Table 6 Formulae for calculating mean position of a tag in two dimensions$\left(\overline{\mathit{{\rm X}}},\overline{\mathit{{\rm Y}}}\right)$ during a time interval Δ t for observation-weighted Simpfendorfer et al.[7] and model-weighted positioning estimators using arithmetic and harmonic approaches

Observation-weighted*

$\overline{\mathrm{{\rm X}}}=\frac{{\displaystyle {\sum }_{i=1}^n{R}_i{X}_i}}{{\displaystyle {\sum }_{i=1}^n{R}_i}}$

$\overline{Y}=\frac{{\displaystyle {\sum }_{i=1}^n{R}_i{Y}_i}}{{\displaystyle {\sum }_{i=1}^n\mathit{Ri}}}$

$\overline{X}=\frac{{\displaystyle {\sum }_{i=1}^n{R}_i}}{{\displaystyle {\sum }_{i=1}^n\left(\frac{R_i}{X_i}\right)}}$

$\overline{Y}=\frac{{\displaystyle {\sum }_{i=1}^n{R}_i}}{{\displaystyle {\sum }_{i=1}^n\left(\frac{R_i}{Y_i}\right)}}$

Model-weighted

$\overline{X}=\frac{{\displaystyle {\sum }_{i=1}^n\left({\omega }_i{X}_i\right)}}{{\displaystyle {\sum }_{i=1}^n{\omega }_i}}$

$\overline{Y}=\frac{{\displaystyle {\sum }_{i=1}^n\left({\omega }_i{Y}_i\right)}}{{\displaystyle {\sum }_{i=1}^n{\omega }_i}}$

$\overline{X}=\frac{{\displaystyle {\sum }_{i=1}^n{\omega }_i}}{{\displaystyle {\sum }_{i=1}^n\left({\omega }_i{X}_i\right)}}$

$\overline{\mathit{Y}}=\frac{{\displaystyle {\sum }_{i=1}^n{\omega }_i}}{{\displaystyle {\sum }_{i=1}^n\left({\omega }_i{Y}_i\right)}}$