Abstract: In passive sonar systems, the relative motion between a target and the receiver induces Doppler shifts in received line-spectrum signals, resulting in frequency broadening. This phenomenon causes a degradation in the integration gain of conventional coherent integration methods. To address this limitation, a generalized Radon-Doppler transform is proposed in this paper. A time-frequency spectrum model for the received time-varying line-spectrum signal radiated by a moving target is established in the time-frequency domain. Expressions for the frequency offset and phase offset between adjacent time instants, characterized by the target’s multi-dimensional motion parameters, are derived. The proposed method combines the generalized Radon transform with a Doppler phase compensation factor. Based on an optimization framework involving a search over a multi-dimensional parameter space, both the nonlinear frequency shift and phase deviation of the signal are simultaneously corrected to achieve coherent integration. To enhance the efficiency of this high-dimensional parameter search, the random drift particle swarm optimization (RDPSO) algorithm is utilized. A uniform initialization strategy for the particle swarm, a parallel fitness evaluation approach, and an adaptive mutation mechanism are incorporated. These enhancements significantly improve the algorithm’s global search capability. Results from simulations and processing of the SwellEx-96 experimental dataset demonstrate that the proposed algorithm effectively achieves coherent accumulation of time-varying line-spectrum signals. Compared to existing methods, superiorly concentrated spectral estimates are obtained, leading to a significant enhancement in target detection performance.