As machine learning (ML) techniques gain prominence in power system research, validating these methods' effectiveness under real-world conditions requires real-time hardware-in-the-loop (HIL) simulations. HIL simulation platforms enable the integration of computational models with physical devices, allowing rigorous testing across diverse scenarios critical to system resilience and reliability. In this study, we develop a SafePowerGraph-HIL framework that utilizes HIL simulations on the IEEE 9-bus system, modeled in Hypersim, to generate high-fidelity data, which is then transmitted in real-time via SCADA to an AWS cloud database before being input into a Heterogeneous Graph Neural Network (HGNN) model designed for power system state estimation and dynamic analysis. By leveraging Hypersim's capabilities, we simulate complex grid interactions, providing a robust dataset that captures critical parameters for HGNN training. The trained HGNN is subsequently validated using newly generated data under varied system conditions, demonstrating accuracy and robustness in predicting power system states. The results underscore the potential of integrating HIL with advanced neural network architectures to enhance the real-time operational capabilities of power systems. This approach represents a significant advancement toward the development of intelligent, adaptive control strategies that support the robustness and resilience of evolving power grids.
This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state, whose dynamics is linear and stable. The observer's state is then mapped back to the original system coordinates via the inverse map to obtain the state estimate. However, finding this transformation and its inverse is quite challenging. We propose to sequentially approximate these maps by neural networks that are trained using physics-informed learning. We generate synthetic data for training by numerically solving the system and observer dynamics. Theoretical guarantees for the robustness of state estimation against approximation error and system uncertainties are provided. Additionally, a systematic method for optimizing observer performance through parameter selection is presented. The effectiveness of the proposed approach is demonstrated through numerical simulations on benchmark examples and its application to sensor fault detection and isolation in a network of Kuramoto oscillators using learned KKL observers.
This paper deals with the state estimation of stochastic systems and examines the possible employment of tensor decompositions in grid-based filtering routines, in particular, the tensor-train decomposition. The aim is to show that these techniques can lead to a massive reduction in both the computational and storage complexity of grid-based filtering algorithms without considerable tradeoffs in accuracy. This claim is supported by an algorithm descriptions and numerical illustrations.
We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.
Extremum-seeking control (ESC) is widely used to optimize performance when the system dynamics are uncertain. However, sensitivity to sensor noise is an important issue in ESC implementation due to the use of high-pass filters or gradient estimators. To reduce the sensitivity of ESC to noise, this paper investigates the use of adaptive input and state estimation (AISE) for numerical differentiation. In particular, this paper develops extremum-seeking control with adaptive input and state estimation (ESC/AISE), where the high-pass filter of ESC is replaced by AISE to improve performance under sensor noise. The effectiveness of ESC/AISE is illustrated via numerical examples.
Trajectory prediction is a crucial element of guidance, navigation, and control systems. This paper presents two novel trajectory-prediction methods based on real-time position measurements and adaptive input and state estimation (AISE). The first method, called AISE/va, uses position measurements to estimate the target velocity and acceleration. The second method, called AISE/FS, models the target trajectory as a 3D curve using the Frenet-Serret formulas, which require estimates of velocity, acceleration, and jerk. To estimate velocity, acceleration, and jerk in real time, AISE computes first, second, and third derivatives of the position measurements. AISE does not rely on assumptions about the target maneuver, measurement noise, or disturbances. For trajectory prediction, both methods use measurements of the target position and estimates of its derivatives to extrapolate from the current position. The performance of AISE/va and AISE/FS is compared numerically with the $\alpha$-$\beta$-$\gamma$ filter, which shows that AISE/FS provides more accurate trajectory prediction than AISE/va and traditional methods, especially for complex target maneuvers.
The goal of target tracking is to estimate target position, velocity, and acceleration in real time using position data. This paper introduces a novel target-tracking technique that uses adaptive input and state estimation (AISE) for real-time numerical differentiation to estimate velocity, acceleration, and jerk from position data. These estimates are used to model the target motion within the Frenet-Serret (FS) frame. By representing the model in SE(3), the position and velocity are estimated using the invariant extended Kalman filter (IEKF). The proposed method, called FS-IEKF-AISE, is illustrated by numerical examples and compared to prior techniques.
