ChanAlgorithm3D: TDOA-Based 3D Localization Using Chan's Algorithm

Chan's Algorithm is a classical localization method based on Time Difference of Arrival (TDOA), widely used in signal processing and positioning technologies. This algorithm determines target positions by measuring the time differences of signal arrivals at different receivers, particularly suitable for high-precision 3D localization requirements. The implementation typically involves matrix operations and least-square solutions to handle TDOA measurements efficiently.

In TDOA positioning systems, signals transmitted from a source are captured by multiple receivers, each recording arrival times. The time differences form hyperbolic or hyperboloid equations. Chan's Algorithm employs mathematical modeling and optimization techniques to transform these nonlinear equations into linear forms through Taylor series expansion or analytical solutions, enabling efficient computation of target coordinates. Code implementation often includes error covariance matrix processing to enhance solution stability.

Compared to other localization methods, Chan's Algorithm features reduced computational complexity and higher stability, making it suitable for real-time positioning scenarios. The algorithm effectively mitigates measurement errors through weighted least-square optimization and improves positioning accuracy. These advantages make it widely applicable in wireless communications, radar tracking, and UAV navigation systems. The MATLAB implementation typically utilizes matrix inversion functions and coordinate transformation algorithms to achieve optimal 3D positioning results.