On each arc we randomly choose 100 points. Gaussian noise with zero-mean and standard deviation is added to the points. The noise levels are 0, 1, 2, 3, 4, 5, respectively. For each noise level, we perform 100 independent trials, and the mean values and standard deviations of these recovered parameters are computed over each run. The errors compared to the ground truth are defined as Display Formulawhere and are the ground truth, , , and are the estimated parameters of -th trail, and is the number of trails. Although the fitting error increases with the noise level, the comparison results of the three approaches are similar for different noise levels. For the sake of brevity, we only provide the fitting results when , as shown in Tables 2003–4. The three fitting approaches described in Sec. 3 are indicated by subscripts , and , respectively.