Chan's Algorithm for TDOA Localization with Weighted Least Squares Implementation

In this article, we discuss Chan's algorithm for TDOA (Time Difference of Arrival) localization. TDOA localization is a positioning technique based on time difference measurements, which determines the receiver's location by measuring the time differences of signal arrivals at different base stations. Chan's algorithm represents a widely used TDOA approach that estimates the receiver's position through nonlinear least squares solutions of time difference equations. Compared to other TDOA algorithms, Chan's method demonstrates superior accuracy and faster computational performance. The algorithm implementation requires two-stage weighted least squares (WLS) computations to achieve more precise position estimation results. The first WLS calculation provides an initial position estimate, while the second WLS refinement incorporates covariance matrix weighting to reduce estimation errors. We will provide detailed explanations of Chan's algorithm principles and the WLS computation process, including mathematical formulations for the hyperbolic positioning equations and weighting strategies. Additionally, we'll discuss practical implementation considerations such as matrix conditioning and convergence criteria to better understand the application of TDOA localization technology in real-world scenarios.