When in WSNs sensors receive different noise intensities or the wireless transmission channel has the shadow fading effect, the association metrics estimation method for range ratios of arrival (RROA) and the passive source localization algorithm based on RROA are studied. Firstly, the eigenvector decomposition (EVD) approach is used to estimate the RROA association metrics. The noise intensity received by each sensor can be estimated by performing EVD on the covariance matrix of the received signal. Secondly, by rotating the array reference point at each of the array sensors, a number of covariance matrices are constructed and the EVD approach can be used to cancel the shadow fading effect. Thus RROA association metrics can be estimated reliably. Finally, the weighted-least-squares (WLS) algorithm based on the RROA association metrics is proposed. The proposed approach is robust to channel shadow fading effect and different noise intensities received.