Algorithm 8: Generation of synthetic data

Step 1:Initialize the number of measurements K and the radius of sphere r Step 2: Calculate Golden Ratio: $\phi =\frac{1+\sqrt{5}}{2}$ Step 3: for each $k=1,2,\cdots ,K$ do:         $\theta =\frac{2\pi k}{\phi }$         $\varphi =\arccos \left(1-\frac{2(k-0.5)}{K}\right)$         $m_k=\left[m_x,m_y,m_z\right]=\left[rcos\theta sin\varphi ,rsin\theta sin\varphi ,rcos\varphi \right]$ Step 4: Pick the scaling parameter, $\alpha$, the perturbation matrix, E         and the perturbation vector, e. Step 5: Calculate T and h according to (66). Step 6: Generate a sequence of white noise: $\epsilon \sim \mathcal{N}(0,{\sigma }^2)$ Step 7: Calculate the measurement vectors: $y_k=T{m}_k+h+{\epsilon }_k$ (2)