In this paper we propose reduced complexity adaptive methods for compensating cross-correlation interference in global positioning system (GPS) receivers operating in weak signal conditions. The idea is to use modified codes in GPS receivers which minimize the mean squared error (MSE) during signal tracking process. In addition, complexity reduction constraints are also included such as autocorrelation thresholding, autocorrelation quantization and so-called group-weighting of modified code elements. The new methods improve the robustness of the system in weak signal conditions while the complexity of the implementation can be traded against the performance.