$K^+p$ ($K^+p$ $\oplus$ $K^-\overline{p}$) correlation functions obtained in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ in the 0-20% (left), 20-40% (middle) and 40-100% (right) centrality intervals. The measurement is shown by the black markers. The vertical error bars and the boxes represent the statistical and systematic uncertainties, respectively. The red band in the upper panels represents the model calculation and its systematic uncertainty as described in the text. The $r_\mathrm{core}$ and $r_{\rm eff}$ values of the source are reported with their statistical and systematical uncertainties, respectively. Bottom panels represent the data-to-model comparison.