GPS Satellite Positioning: Calculating User Position Using Pseudorange Observations

In the modern era, GPS satellite positioning has become an indispensable part of contemporary life. By utilizing pseudorange observations to calculate user positions, it provides significant convenience for daily activities. This system plays crucial roles in navigation, transportation, and map positioning applications. The position calculation algorithm typically involves collecting pseudorange measurements from multiple satellites and solving the navigation equations using least squares estimation or similar mathematical methods. During position computation, the system employs cross-validation using data from multiple satellites (typically requiring at least 4 satellites for 3D positioning) to ensure result accuracy through geometric dilution of precision (GDOP) calculations. The core implementation involves solving the following equation: ρ = ||s - u|| + c·δt + ε, where ρ represents pseudorange, s is satellite position, u is user position, c is light speed, δt is clock bias, and ε encompasses various error factors. Furthermore, GPS satellite positioning finds extensive applications in military domains, providing soldiers with precise location information through enhanced algorithms like differential GPS (DGPS) and real-time kinematic (RTK) positioning to ensure operational success. In summary, GPS satellite positioning stands as one of the most critical technologies in modern science, offering not only practical conveniences but also enabling exploration of unknown territories through advanced positioning algorithms and error correction techniques.