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Correction to: Annals of Biomedical Engineering (2021) https://doi.org/10.1007/s10439-020-02716
This Erratum is to correct equations 6, 7, 8, and 9.
$$\begin{aligned} R_{Iz} = \left[ z_{{\text {top}}}, z_{{\text {top}}} + {\upsilon}_{\max } \Delta t \right] \in \left[ z_{{\text {top}}}, z_0 \right ] \ R_{{ {Ip}}} = \left[ 0, \theta _{{\text {p,max}}}\right]\end{aligned}$$
(6)
$$\begin{aligned} R_{Iz} = \left[ z_k-z_{{ {unc}}}, z_k+{\upsilon}_{\max} \Delta t+ z_{{ {unc}}}\right] \! \in \! \left[ z_0, z_{{{EGJ}}}\!-\!d \right) \\ R_{Ip} = \left[ \theta _{{{p}},k}-\phi _{R1}-\theta _{{{p,unc}}}, \theta _{{\text {p}},k}+\phi _{R1}+\theta _{{{p,unc}}} \right] \in \left[ 0, \theta _{{ {p,max}}}\right]\end{aligned}$$
(7)
$$\begin{aligned} R_{Iz} = \left[ z_k-z_{{ {unc}}}, z_k+{\dot{z}}_k\Delta t + \frac{1}{2}g\Delta t^2 +z_{{{unc}}}\right] \in \left[ z_{{ {EGJ}}}-d, z_{bottom}\right] \\ R_{{ {Ip}}} = \left[ \theta _{{\text {p}},k}-\phi _{R2}-\theta _{{ {p,unc}}}, \theta _{{{p}},k}+ \phi _{R2}+\theta _{{{p,unc}}}\right] \in \left[ 0, \pi \right]\end{aligned} $$
(8)
$$\begin{aligned} & \varvec{B_{thresh_j,k+1}} = \varvec{B_{thresh_j,k}} + \varvec{K_{p_j,k}}(z) e_{j,k} +\varvec{K_{d_j,k}} \frac{de_{j,k}}{dt} \nonumber \\ & \varvec{K_{p_j,k}}(z) = \alpha(z) |\varvec{B_{sensor_j,k}}| \nonumber \\ & \varvec{K_{d_j,k}} = \beta |\varvec{B_{sensor_j,k}}| \nonumber \\ & e_{j,k} = n_{target} - n_{j,k} \nonumber \\ & \frac{de_{j,k}}{dt} = \frac{e_{j,k}-e_{j,k-1}}{t_{k}-t_{k-1}}\end{aligned}$$
(9)
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Miyasaka, M., Tiong, A.M.H., Phan, P.T. et al. Correction to: Two Magnetic Sensor Based Real-Time Tracking of Magnetically Inflate Swallowable Intragastric Balloon. Ann Biomed Eng 49, 1267 (2021). https://doi.org/10.1007/s10439-021-02737-8
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DOI: https://doi.org/10.1007/s10439-021-02737-8