This paper presents an end-to-end, CPU/GPU-based real-time framework for code-independent static positioning using signals of opportunity (SoOP) from IridiumNext and Orbcomm. The proposed architecture combines low-cost SDR signal acquisition with Doppler feature extraction, satellite identification, and fast orbital dynamics prediction, followed by parallel robust/nonlinear estimation and fusion. To mitigate the problems of outliers and non-ideal Doppler conditions, a Huber nonlinear least-squares stage is used for robust initialization, while EKF and UKF provide sequential refinement. To accommodate variations in measurement uncertainty and potentially multimodal state distributions, an interacting multiple-model unscented Kalman filter (IMM-UKF) and a Gaussian sum filter (GSF) are implemented, respectively. These five estimators operate concurrently, and their outputs are fused using a heatmap-based accumulation with anisotropic rotated Gaussian kernels and adaptive search-range control, enabling stable real-time operation under intermittent satellite availability. In a 30-minute outdoor static experiment (15° elevation mask, cloudy conditions, −8°C), five IridiumNext and four Orbcomm satellites were detected (of 13 and seven that were predicted to be visible, respectively). Post-processing analysis revealed approximately Gaussian but non-zero-mean Doppler residuals, indicating effective frequency offsets potentially associated with receiver and transmitter oscillator uncertainties. An investigation of zero-Doppler crossing (ZDC) events highlighted their potential for coarse frequency-bias calibration. With a processing window of δt=0.01s, the system achieved a minimum 2D positioning error of ~1m and a final 2D error of ~9.91m at the end of the test, thus demonstrating the feasibility of real-time, code-independent SoOP static positioning with meter-level performance under real-world conditions.