High-precision hyperboloid location method using passive time-difference-of-arrival measurements

The authors consider the minimum square error formulation of the three-dimensional target location problem and provide an efficient solution for this minimisation problem. Two target location scenarios are investigated and it has been found that the convexity of the nonlinear least squares problem depends on the geometric relationship between the receivers and the target. The authors discover that the non-linear least squares problem is not always non-convex. The corresponding non-linear least squares problem is non-convex and sensitive to initial value only when the three time-difference-of-arrival location hyperboloids form two intersections. The convergence of the iterative method is proved when the objective function is convex in the location region. Simulation results demonstrate the effectiveness of the proposed method both in non-convex and convex scenarios, when a proper relative simple initial value is given.