In this overview paper, data-driven learning model-based cooperative localization and location data processing are considered, in line with the emerging machine learning and big data methods. We first review (1) state-of-the-art algorithms in the context of federated learning, (2) two widely used learning models, namely the deep neural network model and the Gaussian process model, and (3) various distributed model hyper-parameter optimization schemes. Then, we demonstrate various practical use cases that are summarized from a mixture of standard, newly published, and unpublished works, which cover a broad range of location services, including collaborative static localization/fingerprinting, indoor target tracking, outdoor navigation using low-sampling GPS, and spatio-temporal wireless traffic data modeling and prediction. Experimental results show that near centralized data fitting- and prediction performance can be achieved by a set of collaborative mobile users running distributed algorithms. All the surveyed use cases fall under our newly proposed \textit{Federated Localization (FedLoc)} framework, which targets on collaboratively building accurate location services without sacrificing user privacy, in particular, sensitive information related to their geographical trajectories. Future research directions are also discussed at the end of this paper.

The integration of Distributed Energy Resources (DERs) into distribution systems greatly increases the system complexity and introduces two-way power flow. Conventional protection schemes are based upon local measurements and simple linear system models, and are thus not capable of handling the new complexity and power flow patterns in systems with high DER penetration. In this paper, we propose a data-driven protection framework to address the challenges introduced by DERs. Firstly, considering the limited available data under fault conditions, we adopt the Support Vector Data Description (SVDD) method, a commonly used one-class classifier, for distribution system fault detection, which only requires the normal data for its training process. Secondly, incremental learning is incorporated into the proposed SVDD-based protection framework to accommodate variations of the integration level of DERs in distribution systems over time. In particular, the artificial uniform-hyperspherical data generation model is incorporated into the incremental SVDD to boost the training speed. Finally, we validate the proposed method under the IEEE 123-node test feeder. Simulation results demonstrate that our proposed SVDD-based fault detection framework significantly improves the robustness and resilience against DERs in comparison with conventional protection systems. Meanwhile, the proposed online updating model outperforms the existing incremental SVDD models in terms of successful training speed.

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational inference approaches, particularly under the more realistic non-mean-field (NMF) assumption, including extensive training effort, compromised inference accuracy, and infeasibility for online applications, among others. In this paper, we tackle these challenges by incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the NMF variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO). Moreover, owing to the streamlined parameterization via the EnKF, the new GPSSM model can be easily accommodated in online learning applications. We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting. We also provide detailed analysis and fresh insights for the proposed algorithms. Comprehensive evaluation across diverse real and synthetic datasets corroborates the superior learning and inference performance of our EnKF-aided variational inference algorithms compared to existing methods.

The integration of Distributed Energy Resources (DERs) introduces a non-conventional two-way power flow which cannot be captured well by traditional model-based techniques. This brings an unprecedented challenge in terms of the accurate localization of faults and proper actions of the protection system. In this paper, we propose a data-driven fault localization strategy based on multi-level system regionalization and the quantification of fault detection results in all subsystems/subregions. This strategy relies on the tree segmentation criterion to divide the entire system under study into several subregions, and then combines Support Vector Data Description (SVDD) and Kernel Density Estimation (KDE) to find the confidence level of fault detection in each subregion in terms of their corresponding p-values. By comparing the p-values, one can accurately localize the faults. Experiments demonstrate that the proposed data-driven fault localization can greatly improve the accuracy of fault localization for distribution systems with high DER penetration.

Gaussian process state-space models (GPSSMs) offer a principled framework for learning and inference in nonlinear dynamical systems with uncertainty quantification. However, existing GPSSMs are limited by the use of multiple independent stationary Gaussian processes (GPs), leading to prohibitive computational and parametric complexity in high-dimensional settings and restricted modeling capacity for nonstationary dynamics. To address these challenges, we propose an efficient transformed Gaussian process state-space model (ETG-PSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems. Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive non-stationary implicit process prior that can capture complex transition dynamics while significantly reducing model complexity. For the inference of the implicit process, we develop a variational inference algorithm that jointly approximates the posterior over the underlying GP and the neural network parameters defining the normalizing flows. To avoid explicit variational parameterization of the latent states, we further incorporate the ensemble Kalman filter (EnKF) into the variational framework, enabling accurate and efficient state estimation. Extensive empirical evaluations on synthetic and real-world datasets demonstrate the superior performance of our ETGPSSM in system dynamics learning, high-dimensional state estimation, and time-series forecasting, outperforming existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyperparameter optimization. This article presents a novel GP linear multiple kernel (LMK) and a generic sparsity-aware distributed learning framework to optimize the hyperparameters. The newly proposed grid spectral mixture product (GSMP) kernel is tailored for multidimensional data, effectively reducing the number of hyperparameters while maintaining good approximation capability. We further demonstrate that the associated hyperparameter optimization of this kernel yields sparse solutions. To exploit the inherent sparsity of the solutions, we introduce the sparse linear multiple kernel learning (SLIM-KL) framework. The framework incorporates a quantized alternating direction method of multipliers (ADMMs) scheme for collaborative learning among multiple agents, where the local optimization problem is solved using a distributed successive convex approximation (DSCA) algorithm. SLIM-KL effectively manages large-scale hyperparameter optimization for the proposed kernel, simultaneously ensuring data privacy and minimizing communication costs. The theoretical analysis establishes convergence guarantees for the learning framework, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our proposed methods.