To improve the extraction accuracy of weak Coriolis acceleration signals in accelerometer-based north-seeking systems, a three-stage collaborative signal processing framework based on CiSSA-GSWOA-VMD is proposed. In the first stage, circulant singular spectrum analysis (CiSSA) is applied to the raw accelerometer output, where effective components with distinct periodic characteristics are extracted through frequency-feature mapping of the cyclic matrix, thereby suppressing broadband noise. In the second stage, a global-search whale optimization algorithm (GSWOA) is employed to adaptively optimize the key parameters of variational mode decomposition (VMD). In the final stage, the optimized VMD is applied to the selected components to further remove residual noise and accurately isolate the target signal. Experimental results demonstrate that, in terms of solution accuracy, the proposed method reduces the overall average MAE by 1.781° and 2.276° compared with EWT and the original CiSSA, respectively. Relative to the CiSSA-VMD method, the overall average MAE is further reduced by 1.271°. With regard to solution stability, the average standard deviation decreases by approximately 1.048° and 0.489° compared with EWT and CiSSA, respectively, and by 0.140° compared with CiSSA-VMD. Overall, the proposed framework outperforms EWT and the original CiSSA in both solution accuracy and robustness, while achieving a small but robust performance improvement compared to the CiSSA-VMD method. It is suitable for high-precision extraction of weak Coriolis components in accelerometer-based north-seeking systems under high-noise environments.