Extended Kalman Filter Positioning Algorithm for TDOA-AOA Localization

In navigation and positioning systems, researchers and engineers have developed diverse algorithms to precisely determine object locations. The TDOA-AOA (Time Difference of Arrival - Angle of Arrival) positioning algorithm utilizes hybrid measurements combining signal time differences and incident angles to estimate receiver positions. Implementation typically involves matrix operations for solving hyperbolic equations from TDOA data and trigonometric calculations for AOA triangulation, often coded in MATLAB or Python using optimization libraries like SciPy.

To overcome accuracy limitations in noisy environments, researchers have integrated Extended Kalman Filter (EKF) techniques with the TDOA-AOA framework. The EKF algorithm operates recursively by linearizing nonlinear measurement models through Jacobian matrix calculations at each time step. Key implementation steps include: 1) State vector initialization containing position and velocity components, 2) Prediction phase using system dynamics models, 3) Update phase incorporating TDOA/AOA measurements with covariance matrices. The fusion algorithm significantly improves tracking robustness for moving targets by handling non-Gaussian noise and system nonlinearities.

This enhanced TDOA-AOA-EKF solution proves particularly valuable for precision indoor positioning in GPS-denied environments like warehouses and hospitals. The algorithm's C++/Python implementation typically features modular design with separate classes for sensor data preprocessing, Kalman filter iteration, and position refinement, achieving sub-meter accuracy through adaptive noise covariance tuning.