Bearing-only multi-target localization (BOMTL) determines the positions of multiple targets by intersecting bearing lines from multiple spatial locations. However, non-ideal measurements can result in a large number of ghost targets. A β-S-dimensional assignment (β-SDA) method incorporating waveguide characteristics is proposed to address the BOMTL problem in shallow water with low detection rates. The estimated distance for the warping transformation is derived from the intersection points of the bearing lines, then the autocorrelation function of the broadband beamforming output is transformed using a warping operator to obtain the corresponding characteristic spectrum. The peaks in the characteristic spectrum correspond to the cross-correlation terms of the normal modes, with the frequencies of these peaks related to the ratio of the actual distance to the estimated distance of the sound source. The global target localization results are obtained using the proposed method, which incorporates confidence coefficients derived from the characteristic spectrum and geometric intersection information from the bearing lines. Simulation and sea trial data demonstrate that the β-SDA method effectively overcomes the limitation of pure bearing-only localization in low detection rate scenarios under a given signal-to-noise ratio (SNR), and can localize target positions without requiring precise prior environmental parameters.