An Asymptotically Efficient Hyperbolic Localization of a Moving Target by a Distributed Radar Network With Sensors Uncertainties

This article addresses the moving target localization in a distributed radar network (DRN) with sensor uncertainties. It is assumed that the positions and velocities of the sensors are independent normal random variables with known means and variances. Assuming reference sensors on both sides of transmitters (Txs) and receivers (Rxs), we convert the elliptical localization to a hyperbolic localization problem. We introduce nuisance variables (NVs), remove dependent hyperbolic equations, establish a pseudo-linear system, and solve it by a two-stage weighted least squares (TSWLSs) estimator. Subsequently, we propose two alternative estimators to reduce the computational complexity (CC) while preserving the accuracy by selecting hyperbolas either at Txs or at Rxs. Moreover, we investigate the impact of the number and type of NVs on localization performance. Numerical simulations confirm our theoretical results and indicate that utilizing all NVs and applying averaging techniques to eliminate dependent hyperbolas produce the most accurate estimate. In addition, our proposed method has several advantages over state-of-the-art competitive methods: 1) its performance is maintained and remains closer to the Cramér–Rao lower bound (CRLB) in different random configurations of sensors and relative motions of the sensors and the target; 2) it is asymptotically efficient, achieving the CRLB up to relatively high noise levels (around 32 dB) and uncertainty levels (around 20 dB); 3) it has similar order of complexity as other methods and performs satisfactorily under practical real-time scenarios; and 4) it involves more independent equations and leads to a significant improvement in accuracy, particularly when the number of Txs or Rxs dominates the other.