Dispersive interferometry (DPI) stands as a formidable method in both scientific and industrial realms, offering the capability for numerous measurement scenarios with remarkable accuracy over extensive ranges. The advent of on-chip soliton microcombs (SMCs) boasting a high repetition rate illuminates a promising pathway toward measurements free from dead zones. However, its application scenarios are considerably constrained by the nonmeasurable range (NMR)�the region proximate to the measurement period's extreme points, which is circumscribed by the fast Fourier transform (FFT) steps and symmetry of the data calculation procedure. Here, we introduce an NMR elimination method that refines the DPI structure by engendering an asymmetric interference spectrum. Furthermore, a phase saltation tracking (PST) method for demodulating is devised, enabling measurements without NMR. Both simulation analyses and experimental outcomes affirm that our proposed method significantly enhances the performance of the DPI system by eliminating NMR and improving measurement precision. The Allan deviation of our method consistently remains lower than the DPI measurement results under identical conditions over an average time of 125 s, achieving 7.43 nm at 125 s. This method holds promising potential for application in emerging fields such as optical coherence tomography (OCT), long-distance ranging, and precision light detection and ranging (LIDAR).