Closed form Solution of Moving Source Localization Using TDOA and FDOA Measurements Under Sensor Location Errors

The moving source localization is very sensitive to the knowledge of sensor locations. In this paper, we propose a two-stage closed-form method for locating a moving source by using Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) measurements in the presence of random errors in sensor locations. In the first stage, we establish a series of pseudo-linear equations by introducing the auxiliary variables and obtain an initial location estimation based on the bias reduced criteria and the Lagrange multiplier theory. In the second stage,we propose a modified weighted least squares method to obtain the final estimation by exploring the relationship between the auxiliary variables and the moving source location and velocity. The proposed method is in closed form and therefore computationally efficient as well as free from the divergence problem unlike iterative techniques. Simulations show the better performance of the proposed method.