In this letter, a received signal strength difference (RSSD) approach is presented to localize a source with unknown transmit power in the presence of sensor position errors. The performance of conventional least squares (LS) algorithms is degraded because they consider measurement errors rather than estimation errors. An algorithm is presented here to overcome this problem. First, a robust minimax mean squared error (MSE) estimator is developed based on the estimation error for bounded location estimation and sensor position errors to minimize the worst case sum of the variance and squared norm of the bias. This nonlinear problem is solved by transforming the nonconvex objective function into a convex optimization problem using the S-procedure, relaxation, and semidefinite programming. This problem is extended to the unknown path loss exponent case. Necessary and sufficient conditions are given for convergence of the proposed RSSD convex relaxation of MSE semidefinite programming (RCRM-SDP) approach. Simulation results are presented which confirm the robustness of this method for sufficiently large signal to noise ratios (SNRs).

中文翻译：

---

改进的基于 RSSD 的源定位，具有未知的传感器位置误差


在这封信中，提出了一种接收信号强度差（RSSD）方法，用于在存在传感器位置误差的情况下定位具有未知发射功率的源。传统最小二乘 (LS) 算法的性能会下降，因为它们考虑的是测量误差而不是估计误差。这里提出了一种算法来克服这个问题。首先，基于有界位置估计的估计误差和传感器位置误差开发了鲁棒的最小最大均方误差（MSE）估计器，以最小化方差和偏差平方范数的最坏情况和。该非线性问题是通过使用 S 过程、松弛和半定规划将非凸目标函数转换为凸优化问题来解决的。这个问题被扩展到未知路径损耗指数的情况。给出了所提出的 RSSD 凸松弛 MSE 半定规划 (RCRM-SDP) 方法收敛的充分必要条件。仿真结果证实了该方法对于足够大的信噪比 (SNR) 的鲁棒性。