Solving Pseudorange Positioning Equations with MATLAB Implementation

In this study, we require the development of a MATLAB program to solve pseudorange positioning equations for processing actual measurement data and determining receiver position along with clock bias information. We provide two datasets, each containing 8 channels: X, Y, and Z coordinates represent the tracked satellites' positions in the WGS-84 coordinate system, while Range denotes the corresponding corrected pseudorange measurements. To better understand this data, we must thoroughly examine its significance and implications for our research. Allow me to elaborate on these aspects in detail. First, pseudorange positioning equations constitute a fundamental method for receiver positioning based on signal transmission time differences between satellites and receivers. These time differences can be calculated through pseudorange measurements using mathematical models that account for signal propagation delays. In MATLAB implementation, this typically involves constructing observation equations and applying linearization techniques through Taylor series expansion around an initial position estimate. Second, the WGS-84 coordinate system serves as a standardized terrestrial reference framework for precise position determination. Our code must incorporate coordinate transformations and Earth geometry calculations to ensure accurate positioning results. The algorithm implementation requires handling geometric dilution of precision (GDOP) considerations and satellite constellation geometry. Finally, accurate measurement of satellite positions and clock bias information is crucial in our research, as these parameters directly determine receiver positioning accuracy and timing synchronization. Our MATLAB solution will employ iterative least-squares estimation algorithms, potentially enhanced with Kalman filtering for dynamic scenarios. The program structure includes data preprocessing modules, matrix operations for normal equation solutions, and convergence checks for iterative refinement. Key functions involve implementing measurement residual calculations, Jacobian matrix computations for partial derivatives, and weight matrix configurations based on measurement quality indicators.