The steady increase in data generation by GPS systems poses storage challenges. Previous studies show the need to address trajectory compression. The demand for accuracy and the magnitude of data require effective compression strategies to reduce storage. It is posited that the combination of TD-TR simplification, Kalman noise reduction, and analysis of road network information will improve the compression ratio and margin of error. The GR algorithm is developed, integrating noise reduction and path compression techniques. Experiments are applied with trajectory data sets collected in the cities of California and Beijing. The GR algorithm outperforms similar algorithms in compression ratio and margin of error, improving storage efficiency by up to 89.090%. The combination of proposed techniques presents an efficient solution for GPS trajectory compression, allowing to improve storage in trajectory analysis applications.