Chan Algorithm: Implementing Localization Using TDOA Parameters

This document introduces the classical Chan algorithm, which implements localization functionality using Time Difference of Arrival (TDOA) parameters. To gain deeper insights into this algorithm, we first examine the role of TDOA parameters in positioning systems - these parameters represent the time differences of signal arrivals between multiple base stations, forming hyperbolic position equations. The core implementation involves solving these nonlinear equations through a two-step weighted least squares (WLS) approach: initially estimating a rough position, then refining it with error covariance weighting. The algorithm's mathematical foundation leverages matrix operations for efficient computation, typically implemented through pseudoinverse calculations of geometric matrices. When comparing with other localization algorithms, Chan's method demonstrates superior performance in line-of-sight conditions with moderate noise levels, though it may suffer from performance degradation under severe non-line-of-sight scenarios. The algorithm's key advantage lies in its closed-form solution that avoids iterative computations, making it suitable for real-time applications. Implementation typically requires careful handling of measurement noise through covariance matrix estimation and proper configuration of base station geometry parameters. Ultimately, the Chan algorithm remains a valuable and classical positioning technique worthy of in-depth study and practical implementation in modern localization systems.