Algorithm 2 Measured Footprint Optimisation

Input: Experimental pressure values $\left\{{\overline{P}}_{ij}(t)\right\}$ provided by the PSM at time t

Input: Set of measured footprints ${\left\{A_k(x,y)\right\}}_{k=1,\dots ,n_k}$

Input: PSM geometry parameters $\theta$

Output: CoP estimate $(x_E(t),y_E(t)))$ at time t 1: $$(x^k{(t)}^{*},y^k{(t)}^{*})\leftarrow \underset{\{x^k,y^k\}}{min}\left\{\sum _i\sum _j{\left(\sum _{k=1}^{n_k}{A}_k\left(x_j+x^k(t),y_i+y^k(t)\right)-{\overline{P}}_{ij}(t)\right)}^2\right\}$$ (38)         ▹ Compute footprint locations (by combining (24) with (23)) 2: $$\begin{array}{cc}\hfill & x_E(t)\leftarrow {\displaystyle \frac{{\int \int }_{A}x{\sum }_{k=1}^{n_k}{A}_k\left(x+x^k{(t)}^{*},y+y^k{(t)}^{*}\right)dA}{{\int \int }_A{\sum }_{k=1}^{n_k}{A}_k\left(x+x^k{(t)}^{*},y+y^k{(t)}^{*}\right)dA}},\hfill \end{array}$$ (39) $$\begin{array}{cc}\hfill & \hfill y_E(t)\leftarrow {\displaystyle \frac{{\sum }_{y\in \mathcal{Y}}{\sum }_{x\in \mathcal{X}}y{\sum }_{k=1}^{n_k}{A}_k\left(x+x^k{(t)}^{*},y+y^k{(t)}^{*}\right)\Delta x\Delta y}{{\sum }_{y\in \mathcal{Y}}{\sum }_{x\in \mathcal{X}}{\sum }_{k=1}^{n_k}{A}_k\left(x+x^k{(t)}^{*},y+y^k{(t)}^{*}\right)\Delta x\Delta y}}\end{array}$$ (40)               ▹ Compute CoP (by combining (26) with (23) 3:return  $(x_E(t),y_E(t)))$