Wireless sensor networks (WSNs) are critical components in modern cyber-physical systems, enabling efficient data collection and fusion through spatially distributed sensors. However, the inherent risks of eavesdropping and packet dropouts in such networks pose significant challenges to secure state estimation. In this paper, we address the privacy-preserving fusion estimation (PPFE) problem for multi-sensor systems under multiple packet dropouts and eavesdropping attacks. To mitigate these issues, we propose a distributed encoding-based privacy-preserving mechanism (PPM) within a control-theoretic framework, ensuring data privacy during transmission while maintaining the performance of legitimate state estimation. A centralized fusion filter is developed, accounting for the coupling effects of packet dropouts and the encoding-based PPM. Boundedness conditions for the legitimate user's estimation error covariance are derived via a modified algebraic Riccati equation. Additionally, by demonstrating the divergence of the eavesdropper's mean estimation error, the proposed PPFE algorithm's data confidentiality is rigorously analyzed. Simulation results for an Internet-based three-tank system validate the effectiveness of the proposed approach, highlighting its potential to enhance privacy without compromising estimation accuracy.
This paper addresses the problem of distributed resilient state estimation and control for linear time-invariant systems in the presence of malicious false data injection sensor attacks and bounded noise. We consider a system operator (defender) capable of deploying cybersecurity measures to counteract the sensor compromises. Although such measures enhance resilience against adversarial attacks, they may incur substantial costs; hence, it is crucial to select countermeasures to balance resilience gains and cost efficiency strategically. We first demonstrate that the system's resilience against attacks is maximized through the appropriate implementation of security measures, implying that no attacker can execute undetectable sensor attacks. Building on this analysis, we propose an algorithm that identifies the optimal security measure. While determining this measure is NP-hard in general, we also derive sufficient conditions under which efficient computation is feasible. Furthermore, we develop a distributed resilient state estimation and control scheme informed by the optimal security measure and establish conditions that guarantee bounded estimation and control errors. Finally, we validate the efficacy of our approach via numerical simulations of a vehicle platooning scenario.
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive maintenance. Standard filtering assumes prior knowledge of noise statistics to extract latent system states from noisy sensor data. However, real-world scenarios involve abnormalities like outliers, biases, drifts, and missing observations with unknown or partially known statistics, limiting conventional approaches. This thesis presents novel robust nonlinear filtering methods to mitigate these challenges. Based on insights from our filtering proposals, we extend the formulations to offline estimation/learning setups and propose smoothing extensions. Our methods leverage Bayesian inference frameworks, employing both deterministic and stochastic approximation techniques including Variational Inference (VI) and Particle Filters/Sequential Monte Carlo (SMC). We also study theoretical estimation limits using Bayesian Cram\'er-Rao bounds (BCRBs) in the context of measurement abnormalities. To validate the performance gains of the proposed methods, we perform simulations and experiments in scenarios including target tracking, indoor localization, 3D point cloud registration, mesh registration, and pose graph optimization. The fundamental nature of the work makes it useful in diverse applications, with possible future extensions toward developing outlier-robust machine learning pipelines, learning system dynamics from anomalous data, and addressing challenges in generative AI where standard diffusion models struggle with outliers, imbalanced datasets, and mode collapse.
We consider the problem of safe control in discrete autonomous agents that use learned components for imperfect perception (or more generally, state estimation) from high-dimensional observations. We propose a shield construction that provides run-time safety guarantees under perception errors by restricting the actions available to an agent, modeled as a Markov decision process, as a function of the state estimates. Our construction uses conformal prediction for the perception component, which guarantees that for each observation, the predicted set of estimates includes the actual state with a user-specified probability. The shield allows an action only if it is allowed for all the estimates in the predicted set, resulting in a local safety guarantee. We also articulate and prove a global safety property of existing shield constructions for perfect-perception agents bounding the probability of reaching unsafe states if the agent always chooses actions prescribed by the shield. We illustrate our approach with a case-study of an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs.
