Algorithm 6: Wu and Shi [4]

Initial Estimate Step 1: Calculate $Y_k$, $k=1,2,\cdots ,K$ from (55) and form the matrix $Y={\left[\begin{array}{cccc}{Y}_1^T& Y_2^T& \cdots & Y_K^T\end{array}\right]}^T$. Step 2: Find the eigenvector of $Y^{T}Y$ corresponding to its minimum (or zero) eigenvalue and denote it as $z_e={\left[\begin{array}{ccc}\mathrm{vec}{\left(A_e\right)}^T& b_e^T& c_e\end{array}\right]}^T$. Step 3: Calculate $z=a{z}_e$ where $\alpha =4/\left(b_e^T{A}_e^{-1}{b}_e-4c_e\right)$. Step 4: Extract $\mathrm{vec}\left(A\right)$, b and c from z. Step 5: Calculate an initial estimate of the unknowns using (57).   Gauss–Newton Method Step 6: Use the initial estimates to initialize the vector x of (53) Step 7: Update x using (54). Step 8: Evaluate the cost $J\left(x\right)$ of (52). Step 9: Repeat steps 7-8 until $J\left(x\right)$ becomes sufficiently small.