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.

We implement a wireless indoor tracking system based on the variational Gaussian process state-space model (GPSSM) with smartphone-collected WiFi received signal strength and inertial measurement unit readings. We adapt the existing variational GPSSM framework to wireless tracking scenarios, and provide a practical learning procedure for the variational GPSSM. The proposed system explores both the expressive power of the non-parametric Gaussian process model and its natural mechanism for integrating the state-of-the-art tracking techniques designed upon state-space model. Experimental results obtained from a real office environment validate the outstanding performance of the variational GPSSM in comparison with the traditional parametric state-space model in terms of tracking accuracy.

We propose a modified spectral mixture (SM) kernel that serves as a universal stationary kernel for temporal Gaussian process regression (GPR). The kernel is named grid spectral mixture (GSM) kernel as we fix the frequency and variance parameters in the original SM kernel to a set of pre-selected grid points. The hyper-parameters are the non-negative weights of all sub-kernel functions and the resulting optimization task falls under the difference-of-convex programming. Due to the nice structure of the optimization problem, the hyper-parameters are solved by an efficient majorization-minimization method instead of the gradient descent methods. It turns out that the solution is sparse, which provides us with a principled guideline to identify the important frequency components of the data. Experimental results based on various classic time series data sets corroborate that the proposed GPR with GSM kernel significantly outperforms the GPR with SM kernel in terms of both the mean-squared-error (MSE) and the stability of the optimization algorithm.