The performance of disturbance observers is strongly influenced by the level of prior knowledge about the disturbance model. The simultaneous input and state estimation (SISE) algorithm is widely recognized for providing unbiased minimum-variance estimates under arbitrary disturbance models. In contrast, the Kalman filter-based disturbance observer (KF-DOB) achieves minimum mean-square error estimation when the disturbance model is fully specified. However, practical scenarios often fall between these extremes, where only partial knowledge of the disturbance model is available. This paper investigates the inherent bias-variance trade-off in KF-DOB when the disturbance model is incomplete. We further show that SISE can be interpreted as a special case of KF-DOB, where the disturbance noise covariance tends to infinity. To address this trade-off, we propose two novel estimators: the multi-kernel correntropy Kalman filter-based disturbance observer (MKCKF-DOB) and the interacting multiple models Kalman filter-based disturbance observer (IMMKF-DOB). Simulations verify the effectiveness of the proposed methods.
In this letter, we propose an airborne maneuverable bi-static integrated sensing and communication system where both the transmitter and receiver are unmanned aerial vehicles. By timely forming a dynamic bi-static range based on the motion information of the target, such a system can provide an adaptive two dimensional tracking and communication services. Towards this end, a trajectory optimization problem for both transmits and receive UAV is formulated to achieve high-accurate motion state estimation by minimizing the time-variant Cramer Rao bound, subject to the sufficient communication signal-to-noise ratio to maintain communication channel prediction error. Then we develop an efficient approach based on the successive convex approximation technique and the S-procedure to address the problem. Numerical results demonstrate that our proposed airborne maneuverable bi-static ISAC system is able to obtain higher tracking accuracy compared with the static or semi-dynamic ISAC system.
This paper proposes an Online Control-Informed Learning (OCIL) framework, which employs the well-established optimal control and state estimation techniques in the field of control to solve a broad class of learning tasks in an online fashion. This novel integration effectively handles practical issues in machine learning such as noisy measurement data, online learning, and data efficiency. By considering any robot as a tunable optimal control system, we propose an online parameter estimator based on extended Kalman filter (EKF) to incrementally tune the system in an online fashion, enabling it to complete designated learning or control tasks. The proposed method also improves the robustness in learning by effectively managing noise in the data. Theoretical analysis is provided to demonstrate the convergence of OCIL. Three learning modes of OCIL, i.e. Online Imitation Learning, Online System Identification, and Policy Tuning On-the-fly, are investigated via experiments, which validate their effectiveness.
Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of high-dimensional measurements and analyze state estimation in linear time-invariant systems with infinite-dimensional measurements but finite-dimensional states, both corrupted by additive noise. We propose a linear filter and derive the corresponding optimal gain functional in the sense of the minimum mean square error, analogous to the classic Kalman filter. By modeling the measurement noise as a wide-sense stationary random field, we are able to derive the optimal linear filter explicitly, in contrast to previous derivations of Kalman filters in distributed-parameter settings. Interestingly, we find that we need only impose conditions that are finite-dimensional in nature to ensure that the filter is asymptotically stable. The proposed filter is verified via simulation of a linearized system with a pinhole camera sensor.
This paper examines the problem of estimating the states, including state of charge, of battery cells connected in parallel. Previous research highlights the importance of this problem, and presents multiple approaches for solving it. Algorithm scalability and observability analysis can both be challenging, particularly because the underlying pack dynamics are governed by differential algebraic equations. Our work addresses these challenges from a novel perspective that begins by inverting the causality of parallel pack dynamics, which breaks the pack model's underlying algebraic loop. This simplifies observability analysis and observer design significantly, leading to three novel contributions. First, the paper derives mathematical conditions for state observability that apply regardless of the number of battery cells and the order of their individual dynamics. Second, the paper presents an approach for grouping battery cells such that their lumped dynamics are observable. Finally, the paper presents a novel pack state estimator that achieves computational tractability by employing inverse dynamic modeling. We conclude by presenting a Monte Carlo simulation study of this estimator using experimentally-parameterized models of two battery chemistries. The simulation results highlight the computational benefits of both the clustering strategy and inverse dynamics approach for state estimation.
