State Estimation from Range-Only Measurements

In this paper, a method of state estimation from range-only measurements is presented. This makes it possible to use low-cost sensor networks which cannot provide accurate azimuth information to replace large antennas for target tracking and other applications. Firstly, the time evolving equation of target range is formulated. The sub-state vector is constructed by range, Doppler and the derivative of the product of range and Doppler with respect to time. The sub-state equation corresponding to the nearly constant velocity (NCV) motion is derived by explicit substitutions according to the relationship between sub-state and Cartesian states. Then the unscented Kalman filter (UKF) is employed to extract the sub-state from range-only measurements. The filter initialization is derived by two-point differencing method. At last, the performance of the proposed method is compared against the posterior Cramer-Rao Lower Bound (PCRLB) for filtering in sub-state space and the existing method with approximate model in the numerical simulations. The results demonstrate the effectiveness of the proposed method.