=\mathrm{Interp}(y_n[m],\tilde{t}={\alpha }_{n}k{T}_s)$

7: Transformed signal: $y_n(\tilde{t})=\exp \left(-j2\pi K_{\mathrm{Ref}}\tau {\tilde{t}}^{\prime }\right)$

8: Apply FFT transform to $y_n(\tilde{t})$ to obtain peak frequency $f_{\mathrm{peak}}$

9: Calculate beat frequency: $f_{\mathrm{beat}}=K_{\mathrm{Ref}}\tau$

10: Calculate range: $R={\displaystyle \frac{c\cdot f_{\mathrm{peak}}}{2K_{\mathrm{Ref}}}}$