The Space Domain Awareness (SDA) community routinely tracks satellites in orbit by fitting an orbital state to observations made by the Space Surveillance Network (SSN). In order to fit such orbits, an accurate model of the forces that are acting on the satellite is required. Over the past several decades, high-quality, physics-based models have been developed for satellite state estimation and propagation. These models are exceedingly good at estimating and propagating orbital states for non-maneuvering satellites; however, there are several classes of anomalous accelerations that a satellite might experience which are not well-modeled, such as satellites that use low-thrust electric propulsion to modify their orbit. Physics-Informed Neural Networks (PINNs) are a valuable tool for these classes of satellites as they combine physics models with Deep Neural Networks (DNNs), which are highly expressive and versatile function approximators. By combining a physics model with a DNN, the machine learning model need not learn astrodynamics, which results in more efficient and effective utilization of machine learning resources. This paper details the application of PINNs to estimate the orbital state and a continuous, low-amplitude anomalous acceleration profile for satellites. The PINN is trained to learn the unknown acceleration by minimizing the mean square error of observations. We evaluate the performance of pure physics models with PINNs in terms of their observation residuals and their propagation accuracy beyond the fit span of the observations. For a two-day simulation of a GEO satellite using an unmodeled acceleration profile on the order of $10^{-8} \text{ km/s}^2$, the PINN outperformed the best-fit physics model by orders of magnitude for both observation residuals (123 arcsec vs 1.00 arcsec) as well as propagation accuracy (3860 km vs 164 km after five days).
Water distribution systems (WDS) are an integral part of critical infrastructure which is pivotal to urban development. As 70% of the world's population will likely live in urban environments in 2050, efficient simulation and planning tools for WDS play a crucial role in reaching UN's sustainable developmental goal (SDG) 6 - "Clean water and sanitation for all". In this realm, we propose a novel and efficient machine learning emulator, more precisely, a physics-informed deep learning (DL) model, for hydraulic state estimation in WDS. Using a recursive approach, our model only needs a few graph convolutional neural network (GCN) layers and employs an innovative algorithm based on message passing. Unlike conventional machine learning tasks, the model uses hydraulic principles to infer two additional hydraulic state features in the process of reconstructing the available ground truth feature in an unsupervised manner. To the best of our knowledge, this is the first DL approach to emulate the popular hydraulic simulator EPANET, utilizing no additional information. Like most DL models and unlike the hydraulic simulator, our model demonstrates vastly faster emulation times that do not increase drastically with the size of the WDS. Moreover, we achieve high accuracy on the ground truth and very similar results compared to the hydraulic simulator as demonstrated through experiments on five real-world WDS datasets.
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural phenomena makes it extremely challenging to develop full-order models (FOMs) and apply them to studying many quantities of interest. In contrast, appropriate reduced-order models (ROMs) are favored due to their high computational efficiency and ability to describe the key dynamics and statistical characteristics of natural phenomena. Taking the viscous Burgers equation as an example, this paper constructs a Convolutional Autoencoder-Reservoir Computing-Normalizing Flow algorithm framework, where the Convolutional Autoencoder is used to construct latent space representations, and the Reservoir Computing-Normalizing Flow framework is used to characterize the evolution of latent state variables. In this way, a data-driven stochastic parameter reduced-order model is constructed to describe the complex system and its dynamic behavior.
This paper investigates the impact of observations on atmospheric state estimation in weather forecasting systems using graph neural networks (GNNs) and explainability methods. We integrate observation and Numerical Weather Prediction (NWP) points into a meteorological graph, extracting $k$-hop subgraphs centered on NWP points. Self-supervised GNNs are employed to estimate the atmospheric state by aggregating data within these $k$-hop radii. The study applies gradient-based explainability methods to quantify the significance of different observations in the estimation process. Evaluated with data from 11 satellite and land-based observations, the results highlight the effectiveness of visualizing the importance of observation types, enhancing the understanding and optimization of observational data in weather forecasting.
Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian distributions defined at different reference points on the group. In this paper we approximate distributions at different points in the group in a single set of exponential coordinates and then use classical Gaussian fusion to obtain the fused posteriori in those coordinates. We consider several approximations including the exact Jacobian of the change of coordinate map, first and second order Taylor's expansions of the Jacobian, and parallel transport with and without curvature correction associated with the underlying geometry of the Lie group. Preliminary results on SO(3) demonstrate that a novel approximation using parallel transport with curvature correction achieves similar accuracy to the state-of-the-art optimisation based algorithms at a fraction of the computational cost.
