Algorithm 1 Three-Dimensional Empirical AoA Localization

Input: AoA readings at fixed reader nodes, three-dimensional location of $N’$ readers, phase error profile Output: Estimated three-dimensional location $\widehat{F}$ of a tag $T_k$ 1. A tag broadcasts its unique identifiers 2. $N$ readers receive the signals from the tags ($N\subseteq N\prime$) 3. Each reader $R_n$ reports the measured AoA ${\theta }_h$ and ${\theta }_v$ to a central database 4. Map ${\theta }_h$ and ${\theta }_v$ to their corresponding AoA error ${\epsilon }_h$ and ${\epsilon }_v$ 5. If $N\ge 2$ 6. For n = 1 to N 7. Compute $m_{n,v}$ and $m_{n,h}$ 8. Compute the vectors ${\overrightarrow{d}}_{n,1}$ and ${\overrightarrow{d}}_{n,2}$ 9. End for 10Else 11Tag cannot be localized by one reader 12End If 13For I = 1 to $\left(\begin{array}{c}N\\ 2\end{array}\right)$ 14Compute min $|\overrightarrow{PQ}|$ 15Compute estimated location ${\widehat{F}}_{i,k}$ 16End For 17For I = 1 to $\left(\begin{array}{c}N\\ 2\end{array}\right)$ 18Compute ${\mathsf{\Psi }}_{i,k}^{\prime }$, ${\mathsf{\Theta }}_{i,k}^{\prime }$ 19Compute $w_{i,k}$ 20End For 21Compute ${\widehat{F}}_k$