GPS Positioning Algorithm Simulation: Navigation and Location Calculation Principle Emulation

GPS positioning algorithm simulation is a core technology for validating navigation solution principles by emulating satellite signals and receiver workflows. A typical simulation program develops from the following dimensions:

Satellite Signal Simulation The simulation requires constructing a virtual satellite constellation, calculating orbital positions of each satellite at specific times (simulated via ephemeris parameters), and modeling influencing factors such as satellite clock errors and ionospheric delays to provide data foundations for subsequent pseudorange measurements.

Pseudorange Measurement Model Receivers calculate pseudoranges (distance values containing errors) by measuring signal propagation time. The simulation must incorporate noise models including clock biases, atmospheric delays, and multipath effects to generate observation data resembling real-world scenarios. In code implementation, this typically involves generating Gaussian-distributed error terms using functions like randn() to simulate stochastic noise components.

Core Positioning Algorithm Least squares methods or Kalman filtering serve as key techniques for solving user positions. The program must solve quaternary nonlinear equations (three-dimensional coordinates + receiver clock bias) through iterative approximation for optimal solutions. Implementation-wise, algorithms often employ matrix operations (e.g., matrix inversion via pinv() in MATLAB) and iterative convergence checks using while/for loops with tolerance thresholds.

Error Analysis and Improvement The advantage of simulation programs lies in controllable error injection (e.g., artificially increasing clock bias noise), enabling analysis of different factors' impact on positioning accuracy and testing optimization algorithms like differential correction and multi-system fusion. Code implementations typically feature modular error injection functions and comparative analysis modules using statistical functions (std(), mean()) for precision evaluation.

Such simulations are commonly used for teaching demonstrations, receiver design verification, or feasibility studies of novel positioning algorithms (e.g., anti-jamming techniques).