This paper considers the state estimation problem for discrete-time linear systems under event-triggered scheme. In order to improve performance, a novel event-triggered scheme based on confidence level is proposed using the chi-square distribution and mild regularity assumption. In terms of the novel event-triggered scheme, a minimum mean squared error (MMSE) state estimator is proposed using some results presented in this paper. Two algorithms for communication rate estimation of the proposed MMSE state estimator are developed where the first algorithm is based on information with one-step delay, and the second algorithm is based on information with two-step delay. The performance and effectiveness of the proposed MMSE state estimator and the two communication rate estimation algorithms are illustrated using a target tracking scenario.
Although an ever-growing number of applications employ deep learning based systems for prediction, decision-making, or state estimation, almost no certification processes have been established that would allow such systems to be deployed in safety-critical applications. In this work we consider real-world problems arising in aviation and other safety-critical areas, and investigate their requirements for a certified model. To this end, we investigate methodologies from the machine learning research community aimed towards verifying robustness and reliability of deep learning systems, and evaluate these methodologies with regard to their applicability to real-world problems. Then, we establish a new framework towards deep learning certification based on (i) inherently safe design, and (ii) run-time error detection. Using a concrete use case from aviation, we show how deep learning models can recover disentangled variables through the use of weakly-supervised representation learning. We argue that such a system design is inherently less prone to common model failures, and can be verified to encode underlying mechanisms governing the data. Then, we investigate four techniques related to the run-time safety of a model, namely (i) uncertainty quantification, (ii) out-of-distribution detection, (iii) feature collapse, and (iv) adversarial attacks. We evaluate each for their applicability and formulate a set of desiderata that a certified model should fulfill. Finally, we propose a novel model structure that exhibits all desired properties discussed in this work, and is able to make regression and uncertainty predictions, as well as detect out-of-distribution inputs, while requiring no regression labels to train. We conclude with a discussion of the current state and expected future progress of deep learning certification, and its industrial and social implications.
This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally reaches the Dirac delta distribution with minimal effort. The Wasserstein metric is used to quantify the effort of transporting from one distribution to another. We hypothesize that minimizing the Wasserstein distance between the posterior error and the Dirac delta distribution results in optimal information fusion and posterior state uncertainty. Framework validation is demonstrated by the successful recovery of the classical Kalman filter for linear systems with Gaussian uncertainties. Notably, the proposed Wasserstein filter does not rely on particle representation of uncertainty. Furthermore, the classical result for the Gaussian Sum Filter (GSF) is retrieved from the Wasserstein framework. This approach analytically exhibits the suboptimality of GSF and enables the use of nonlinear optimization techniques to enhance the accuracy of the Gaussian sum estimator.
As networked control systems continue to evolve, ensuring the privacy of sensitive data becomes an increasingly pressing concern, especially in situations where the controller is physically separated from the plant. In this paper, we propose a secure control scheme for computing linear quadratic control in a networked control system utilizing two networked controllers, a privacy encoder and a control restorer. Specifically, the encoder generates two state signals blurred with random noise and sends them to the controllers, while the restorer reconstructs the correct control signal. The proposed design effectively preserves the privacy of the control system's state without sacrificing the control performance. We theoretically quantify the privacy-preserving performance in terms of the state estimation error of the controllers and the disclosure probability. Moreover, we extend the proposed privacy-preserving scheme and evaluation method to cases where collusion between two controllers occurs. Finally, we verify the validity of our proposed scheme through simulations.
Self-balancing exoskeletons are a key enabling technology for individuals with mobility impairments. While the current challenges focus on human-compliant hardware and control, unlocking their use for daily activities requires a scene perception system. In this work, we present Exosense, a vision-centric scene understanding system for self-balancing exoskeletons. We introduce a multi-sensor visual-inertial mapping device as well as a navigation stack for state estimation, terrain mapping and long-term operation. We tested Exosense attached to both a human leg and Wandercraft's Personal Exoskeleton in real-world indoor scenarios. This enabled us to test the system during typical periodic walking gaits, as well as future uses in multi-story environments. We demonstrate that Exosense can achieve an odometry drift of about 4 cm per meter traveled, and construct terrain maps under 1 cm average reconstruction error. It can also work in a visual localization mode in a previously mapped environment, providing a step towards long-term operation of exoskeletons.
