Non-GPS localization has gained much interest from researchers and industries recently because GPS might fail to meet the accuracy requirements in shadowing environments. The two most common range-based non-GPS localization methods, namely Received Signal Strength Indicator (RSSI) and Angle-of-Arrival (AOA), have been intensively mentioned in the literature over the last decade. However, an in-depth analysis of the weighted combination methods of AOA and RSSI in shadowing environments is still missing in the state-of-the-art. This paper proposes several weighted combinations of the two RSSI and AOA components in the form of pAOA + qRSSI, devises the mathematical model for analyzing shadowing effects, and evaluates these weighted combination localization methods from both accuracy and precision perspectives. Our simulations show that increasing the number of anchors does not necessarily improve the precision and accuracy, that the AOA component is less susceptible to shadowing than the RSSI one, and that increasing the weight of the AOA component and reducing that of the RSSI component help improve the accuracy and precision at high Signal-to-Noise Ratios (SNRs). This observation suggests that some power control algorithm could be used to increase automatically the transmitted power when the channel experiences large shadowing to maintain a high SNR, thus guaranteeing both accuracy and precision of the weighted combination localization techniques.