Preprocessed signals from Global Positioning System (GPS) satellites can be used for ionospheric research. Important ionospheric characteristics are for example ionospheric propagation delays and scintillations. These characteristics are important for understanding the ionosphere and showing how the ionosphere reacts to external forces (e.g., geomagnetic disturbance, solar eclipse, etc.). Dual-frequency systems use an approach based on the difference between two pseudoranges. However, this approach has two possible disadvantages: 1) the price of the dual frequency receiver is relatively high and 2) both pseudoranges can affect the obtained results so the operators cannot separately analyze their relative contribution. The objective of the article is to demonstrate an algorithm for processing data from a GPS receiver. The algorithm does not merge the pseudoranges obtained from different carrier waves. Accordingly, it was decided to use whitening filters to accomplish this task for every frequency separately. Compared with the dual-frequency approach, the obtained results of the newly developed algorithm demonstrate that this algorithm works accurately, and the propagation delays can be estimated independently of the used frequency.