Algorithm 1: SRP with the waveform refinement procedure

Parameter Setting (1) Set the maximum steering TDOA error $\mathsf{\Delta }{\tau }_{max}=\mathsf{\Delta }{\tau }_{max}^C+\mathsf{\Delta }{\tau }_{max}^S$, where the sub-items $\mathsf{\Delta }{\tau }_{max}^C$ and $\mathsf{\Delta }{\tau }_{max}^S$ are determined by the wind and the synchronization error of sensors, respectively. (2) Set the grid distance $d_g$ and searching region $\mathcal{V}$ that meet the system requirement. Then the searching grid set ${\mathbf{X}}_g$ is generated. (3) Set the waveform function $u_e\left(\tau \right)=e^{-{\left({\mathsf{\Omega }}_d{F}_s\tau \right)}^2}$ and $\alpha =$0.5. (4) Set $c=$0.001 and compute the bandwidth ${\mathsf{\Omega }}_B$ using Equation (32). Band selecting (1) Set up the passband $\left[{\mathsf{\Omega }}_L,{\mathsf{\Omega }}_U\right]$ (2) Pick up $N_q$ highest PSD bands of the source or divide the passband uniformly. Source Localization (1) Calculate the refinement waveform (WR)-SRP function $P^{WR}\left(\mathbf{x}\right)$ by Equation (29) at all $\mathbf{x}\in {\mathbf{X}}_g$. (2) Estimate the source location ${\widehat{\mathbf{x}}}_s$ by Equation (11).