Table 1 Summary of key notations

N

Number of DUs

K

Number of initial clusters

H

Flying height

M

Number of SPs

\(R_{c}^{\mathrm{max}}\)

Maximum coverage radius of UAV

\({\mathbf{w}}_{d}[n]\)

Coordinates of the nth DU

\({\mathbf{w}}_{u}[m]\)

Coordinates of the mth SP

\({\mathbf{w}}_{u}^{k}[m_{i}]\)

Coordinates of the \(m_{i}\)th SP obtained during the clustering phase

\({\mathbf{w}}_{u}^{a}[m_{a}]\)

Coordinates of the \(m_{a}\)thSP obtained during the supplementary phase

\({\mathbf{w}}_{d}^{c}[n_{c}]\)

Coordinates of \(n_{c}\)-th DU that can be covered during the clustering phase

\({\mathbf{w}}_{d}^{\mathrm{unc}}[n_{\mathrm{unc}}]\)

Coordinates of \(n_{\mathrm{unc}}\)-th DU that cannot be covered during the clustering phase

\(r_{i}^{k}\)

Sum throughput of covered DU by UAV at \(w_{u}^{k}[i]\)

\(\rho _{e}\)

Joint evaluation index

\(L_{\mathrm{sum}}\)

Length of UAV’s trajectory