Dispersed fringe sensors are a promising approach for sensing the large-scale physical step between adjacent segments with acceptable accuracy. However, the nature of dispersion in a dispersed fringe sensor leads to the ideal dispersed fringe pattern becoming vulnerable to noise, particularly at low light levels. A reliable merit-function-based algorithm with an active actuation is introduced here. The feasibility of our algorithm is numerically demonstrated, and Monte Carlo experiments for different signal-to-noise ratios are conducted to assess its robustness. The results show that the method is valid even when the signal-to-noise ratio is as low as 1.