Erratum to: The Journal of the Astronautical Sciences, Vol. 57,

       Nos. 1 and 2, January-June 2009, pp. 233-260

       DOI 10.1007/BF03321503

Equation (69) should read

$$\mathsf{r} = \tilde{\mathsf{H}} \mathsf{e}^{-}_{*} + \mathsf{u}_{d} + \mathsf{v}$$
(69)

The comment between equations (77) and (78) should read

“with \(P_{*}^{-}=P(t_{*}^{-})\),”

Equation (82) should read

$$\begin{array}{@{}rcl@{}} &=\left\{ \begin{array}{llll} \mathsf{Q}_{d}(t_{i},t_{*}) \mathsf{\Phi}^{\mathsf{\scriptscriptstyle{T}}}(t_{j},t_{i}) & t_{*} < t_{i} \leq t_{j}, \\ \mathsf{\Phi}(t_{i},t_{j})\mathsf{Q}_{d}(t_{j},t_{*}) & t_{*} < t_{j} \leq t_{i}, \\ \mathsf{\Phi}(t_{i},t_{*})\mathsf{Q}_{d}(t_{*},t_{j}) \mathsf{\Phi}^{\mathsf{\scriptscriptstyle{T}}}(t_{j},t_{*}) & t_{i} \leq t_{j} < t_{*}, \\ \mathsf{\Phi}(t_{i},t_{*})\mathsf{Q}_{d}(t_{*},t_{i}) \mathsf{\Phi}^{\mathsf{\scriptscriptstyle{T}}}(t_{j},t_{*}) & t_{j} \leq t_{i} < t_{*}, \\ \mathsf{0} & \text{otherwise}. \end{array}\right. \end{array}$$
(82)

Equations (86)–(88) should read

$$\begin{array}{@{}rcl@{}} \mathsf{N}_{d}(t) &=& \mathrm{E}\left[{\mathsf{e}_{w*}^{+} \mathsf{w}_{d}^{\mathsf{\scriptscriptstyle{T}}}(t,t_{*})}\right] \end{array}$$
(86)
$$= -\mathrm{E}\left[{\textstyle{\tilde{\mathsf{S}}_{*}{\sum}_{i}} \mathsf{K}_{i} \mathsf{u}_{di} \mathsf{w}_{d}^{\mathsf{\scriptscriptstyle{T}}}(t,t_{*})}\right]$$
(87)
$$= -\tilde{\mathsf{S}}_{*}\textstyle{{\sum}_{i}} \mathsf{K}_{i} \mathsf{H}_{i} \mathsf{Q}_{d}(t_{*};t,t_{i})$$
(88)

The line immediately above equation (94) should read

“at epoch. In equation (75) the matrix \(\left (\mathsf {I}_{n} -\tilde {\mathsf {S}}_{*} \textstyle {{\sum }_{i}}\mathsf {K}_{i} \tilde {\mathsf {H}}_{i}\right )\) is replaced by”

The assumption made below equation (74) that the errors in \(\mathsf {e}_{a*}^{+}\), \(\mathsf {e}_{v*}^{+}\), and \(\mathsf {e}_{w*}^{+}\) are uncorrelated is certainly valid if t ∗ is prior to all the measurements, so the results of the paper are equally valid in that case. If t ∗ is later than some or all of the measurements, however, it might be more reasonable to assume that \(\mathsf {e}_{a*}^{+}\) includes the process noise accumulated between the beginning of the observation span and t ∗, in which case it has nontrivial correlations with \(\mathsf {e}_{w*}^{+}\). This modifies the manner in which process noise appears in the covariance analysis of the batch estimator [1].