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Dispersed fringe sensor (DFS) is an important phasing sensor of next-generation optical astronomical telescopes. The measurement errors induced by the measurement noise of three piston estimation methods for the DFS including least-squared fitting (LSF) method, frequency peak location (FPL) method and main peak position (MPP) method, are analyzed theoretically and validated experimentally in this paper. The experimental results coincide well with the theoretical analyses. The MPP, FPL, LSF are used respectively when the DFS operates with broadband light (central wavelength: 706 nm, bandwidth: 23 nm). The corresponding root mean square (RMS) value of estimated piston error can be achieved to be 1 nm, 3 nm, 26 nm, respectively. Additionally, the range of DFS with the FPL can be more than 100 μm at the same time. The FPL method can work well both in coarse and fine phasing stages with acceptable accuracy, compared with LSF method and MPP method. [ABSTRACT FROM AUTHOR]