Multi-agent systems are increasingly applied in space missions, including distributed space systems, resilient constellations, and autonomous rendezvous and docking operations. A critical emerging application is collaborative spacecraft servicing, which encompasses on-orbit maintenance, space debris removal, and swarm-based satellite repositioning. These missions involve servicing spacecraft interacting with malfunctioning or defunct spacecraft under challenging conditions, such as limited state information, measurement inaccuracies, and erratic target behaviors. Existing approaches often rely on assumptions of full state knowledge or single-integrator dynamics, which are impractical for real-world applications involving second-order spacecraft dynamics. This work addresses these challenges by developing a distributed state estimation and tracking framework that requires only relative position measurements and operates under partial state information. A novel $\rho$-filter is introduced to reconstruct unknown states using locally available information, and a Lyapunov-based deep neural network adaptive controller is developed that adaptively compensates for uncertainties stemming from unknown spacecraft dynamics. To ensure the collaborative spacecraft regulation problem is well-posed, a trackability condition is defined. A Lyapunov-based stability analysis is provided to ensure exponential convergence of errors in state estimation and spacecraft regulation to a neighborhood of the origin under the trackability condition. The developed method eliminates the need for expensive velocity sensors or extensive pre-training, offering a practical and robust solution for spacecraft servicing in complex, dynamic environments.
Recent advancements in LiDAR-Inertial Odometry (LIO) have boosted a large amount of applications. However, traditional LIO systems tend to focus more on localization rather than mapping, with maps consisting mostly of sparse geometric elements, which is not ideal for downstream tasks. Recent emerging neural field technology has great potential in dense mapping, but pure LiDAR mapping is difficult to work on high-dynamic vehicles. To mitigate this challenge, we present a new solution that tightly couples geometric kinematics with neural fields to enhance simultaneous state estimation and dense mapping capabilities. We propose both semi-coupled and tightly coupled Kinematic-Neural LIO (KN-LIO) systems that leverage online SDF decoding and iterated error-state Kalman filtering to fuse laser and inertial data. Our KN-LIO minimizes information loss and improves accuracy in state estimation, while also accommodating asynchronous multi-LiDAR inputs. Evaluations on diverse high-dynamic datasets demonstrate that our KN-LIO achieves performance on par with or superior to existing state-of-the-art solutions in pose estimation and offers improved dense mapping accuracy over pure LiDAR-based methods. The relevant code and datasets will be made available at https://**.
Fast and robust dynamic state estimation (DSE) is essential for accurately capturing the internal dynamic processes of power systems, and it serves as the foundation for reliably implementing real-time dynamic modeling, monitoring, and control applications. Nonetheless, on one hand, traditional DSE methods based on Kalman filtering or particle filtering have high accuracy requirements for system parameters, control inputs, phasor measurement unit (PMU) data, and centralized DSE communication. Consequently, these methods often face accuracy bottlenecks when dealing with structural or system process errors, unknown control vectors, PMU anomalies, and communication contingencies. On the other hand, deep learning-aided DSE, while parameter-free, often suffers from generalization issues under unforeseen operating conditions. To address these challenges, this paper proposes an effective approach that leverages deep generative models from AI-generated content (AIGC) to assist DSE. The proposed approach employs an encoder-decoder architecture to estimate unknown control input variables, a robust encoder to mitigate the impact of bad PMU data, and latent diffusion model to address communication issues in centralized DSE. Additionally, a lightweight adaptor is designed to quickly adjust the latent vector distribution. Extensive experimental results on the IEEE 39-bus system and the NPCC 140-bus system demonstrate the effectiveness and superiority of the proposed method in addressing DSE modeling imperfection, measurement uncertainties, communication contingencies, and unknown distribution challenges, while also proving its ability to reduce data storage and communication resource requirements.
We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding transfer operator, and develop a spectral method to learn this representation based on the theory of stochastic realization. The embedding may be learned simultaneously using reproducing kernels, for example, constructed with feed-forward neural networks. We also address the generalization of sequential state-estimation (Kalman filtering) in stochastic nonlinear systems, and of operator-based eigen-mode decomposition of dynamics, for the representation. Several examples with synthetic and real-world data are shown to illustrate the empirical characteristics of our methods, and to investigate the performance of our model in sequential state-estimation and mode decomposition.
We introduce Cloth-Splatting, a method for estimating 3D states of cloth from RGB images through a prediction-update framework. Cloth-Splatting leverages an action-conditioned dynamics model for predicting future states and uses 3D Gaussian Splatting to update the predicted states. Our key insight is that coupling a 3D mesh-based representation with Gaussian Splatting allows us to define a differentiable map between the cloth state space and the image space. This enables the use of gradient-based optimization techniques to refine inaccurate state estimates using only RGB supervision. Our experiments demonstrate that Cloth-Splatting not only improves state estimation accuracy over current baselines but also reduces convergence time.