A crucial challenge in decentralized systems is state estimation in the presence of unknown inputs, particularly within heterogeneous sensor networks with dynamic topologies. While numerous consensus algorithms have been introduced, they often require extensive information exchange or multiple communication iterations to ensure estimation accuracy. This paper proposes an efficient algorithm that achieves an unbiased and optimal solution comparable to filters with full information about other agents. This is accomplished through the use of information filter decomposition and the fusion of inputs via covariance intersection. Our method requires only a single communication iteration for exchanging individual estimates between agents, instead of multiple rounds of information exchange, thus preserving agents' privacy by avoiding the sharing of explicit observations and system equations. Furthermore, to address the challenges posed by dynamic communication topologies, we propose two practical strategies to handle issues arising from intermittent observations and incomplete state estimation, thereby enhancing the robustness and accuracy of the estimation process. Experiments and ablation studies conducted in both stationary and dynamic environments demonstrate the superiority of our algorithm over other baselines. Notably, it performs as well as, or even better than, algorithms that have a global view of all neighbors.
Steering models (such as the generalized two-point model) predict human steering behavior well when the human is in direct control of a vehicle. In vehicles under autonomous control, human control inputs are not used; rather, an autonomous controller applies steering and acceleration commands to the vehicle. For example, human steering input may be used for state estimation rather than direct control. We show that human steering behavior changes when the human no longer directly controls the vehicle and the two are instead working in a shared autonomy paradigm. Thus, when a vehicle is not under direct human control, steering models like the generalized two-point model do not predict human steering behavior. We also show that the error between predicted human steering behavior and actual human steering behavior reflects a fundamental difference when the human directly controls the vehicle compared to when the vehicle is autonomously controlled. Moreover, we show that a single distribution describes the error between predicted human steering behavior and actual human steering behavior when the human's steering inputs are used for state estimation and the vehicle is autonomously controlled, indicating there may be a underlying model for human steering behavior under this type of shared autonomous control. Future work includes determining this shared autonomous human steering model and demonstrating its performance.
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.
Distribution system operators (DSOs) must cope with new challenges such as the reconstruction of distribution grids along climate neutrality pathways or the ability to manage and control consumption and generation in the grid. In order to meet the challenges, measurements within the distribution grid often form the basis for DSOs. Hence, it is an urgent problem that measurement devices are not installed in many low-voltage (LV) grids. In order to overcome this problem, we present an approach to estimate pseudo-measurements for non-measured LV feeders based on the metadata of the respective feeder using regression models. The feeder metadata comprise information about the number of grid connection points, the installed power of consumers and producers, and billing data in the downstream LV grid. Additionally, we use weather data, calendar data and timestamp information as model features. The existing measurements are used as model target. We extensively evaluate the estimated pseudo-measurements on a large real-world dataset with 2,323 LV feeders characterized by both consumption and feed-in. For this purpose, we introduce peak metrics inspired by the BigDEAL challenge for the peak magnitude, timing and shape for both consumption and feed-in. As regression models, we use XGBoost, a multilayer perceptron (MLP) and a linear regression (LR). We observe that XGBoost and MLP outperform the LR. Furthermore, the results show that the approach adapts to different weather, calendar and timestamp conditions and produces realistic load curves based on the feeder metadata. In the future, the approach can be adapted to other grid levels like substation transformers and can supplement research fields like load modeling, state estimation and LV load forecasting.
This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose a diffusion-based distributed invariant Unscented Kalman Filter using the inverse covariance intersection (DIUKF-ICI) method to address target tracking in 3D environments. Unlike existing distributed UKFs confined to vector spaces, our approach extends the distributed UKF framework to Lie groups, enabling local estimates to be fused with intermediate information from neighboring agents on Lie groups. To handle the unknown correlations across local estimates, we extend the ICI fusion strategy to matrix Lie groups for the first time and integrate it into the diffusion algorithm. We demonstrate that the estimation error of the proposed method is bounded. Additionally, the algorithm is fully distributed, robust against intermittent measurements, and adaptable to time-varying communication topologies. The effectiveness of the proposed method is validated through extensive Monte-Carlo simulations.