Vision-language navigation (VLN) requires an agent to navigate through an 3D environment based on visual observations and natural language instructions. It is clear that the pivotal factor for successful navigation lies in the comprehensive scene understanding. Previous VLN agents employ monocular frameworks to extract 2D features of perspective views directly. Though straightforward, they struggle for capturing 3D geometry and semantics, leading to a partial and incomplete environment representation. To achieve a comprehensive 3D representation with fine-grained details, we introduce a Volumetric Environment Representation (VER), which voxelizes the physical world into structured 3D cells. For each cell, VER aggregates multi-view 2D features into such a unified 3D space via 2D-3D sampling. Through coarse-to-fine feature extraction and multi-task learning for VER, our agent predicts 3D occupancy, 3D room layout, and 3D bounding boxes jointly. Based on online collected VERs, our agent performs volume state estimation and builds episodic memory for predicting the next step. Experimental results show our environment representations from multi-task learning lead to evident performance gains on VLN. Our model achieves state-of-the-art performance across VLN benchmarks (R2R, REVERIE, and R4R).
The expanding role of Artificial Intelligence (AI) in diverse engineering domains highlights the challenges associated with deploying AI models in new operational environments, involving substantial investments in data collection and model training. Rapid application of AI necessitates evaluating the feasibility of utilizing pre-trained models in unobserved operational settings with minimal or no additional data. However, interpreting the opaque nature of AI's black-box models remains a persistent challenge. Addressing this issue, this paper proposes a science-based certification methodology to assess the viability of employing pre-trained data-driven models in untrained operational environments. The methodology advocates a profound integration of domain knowledge, leveraging theoretical and analytical models from physics and related disciplines, with data-driven AI models. This novel approach introduces tools to facilitate the development of secure engineering systems, providing decision-makers with confidence in the trustworthiness and safety of AI-based models across diverse environments characterized by limited training data and dynamic, uncertain conditions. The paper demonstrates the efficacy of this methodology in real-world safety-critical scenarios, particularly in the context of traffic state estimation. Through simulation results, the study illustrates how the proposed methodology efficiently quantifies physical inconsistencies exhibited by pre-trained AI models. By utilizing analytical models, the methodology offers a means to gauge the applicability of pre-trained AI models in new operational environments. This research contributes to advancing the understanding and deployment of AI models, offering a robust certification framework that enhances confidence in their reliability and safety across a spectrum of operational conditions.
This paper addresses the problem of simultaneous estimation of the position, linear velocity and orientation of a rigid body using single bearing measurements. We introduce a Riccati observer-based estimator that fuses measurements from a 3-axis accelerometer, a 3-axis gyroscope, a single body-frame vector observation (e.g., magnetometer), and a single bearing-to-landmark measurement to obtain the full vehicle's state (position, velocity, orientation). The proposed observer guarantees global exponential convergence under some persistency of excitation (PE) condition on the vehicle's motion. Simulation results are presented to show the effectiveness of the proposed approach.
Manipulating deformable objects remains a challenge within robotics due to the difficulties of state estimation, long-horizon planning, and predicting how the object will deform given an interaction. These challenges are the most pronounced with 3D deformable objects. We propose SculptDiff, a goal-conditioned diffusion-based imitation learning framework that works with point cloud state observations to directly learn clay sculpting policies for a variety of target shapes. To the best of our knowledge this is the first real-world method that successfully learns manipulation policies for 3D deformable objects. For sculpting videos and access to our dataset and hardware CAD models, see the project website: https://sites.google.com/andrew.cmu.edu/imitation-sculpting/home
In this work, we address the problem of sensor selection for state estimation via Kalman filtering. We consider a linear time-invariant (LTI) dynamical system subject to process and measurement noise, where the sensors we use to perform state estimation are randomly drawn according to a sampling with replacement policy. Since our selection of sensors is randomly chosen, the estimation error covariance of the Kalman filter is also a stochastic quantity. Fortunately, concentration inequalities (CIs) for the estimation error covariance allow us to gauge the estimation performance we intend to achieve when our sensors are randomly drawn with replacement. To obtain a non-trivial improvement on existing CIs for the estimation error covariance, we first present novel matrix CIs for a sum of independent and identically-distributed (i.i.d.) and positive semi-definite (p.s.d.) random matrices, whose support is finite. Next, we show that our guarantees generalize an existing matrix CI. Also, we show that our generalized guarantees require significantly fewer number of sampled sensors to be applicable. Lastly, we show through a numerical study that our guarantees significantly outperform existing ones in terms of their ability to bound (in the semi-definite sense) the steady-state estimation error covariance of the Kalman filter.
