Erratum to: GPS Solut DOI 10.1007/s10291-016-0594-1

Some expressions in the math environment in Equations 2, 6, 10 and 11 were displayed incorrectly in the PDF version of the published article. The correct equations are provided below.

$$ \varvec{A} = \left[ {\begin{array}{*{20}c} {\mathbf{0}} \\ {{\text{blkdiag}}\left( {\varvec{\varLambda}_{\text{G}} ,\varvec{\varLambda}_{\text{B}} } \right)} \\ \end{array} } \right] $$
(2)
$$\left[ {\begin{array}{*{20}c} {\hat{\varvec{a}}} \\ {\hat{\varvec{b}}} \\ \end{array} } \right] \sim {\mathcal{N}}\left( {\left[ {\begin{array}{*{20}c} {\varvec{a}} \\ {\varvec{b}} \\ \end{array} } \right],\left[ {\begin{array}{*{20}c} {\varvec{Q}_{{\hat{\varvec{a}}}} }; {\varvec{Q}_{{\hat{\varvec{a}}}{\hat{\varvec{b}}}} } \\ {\varvec{Q}_{{\hat{\varvec{b}}}{\hat{\varvec{a}}}} }; {\varvec{Q}_{{\hat{\varvec{b}}}}} \\ \end{array} } \right]} \right)$$
(6)

The subscripts of both “Q”s are incorrect in the first math expression after Eq. 10. The correct equation and the text read as follows:

$$\varvec{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{b} } = \hat{\varvec{b}} - \varvec{Q}_{{\hat{\varvec{b}}{\hat{\varvec{z}}}_{{\mathbf{\mathcal{I}}}} }} \varvec{Q}_{{\hat{\varvec{z}}_{{\mathbf{\mathcal{I}}}} }}^{ - 1} \left( {\hat{\varvec{z}}_{{\mathcal{I}}} - \varvec{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{z} }} \right)$$
(10)

with \(\varvec{Q}_{{{\hat{\varvec{b}}}{\hat{\varvec{z}}}_{{\mathbf{\mathcal{I}}}} }} = \varvec{Q}_{{\hat{\varvec{b}}}{\hat{\varvec{a}}}} \varvec{Z}_{{\mathcal{I}}}^{\text{T}}\) and \(\varvec{Q}_{{\hat{\varvec{z}}_{{\mathbf{\mathcal{I}}}} }} = \varvec{Z}_{{\mathbf{\mathcal{I}}}} \varvec{Q}_{{\hat{\varvec{a}}}} \varvec{Z}_{{\mathcal{I}}}^{\text{T}}\).

$$\varvec{Q}_{{\hat{\varvec{b}}|\hat{\varvec{z}}_{{\mathbf{\mathcal{L}}}} }} = \varvec{Q}_{{\hat{\varvec{b}}}} - \varvec{Q}_{{{\hat{\varvec{b}}{\hat{\varvec{z}}}}_{{\mathbf{\mathcal{L}}}} }} \varvec{Q}_{{\hat{\varvec{z}}_{{\mathbf{\mathcal{L}}}} }}^{ - 1} \varvec{Q}_{{\hat{\varvec{z}}_{{\mathbf{\mathcal{L}}}} \hat{\varvec{b}}}}$$
(11)

The equations in the original article have been updated accordingly.