In-orbit automated servicing is a promising path towards lowering the cost of satellite operations and reducing the amount of orbital debris. For this purpose, we present a pipeline for automated satellite docking port detection and state estimation using monocular vision data from standard RGB sensing or an event camera. Rather than taking snapshots of the environment, an event camera has independent pixels that asynchronously respond to light changes, offering advantages such as high dynamic range, low power consumption and latency, etc. This work focuses on satellite-agnostic operations (only a geometric knowledge of the actual port is required) using the recently released Lockheed Martin Mission Augmentation Port (LM-MAP) as the target. By leveraging shallow data-driven techniques to preprocess the incoming data to highlight the LM-MAP's reflective navigational aids and then using basic geometric models for state estimation, we present a lightweight and data-efficient pipeline that can be used independently with either RGB or event cameras. We demonstrate the soundness of the pipeline and perform a quantitative comparison of the two modalities based on data collected with a photometrically accurate test bench that includes a robotic arm to simulate the target satellite's uncontrolled motion.
Accurately estimating data in sensor-less areas is crucial for understanding system dynamics, such as traffic state estimation and environmental monitoring. This study addresses challenges posed by sparse sensor deployment and unreliable data by framing the problem as a spatiotemporal kriging task and proposing a novel graph transformer model, Kriformer. This model estimates data at locations without sensors by mining spatial and temporal correlations, even with limited resources. Kriformer utilizes transformer architecture to enhance the model's perceptual range and solve edge information aggregation challenges, capturing spatiotemporal information effectively. A carefully constructed positional encoding module embeds the spatiotemporal features of nodes, while a sophisticated spatiotemporal attention mechanism enhances estimation accuracy. The multi-head spatial interaction attention module captures subtle spatial relationships between observed and unobserved locations. During training, a random masking strategy prompts the model to learn with partial information loss, allowing the spatiotemporal embedding and multi-head attention mechanisms to synergistically capture correlations among locations. Experimental results show that Kriformer excels in representation learning for unobserved locations, validated on two real-world traffic speed datasets, demonstrating its effectiveness in spatiotemporal kriging tasks.
This paper addresses a distributed leader-follower formation control problem for a group of agents, each using a body-fixed camera with a limited field of view (FOV) for state estimation. The main challenge arises from the need to coordinate the agents' movements with their cameras' FOV to maintain visibility of the leader for accurate and reliable state estimation. To address this challenge, we propose a novel perception-aware distributed leader-follower safe control scheme that incorporates FOV limits as state constraints. A Control Barrier Function (CBF) based quadratic program is employed to ensure the forward invariance of a safety set defined by these constraints. Furthermore, new neural network based and double bounding boxes based estimators, combined with temporal filters, are developed to estimate system states directly from real-time image data, providing consistent performance across various environments. Comparison results in the Gazebo simulator demonstrate the effectiveness and robustness of the proposed framework in two distinct environments.
Cloth state estimation is an important problem in robotics. It is essential for the robot to know the accurate state to manipulate cloth and execute tasks such as robotic dressing, stitching, and covering/uncovering human beings. However, estimating cloth state accurately remains challenging due to its high flexibility and self-occlusion. This paper proposes a diffusion model-based pipeline that formulates the cloth state estimation as an image generation problem by representing the cloth state as an RGB image that describes the point-wise translation (translation map) between a pre-defined flattened mesh and the deformed mesh in a canonical space. Then we train a conditional diffusion-based image generation model to predict the translation map based on an observation. Experiments are conducted in both simulation and the real world to validate the performance of our method. Results indicate that our method outperforms two recent methods in both accuracy and speed.
Intelligent real-world systems critically depend on expressive information about their system state and changing operation conditions, e.g., due to variation in temperature, location, wear, or aging. To provide this information, online inference and learning attempts to perform state estimation and (partial) system identification simultaneously. Current works combine tailored estimation schemes with flexible learning-based models but suffer from convergence problems and computational complexity due to many degrees of freedom in the inference problem (i.e., parameters to determine). To resolve these issues, we propose a procedure for data-driven offline conditioning of a highly flexible Gaussian Process (GP) formulation such that online learning is restricted to a subspace, spanned by expressive basis functions. Due to the simplicity of the transformed problem, a standard particle filter can be employed for Bayesian inference. In contrast to most existing works, the proposed method enables online learning of target functions that are nested nonlinearly inside a first-principles model. Moreover, we provide a theoretical quantification of the error, introduced by restricting learning to a subspace. A Monte-Carlo simulation study with a nonlinear battery model shows that the proposed approach enables rapid convergence with significantly fewer particles compared to a baseline and a state-of-the-art method.
