Two New Closed Form Approximate Maximum Likelihood Location Methods Based on Time Difference of Arrival Measurements

摘要

In this paper, we propose two new closed form approximate maximum likelihood location methods via time difference of arrival (TDOA) measurements to determine the location of a target. For both two methods, an initial estimation is acquired by least square method in the first step. Then, supposing that the statistical structure of measurement noise are already known, the maximum likelihood function is derived. At last, for method one, we use first order Taylor expand at the initial point to approximate the residual error for nonlinear measurement equation and substitute it into the maximum likelihood function. While for method two, we use second order Taylor expand at the initial point to approximate the maximum likelihood function. At last, we derive the closed-form solution to both of the methods respectively. The computational complexity of our methods and AML method is derived and we analyze the performance of our two methods. The simulation results show that our methods are more accurate because our methods based on maximum likelihood function and have low computational complexity because we iterate only once.