Time Difference of Arrival (TDoA) Based Positioning Method Using Nonlinear Least Squares (NLS) Algorithm

In wireless communication systems, the Time Difference of Arrival (TDoA)-based Nonlinear Least Squares (NLS) positioning method represents a widely adopted technique. This approach calculates mobile terminal positions by measuring time differences of signal arrivals from multiple base stations. The NLS algorithm effectively minimizes positioning errors through iterative optimization, typically implemented using gradient descent or Gauss-Newton methods in MATLAB/Python with functions like lsqnonlin() or scipy.optimize.least_squares().

Beyond TDoA-based methods, alternative techniques include Received Signal Strength Indicator (RSSI) and Angle of Arrival (AoA) approaches. However, TDoA-based positioning demonstrates superior accuracy and broader applicability, making it predominant in practical implementations. The core algorithm involves solving hyperbolic equations through error minimization, where residual functions compute differences between measured and calculated TDoA values. As wireless communication technology advances, TDoA-based methods continue undergoing optimization through machine learning integration and multipath error mitigation techniques, promising enhanced user experiences in location-based services.