Underwater acoustic positioning using ultrashort baseline (USBL) technology is essential for underwater navigation and ocean surveillance. Many research institutions and commercial organizations have conducted extensive studies on USBL, with wideband processing widely applied to enhance the capabilities of related methods. However, the properties of the wideband correlation spectrum have not been thoroughly explored. This study introduces a linear fitting technique, leveraging the frequency-phase relationship within the spectrum to enhance the USBL performance. By combining iterative reweighted least squares and a random sampling and consensus (RANSAC)-type approach, the method reduces the impact of outliers, particularly in multiple-path and low signal-to-noise ratio (SNR) scenarios. Furthermore, we operate a matched filter before the linear fitting process and suggest rescreening based on the consistency of all array elements in the frequency domain to eliminate more outliers. The proposed method significantly reduces positioning errors in both numerical simulations and sea trial data processing.