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to minimize some desired performance cost over a finite prediction horizon for the worst-case realization of the system's uncertainties, while also ensuring that any specified nonlinear constraints are always satisfied. The solution process relies on an implicit description of the feasible state space through prior measurements and the system dynamics, and assumes that the system is always in the subset of the feasible space that is most detrimental to performance. In doing so, we can guarantee that the system's true state will meet all of the chosen performance criteria without resorting to any explicit state estimation. Under some smoothness assumptions, we also discuss solving these semi-infinite programs through local reduction techniques, which generate optimal scenario sets for the uncertainty realizations to approximate the continuous uncertainty space and speed up the computation of optima. When tested on a two-dimensional nonlinear quadrotor, the developed method achieves robust constraint satisfaction and tracking despite dealing with highly uncertain measurements and system dynamics.
This paper proposes an observer-based formation tracking control approach for multi-vehicle systems with second-order motion dynamics, assuming that vehicles' relative or global position and velocity measurements are unavailable. It is assumed that all vehicles are equipped with sensors capable of sensing the bearings relative to neighboring vehicles and only one leader vehicle has access to its global position. Each vehicle estimates its absolute position and velocity using relative bearing measurements and the estimates of neighboring vehicles received over a communication network. A distributed observer-based controller is designed, relying only on bearing and acceleration measurements. This work further explores the concept of the \textit{Bearing Persistently Exciting} (BPE) formation by proposing new algorithms for bearing-based localization and state estimation of second-order systems in centralized and decentralized manners. It also examines conditions on the desired formation to guarantee the exponential stability of distributed observer-based formation tracking controllers. In support of our theoretical results, some simulation results are presented to illustrate the performance of the proposed observers as well as the observer-based tracking controllers.
This article considers the challenge of accommodating outlier measurements in state estimation. The Risk-Averse Performance-Specified (RAPS) state estimation approach addresses outliers as a measurement selection Bayesian risk minimization problem subject to an information accuracy constraint, which is a non-convex optimization problem. Prior explorations into RAPS rely on exhaustive search, which becomes computationally infeasible as the number of measurements increases. This paper derives a convex formulation for the RAPS optimization problems via transforming the mixed-binary variables into linear constraints. The convex reformulation herein can be solved by convex programming toolboxes, significantly enhancing computational efficiency. We explore two specifications: Full-RAPS, utilizing the full information matrix, and Diag-RAPS, focusing on diagonal elements only. The simulation comparison demonstrates that Diag-RAPS is faster and more efficient than Full-RAPS. In comparison with Kalman Filter (KF) and Threshold Decisions (TD), Diag-RAPS consistently achieves the lowest risk, while achieving the performance specification when it is feasible.
Choosing a nonlinear state estimator for an application often involves a trade-off between local optimality (such as provided by an extended Kalman filter) and (almost-/semi-) global asymptotic stability (such as provided by a constructive observer design based on Lyapunov principles). This paper proposes a filter design methodology that is both global and optimal for a class of nonlinear systems. In particular, systems for which there is an embedding of the state-manifold into Euclidean space for which the measurement function is linear in the embedding space and for which there is a synchronous error construction. A novel observer is derived using the minimum energy filter design paradigm and exploiting the embedding coordinates to solve for the globally optimal solution exactly. The observer is demonstrated through an application to the problem of unit quaternion attitude estimation, by embedding the 3-dimensional nonlinear system into a 4-dimensional Euclidean space. Simulation results demonstrate that the state estimate remains optimal for all time and converges even with a very large initial error.
Cyber-physical systems can be subject to sensor attacks, e.g., sensor spoofing, leading to unsafe behaviors. This paper addresses this problem in the context of linear systems when an omniscient attacker can spoof several system sensors at will. In this adversarial environment, existing results have derived necessary and sufficient conditions under which the state estimation problem has a unique solution. In this work, we consider a severe attacking scenario when such conditions do not hold. To deal with potential state estimation uncertainty, we derive an exact characterization of the set of all possible state estimates. Using the framework of control barrier functions, we propose design principles for system safety in offline and online phases. For the offline phase, we derive conditions on safe sets for all possible sensor attacks that may be encountered during system deployment. For the online phase, with past system measurements collected, a quadratic program-based safety filter is proposed to enforce system safety. A 2D-vehicle example is used to illustrate the theoretical results.