Modern on-road navigation systems heavily depend on integrating speed measurements with inertial navigation systems (INS) and global navigation satellite systems (GNSS). Telemetry-based applications typically source speed data from the On-Board Diagnostic II (OBD-II) system. However, the method of deriving speed, as well as the types of sensors used to measure wheel speed, differs across vehicles. These differences result in varying error characteristics that must be accounted for in navigation and autonomy applications. This paper addresses this gap by examining the diverse speed-sensing technologies employed in standard automotive systems and alternative techniques used in advanced systems designed for higher levels of autonomy, such as Advanced Driver Assistance Systems (ADAS), Autonomous Driving (AD), or surveying applications. We propose a method to identify the type of speed sensor in a vehicle and present strategies for accurately modeling its error characteristics. To validate our approach, we collected and analyzed data from three long real road trajectories conducted in urban environments in Toronto and Kingston, Ontario, Canada. The results underscore the critical role of integrating multiple sensor modalities to achieve more accurate speed estimation, thus improving automotive navigation state estimation, particularly in GNSS-denied environments.
The problem of state estimation has a long history with many successful algorithms that allow analytical derivation or approximation of posterior filtering distribution given the noisy observations. This report tries to conclude previous works to resolve the problem of latent state estimation given image-based observations and also suggests a new solution to this problem.
Solar PV and battery storage systems have become integral to modern power grids. Therefore, bulk grid models in real-time operation must include their physical behavior accurately for analysis and optimization. AC state estimation is critical to building real-time bulk power systems models. However, current ACSE techniques do not include detailed physics and measurements for battery and PV systems. This results in sub-optimal estimation results and subsequent less accurate bulk grid models for real-time operation. To address these challenges, we formulate a circuit-theoretic AC state estimator with accurate PV and battery systems physics and corresponding measurements. First, we propose an aggregated equivalent circuit model of the solar PV, battery, and traditional grid components. Next, we add measurements from PV and battery systems to the traditional measurement set to facilitate accurate estimation of the overall grid model. Finally, we develop a circuit-theoretic joint parameter-state estimation algorithm that can accurately estimate grid, PV, and battery system states and is robust against erroneous parameters. To demonstrate the efficacy of the proposed framework, we estimate the states of 10k node transmission networks with hundreds of battery+PV-tied systems. We compare the accuracy against the estimation of stand-alone grid, battery, and PV systems.
Leakage in water systems results in significant daily water losses, degrading service quality, increasing costs, and aggravating environmental problems. Most leak localization methods rely solely on pressure data, missing valuable information from other sensor types. This article proposes a hydraulic state estimation methodology based on a dual Unscented Kalman Filter (UKF) approach, which enhances the estimation of both nodal hydraulic heads, critical in localization tasks, and pipe flows, useful for operational purposes. The approach enables the fusion of different sensor types, such as pressure, flow and demand meters. The strategy is evaluated in well-known open source case studies, namely Modena and L-TOWN, showing improvements over other state-of-the-art estimation approaches in terms of interpolation accuracy, as well as more precise leak localization performance in L-TOWN.
This paper deals with the state estimation of stochastic models with continuous dynamics. The aim is to incorporate spectral differentiation methods into the solution to the Fokker-Planck equation in grid-based state estimation routine, while taking into account the specifics of the field, such as probability density function (PDF) features, moving grid, zero boundary conditions, etc. The spectral methods, in general, achieve very fast convergence rate of O(c^N )(O < c < 1) for analytical functions such as the probability density function, where N is the number of grid points. This is significantly better than the standard finite difference method (or midpoint rule used in discrete estimation) typically used in grid-based filter design with convergence rate O( 1 / N^2 ). As consequence, the proposed spectral method based filter provides better state estimation accuracy with lower number of grid points, and thus, with lower computational complexity.
This paper deals with state estimation of nonlinear stochastic dynamic models. In particular, the stochastic integration rule, which provides asymptotically unbiased estimates of the moments of nonlinearly transformed Gaussian random variables, is reviewed together with the recently introduced stochastic integration filter (SIF). Using SIF, the respective multi-step prediction and smoothing algorithms are developed in full and efficient square-root form. The stochastic-integration-rule-based algorithms are implemented in Python (within the Stone Soup framework) and in MATLAB and are numerically evaluated and compared with the well-known unscented and extended Kalman filters using the Stone Soup defined tracking scenario.
This paper introduces a novel approach to detect and address faulty or corrupted external sensors in the context of inertial navigation by leveraging a switching Kalman Filter combined with parameter augmentation. Instead of discarding the corrupted data, the proposed method retains and processes it, running multiple observation models simultaneously and evaluating their likelihoods to accurately identify the true state of the system. We demonstrate the effectiveness of this approach to both identify the moment that a sensor becomes faulty and to correct for the resulting sensor behavior to maintain accurate estimates. We demonstrate our approach on an application of balloon navigation in the atmosphere and shuttle reentry. The results show that our method can accurately recover the true system state even in the presence of significant sensor bias, thereby improving the robustness and reliability of state estimation systems under challenging conditions. We also provide a statistical analysis of problem settings to determine when and where our method is most accurate and where it fails.
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.