MATLAB Implementation and Simulation of CHAN Algorithm

CHAN algorithm is a wireless positioning method based on TDOA (Time Difference of Arrival), commonly used in base station localization scenarios. This algorithm processes signal arrival time differences measured by multiple base stations to accurately estimate mobile terminal positions. This article demonstrates how to implement CHAN algorithm simulation in MATLAB environment. ### Simulation Conditions Number of base stations: 3 to 7, randomly distributed in 2D or 3D space. Noise model: Measurement errors follow Gaussian distribution, simulating random interference in real-world signal propagation. Line-of-sight propagation: Assumes no NLOS (Non-Line-of-Sight) errors by default, meaning signals propagate along straight paths. ### Implementation Approach Base station deployment: Generate random coordinates for 3-7 base stations within the simulation area using MATLAB's rand() function, ensuring they are not collinear (2D) or coplanar (3D). Target position setting: Define terminal coordinates and calculate true distances to each base station using Euclidean distance formula. TDOA measurement generation: Add Gaussian noise to true distance differences using randn() function to simulate practical measurement errors. CHAN algorithm solution: - Construct TDOA equations matrix using measured time differences - Implement Weighted Least Squares (WLS) method with pinv() function for position estimation - Apply iterative optimization through for-loops to improve positioning accuracy Performance evaluation: Calculate positioning errors using norm() function, analyze impact of different base station numbers and noise levels on accuracy through statistical analysis. ### Extension Considerations NLOS errors: Extend simulation by implementing NLOS error models (e.g., exponential distribution) using exprnd() function to study impact on CHAN algorithm. Algorithm improvements: Combine Taylor-series expansion or Particle Filter (PF) techniques using optimization工具箱 to enhance positioning performance. CHAN algorithm performs excellently in ideal Gaussian noise environments, suitable for indoor/outdoor positioning systems and UAV navigation. MATLAB simulation allows intuitive verification of positioning accuracy and optimization of parameter configurations through systematic Monte Carlo testing.