Received signal strength (RSS) measurements can be converted to the distance estimates between the emission source and the sensors to construct a system of linear equations, thereby allowing for the use of the weighted linear least squares (WLLS) estimators for location estimation. However, estimating the squared distances from the RSS measurements governed by the log-normal shadowing effect presents a major challenge in such approaches. In this paper, we propose a linear minimum mean square error (LMMSE) estimator of the squared distance between the emission source and the sensor first. Then a LMMSE-aided WLLS (LMMSE-WLLS) location estimator and its unbiased counterpart are presented for source localization. Furthermore, their estimation performance are analyzed in terms of mean square error (MSE) and covariance. It is found that the proposed LMMSE-aided WLLS location estimators have better estimation performance than existing WLLS estimators. Numerical examples also demonstrate the performance superiority of the proposed location estimators for source localization.

Deep state-space models (DSSMs) have gained popularity in recent years due to their potent modeling capacity for dynamic systems. However, existing DSSM works are limited to single-task modeling, which requires retraining with historical task data upon revisiting a forepassed task. To address this limitation, we propose continual learning DSSMs (CLDSSMs), which are capable of adapting to evolving tasks without catastrophic forgetting. Our proposed CLDSSMs integrate mainstream regularization-based continual learning (CL) methods, ensuring efficient updates with constant computational and memory costs for modeling multiple dynamic systems. We also conduct a comprehensive cost analysis of each CL method applied to the respective CLDSSMs, and demonstrate the efficacy of CLDSSMs through experiments on real-world datasets. The results corroborate that while various competing CL methods exhibit different merits, the proposed CLDSSMs consistently outperform traditional DSSMs in terms of effectively addressing catastrophic forgetting, enabling swift and accurate parameter transfer to new tasks.