Electrodermal activity (EDA) is a widely used physiological signal for assessing sympathetic nervous activity, such as arousal, stress, and pain. However, reliable decomposition into tonic and phasic components remains challenging, particularly in noisy environments and across individuals with varying signal morphologies and stimulus responses. We propose ospEDA, a novel Orthogonal Subspace Projection (OSP) based method for EDA decomposition. The method integrates (1) tonic estimation via physiologically motivated valley detection for noise robustness; (2) phasic extraction using OSP to accommodate inter subject variability; and (3) phasic driver estimation through non-negative least squares (NNLS) deconvolution with ridge regularization. We evaluated ospEDA on five real-world datasets and one simulated EDA dataset with ground-truth components, comparing its performance against six existing methods. In simulations with a 20 dB signal to noise ratio (SNR), ospEDA achieved the lowest root mean square error (RMSE) for estimated tonic (0.131) and phasic (0.132) components. Under noisier conditions (10 dB SNR), it maintained superior phasic RMSE (0.293), Pearson correlation (0.782), and R^2 (0.979) values. Furthermore, ospEDA consistently provided the highest F1 scores (0.573, 0.617, 0.638) for sympathetic nerve activity detection across 10, 20, and 30 dB SNR levels, respectively, compared to existing methods. On the real world datasets, ospEDA achieved a stimulus classification AUROC of 0.766 and consistently maintained strong effect sizes (ω^2>0.14) across all five datasets. Overall, ospEDA represents a promising framework for EDA decomposition, showing generally consistent performance and reliable phasic driver estimation under the varying noise conditions, with potential utility for real world physiological monitoring applications.