Quadratic Equality Constrained Tracking Algorithm Using TDOA measurements

Abstract

Moving target tracking using time difference of arrival measurements has received significant attention in recent years. When the target trajectory satisfies quadratic equality constraints, second-order nonlinear equations can be incorporated in the tracking algorithm to improve the accuracy. Existing methods dealing with constraints may suffer from a lack of convergence or large computation, and are often affected by the initial value of the iteration. The proposed algorithm first utilizes standard Kalman filter to update state estimation and then refines it with a maximum likelihood estimator. When solving the constrained maximum likelihood problem, a kind of generalized trust region sub-problem is incorporated to obtain the global optimal solution. Computer simulation results show that the proposed algorithm outperforms the existing methods in tracking accuracy and do not diverge when the initial state is unknown.