Algorithm 1. Spatial Consensus Check

Input: $\left\{\left(\Delta x_{k-n}^G,\Delta y_{k-n}^G\right), \cdots ,\left(\Delta x_k^G,\Delta y_k^G\right),\left(\Delta x_{k-n}^D,\Delta y_{k-n}^D\right), \cdots ,\left(\Delta x_k^D,\Delta y_k^D\right)\right\}$

Output: $\left\{\left(\Delta {\overline{x}}_k, \Delta {\overline{y}}_k\right)\right\}$

for i = 1 to n do $$\Delta {\tilde{x}}_{ki}^G = {\varnothing }_{xi1}^G\Delta x_{k-1}^G+\cdots +{\varnothing }_{xii}^G\Delta x_{k-i}^G+{\theta }_{xi1}^G\Delta y_{k-1}^G+\cdots +{\theta }_{xii}^G\Delta y_{k-i}^G$$ $$\Delta {\tilde{x}}_{ki}^D = {\varnothing }_{xi1}^D\Delta x_{k-1}^D+\cdots +{\varnothing }_{xii}^D\Delta x_{k-i}^D+{\theta }_{xi1}^D\Delta y_{k-1}^D+\cdots +{\theta }_{xii}^D\Delta y_{k-i}^D$$ $$\Delta {\tilde{y}}_{ki}^G = {\varnothing }_{yi1}^G\Delta x_{k-1}^G+\cdots +{\varnothing }_{yii}^G\Delta x_{k-i}^G+{\theta }_{yi1}^G\Delta y_{k-1}^G+\cdots +{\theta }_{yii}^G\Delta y_{k-i}^G$$ $$\Delta {\tilde{y}}_{ki}^D = {\varnothing }_{yi1}^D\Delta x_{k-1}^D+\cdots +{\varnothing }_{yii}^D\Delta x_{k-i}^D+{\theta }_{yi1}^D\Delta y_{k-1}^D+\cdots +{\theta }_{yii}^D\Delta y_{k-i}^D$$

end

$n_1^{\text{'}} = n_2^{\text{'}} =n$

for i = 1 to Max_iters do $$\Delta {\overline{x}}_k = \frac{\Delta {\tilde{x}}_{k1}^G+\cdots +\Delta {\tilde{x}}_{k{n}_1^{\text{'}}}^G+\Delta {\tilde{x}}_{k1}^D+\cdots +\Delta {\tilde{x}}_{k{n}_2^{\text{'}}}^D+\Delta x_k^G+\Delta x_k^D}{n_1^{\text{'}} + n_2^{\text{'}}+2}$$ $$\Delta {\overline{y}}_k = \frac{\Delta {\tilde{y}}_{k1}^G+\cdots +\Delta {\tilde{y}}_{k{n}_1^{\text{'}}}^G+\Delta {\tilde{y}}_{k1}^D+\cdots +\Delta {\tilde{y}}_{k{n}_2^{\text{'}}}^D+\Delta y_k^G+\Delta y_k^D}{n_1^{\text{'}} + n_2^{\text{'}}+2}$$

Compute the distance $\overrightarrow{L}$ of all $n_1^{\text{'}} + n_2^{\text{'}}+2$ points to centroid points.

For a point $\left(\Delta x^{\prime }, \Delta y^{\prime }\right)$, denotes $\overrightarrow{L^{\prime }} = \frac{\mathrm{sum}\left(\overrightarrow{L}\right) - L^{\prime }}{\left(n_1^{\text{'}} + n_2^{\text{'}}+2\right) - 1}$

if $\frac{\Vert \left(\Delta x^{\prime }, \Delta y^{\prime }\right)\Vert - \left(\Delta \overline{x}, \Delta \overline{y}\right)}{\overline{L^{\prime }}}>threshold$, then

Remove this point.

Update $n_1^{\text{'}}$ or $n_2^{\text{'}}$.

end

end