Taylor Series Expansion Least Squares Positioning Algorithm for TDOA Localization with MATLAB Implementation

In this article, we present the implementation of a precise positioning system using Taylor Series Expansion Least Squares Algorithm for TDOA (Time Difference of Arrival) localization through MATLAB source code. This algorithm, originally developed by the GreenSim team, has undergone years of practical testing and debugging, making it widely applicable across various domains. TDOA positioning is a common localization technique that determines signal source locations by measuring time differences of signal arrivals at different receivers. The implementation leverages Taylor series expansion to transform nonlinear problems into linear ones, significantly simplifying the solution process. The MATLAB code employs an iterative approach where the algorithm linearizes the nonlinear TDOA equations using first-order Taylor expansion around an initial position estimate. The least squares method then minimizes the squared differences between measured and calculated TDOA values, providing optimal position solutions through matrix operations and pseudoinverse calculations. We provide complete MATLAB source code that includes key functions for signal processing, time difference calculation, and iterative position refinement. The code demonstrates practical implementation of Jacobian matrix computation for the linearization process and incorporates convergence checks to ensure solution stability. We encourage you to download and experiment with this source code to gain deeper understanding of the Taylor Series Expansion Least Squares Algorithm for TDOA positioning, enabling improved performance in real-world applications through parameter tuning and algorithm customization.