A low-observable distribution system has insufficient measurements for conventional weighted least square state estimators. Matrix completion state estimators have been suggested, but their computational times could be prohibitive. To resolve this problem, a novel and efficient power-flow-embedded projection conic matrix completion method customized for low-observable distribution systems is proposed in this letter. This method can yield more accurate state estimations (2-fold improvement) in a much shorter time (5% or less) than other methods. Case studies on different-scale systems have demonstrated the efficacy of the proposed method when applied to low-observable distribution system state estimation problems.
As the number of heterogeneous redundant sensors on unmanned aerial vehicle (UAV) increases, onboard sensors require a more rational and efficient credibility evaluation system and a resilient fusion framework to achieve the essence of seamless sensor group switching. A simple and efficient sensor credibility evaluation system is proposed to guide the selection of the optimal multi-source sensor submodel combination, thereby providing key model prior knowledge for multi-source resilient fusion. Furthermore, a multi-model interactive resilient fusion framework based on RIEKF is proposed, utilizing the defined sensor credibility indexes to guide the design of the model transition probability matrix, thereby reducing the sensitivity of submodel weights to fusion stability and solving the problem of the model transition matrix lacking a basis for adjustment. Model weights are updated in real time through credibility prior information and submodel posterior probabilities, thus leveraging the adaptive resilience advantage between models to achieve seamless switching between submodels in complex environments. Experimental results show that the algorithm presented in this paper, without using any sensor fault diagnosis and isolation logic, without setting any complex detection timing and thresholds, demonstrates a resilience advantage, thereby enhancing the adaptability of the state estimation system in complex environments.
Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalizing flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalizing flow-based differentiable particle filters' performance through a series of numerical experiments.
Optimal decision-making for trajectory tracking in partially observable, stochastic environments where the number of active localization updates -- the process by which the agent obtains its true state information from the sensors -- are limited, presents a significant challenge. Traditional methods often struggle to balance resource conservation, accurate state estimation and precise tracking, resulting in suboptimal performance. This problem is particularly pronounced in environments with large action spaces, where the need for frequent, accurate state data is paramount, yet the capacity for active localization updates is restricted by external limitations. This paper introduces ComTraQ-MPC, a novel framework that combines Deep Q-Networks (DQN) and Model Predictive Control (MPC) to optimize trajectory tracking with constrained active localization updates. The meta-trained DQN ensures adaptive active localization scheduling, while the MPC leverages available state information to improve tracking. The central contribution of this work is their reciprocal interaction: DQN's update decisions inform MPC's control strategy, and MPC's outcomes refine DQN's learning, creating a cohesive, adaptive system. Empirical evaluations in simulated and real-world settings demonstrate that ComTraQ-MPC significantly enhances operational efficiency and accuracy, providing a generalizable and approximately optimal solution for trajectory tracking in complex partially observable environments.
Accurate detection and diagnosis of abnormal behaviors such as network attacks from multivariate time series (MTS) are crucial for ensuring the stable and effective operation of industrial cyber-physical systems (CPS). However, existing researches pay little attention to the logical dependencies among system working states, and have difficulties in explaining the evolution mechanisms of abnormal signals. To reveal the spatio-temporal association relationships and evolution mechanisms of the working states of industrial CPS, this paper proposes a fine-grained adaptive anomaly diagnosis method (i.e. MAD-Transformer) to identify and diagnose anomalies in MTS. MAD-Transformer first constructs a temporal state matrix to characterize and estimate the change patterns of the system states in the temporal dimension. Then, to better locate the anomalies, a spatial state matrix is also constructed to capture the inter-sensor state correlation relationships within the system. Subsequently, based on these two types of state matrices, a three-branch structure of series-temporal-spatial attention module is designed to simultaneously capture the series, temporal, and space dependencies among MTS. Afterwards, three associated alignment loss functions and a reconstruction loss are constructed to jointly optimize the model. Finally, anomalies are determined and diagnosed by comparing the residual matrices with the original matrices. We conducted comparative experiments on five publicly datasets spanning three application domains (service monitoring, spatial and earth exploration, and water treatment), along with a petroleum refining simulation dataset collected by ourselves. The results demonstrate that MAD-Transformer can adaptively detect fine-grained anomalies with short duration, and outperforms the state-of-the-art baselines in terms of noise robustness and localization performance.