GPS Satellite Positioning: Calculating User Position Using Pseudorange Measurements

In GPS positioning technology, calculating user position using pseudorange measurements is a core process. Pseudorange refers to the time difference between signal transmission from the satellite to reception multiplied by the speed of light. However, due to the clock bias between the receiver and satellite clocks, the measured distance is not the true geometric range, hence termed "pseudorange."

To calculate the user's three-dimensional position (longitude, latitude, altitude) and receiver clock bias, pseudorange observation data from at least four satellites are required. Each satellite's pseudorange equation contains user position coordinates and clock bias terms. By solving this set of nonlinear equations, precise user positioning can be achieved. In code implementation, this typically involves constructing a measurement matrix H and using weighted least squares algorithms to handle the position estimation problem.

Common solving methods include least squares and iterative algorithms. The least squares method linearizes pseudorange equations through Taylor series expansion and gradually approaches the optimal solution. Iterative algorithms start with an initial position estimate and continuously refine it until errors meet accuracy requirements. Practical applications must also account for error corrections from atmospheric delays and multipath effects, which often require implementing ionospheric and tropospheric delay models in the positioning algorithm.