A Bayesian knowledge transfer mechanism that leverages external information to improve the performance of the Kalman fixed-lag interval smoother (FLIS) is proposed. Exact knowledge of the external observation model is assumed to be missing, which hinders the direct application of Bayes' rule in traditional transfer learning approaches. This limitation is overcome by the fully probabilistic design, conditioning the targeted task of state estimation on external information. To mitigate the negative impact of inaccurate external data while leveraging precise information, a latent variable is introduced. Favorably, in contrast to a filter, FLIS retrospectively refines past decisions up to a fixed time horizon, reducing the accumulation of estimation error and consequently improving the performance of state inference. Simulations indicate that the proposed algorithm better exploits precise external knowledge compared to a similar technique and achieves comparable results when the information is imprecise.
Accurate state estimation is essential for monitoring and controlling nonlinear chemical reactors, such as continuous stirred-tank reactors (CSTRs), where limited sensor coverage and process uncertainties hinder real-time observability. This paper introduces a novel multi-observer switching framework that combines several advanced estimators: Extended Luenberger Observer (ELO), Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Quadrature Kalman Filter (QKF), and Particle Filter (PF), operating in parallel. At each sampling instant, a cost function based on the $L_1$ norm and Kullback-Leibler divergence selects the observer, yielding the best agreement with available measurements. The proposed architecture is validated through simulations of both linearized and fully nonlinear CSTR models with up to three reactors in series. Results show that the switching strategy significantly reduces estimation errors compared to single-observer approaches, especially under partial observability and parametric uncertainty. Despite its modular design, the framework remains computationally tractable, making it suitable for real-time industrial applications such as fault detection and model-based predictive control.
We propose a hybrid variational framework that enhances Neural Quantum States (NQS) with a Normalising Flow-based sampler to improve the expressivity and trainability of quantum many-body wavefunctions. Our approach decouples the sampling task from the variational ansatz by learning a continuous flow model that targets a discretised, amplitude-supported subspace of the Hilbert space. This overcomes limitations of Markov Chain Monte Carlo (MCMC) and autoregressive methods, especially in regimes with long-range correlations and volume-law entanglement. Applied to the transverse-field Ising model with both short- and long-range interactions, our method achieves comparable ground state energy errors with state-of-the-art matrix product states and lower energies than autoregressive NQS. For systems up to 50 spins, we demonstrate high accuracy and robust convergence across a wide range of coupling strengths, including regimes where competing methods fail. Our results showcase the utility of flow-assisted sampling as a scalable tool for quantum simulation and offer a new approach toward learning expressive quantum states in high-dimensional Hilbert spaces.
This paper considers the optimal power allocation of a jamming attacker against remote state estimation. The attacker is self-sustainable and can harvest energy from the environment to launch attacks. The objective is to carefully allocate its attack power to maximize the estimation error at the fusion center. Regarding the attacker's knowledge of the system, two cases are discussed: (i) perfect channel knowledge and (ii) unknown channel model. For both cases, we formulate the problem as a Markov decision process (MDP) and prove the existence of an optimal deterministic and stationary policy. Moreover, for both cases, we develop algorithms to compute the allocation policy and demonstrate that the proposed algorithms for both cases converge to the optimal policy as time goes to infinity. Additionally, the optimal policy exhibits certain structural properties that can be leveraged to accelerate both algorithms. Numerical examples are given to illustrate the main results.
This paper presents a generalization of the trajectory general optimal sub-pattern assignment (GOSPA) metric for evaluating multi-object tracking algorithms that provide trajectory estimates with track-level uncertainties. This metric builds on the recently introduced probabilistic GOSPA metric to account for both the existence and state estimation uncertainties of individual object states. Similar to trajectory GOSPA (TGOSPA), it can be formulated as a multidimensional assignment problem, and its linear programming relaxation--also a valid metric--is computable in polynomial time. Additionally, this metric retains the interpretability of TGOSPA, and we show that its decomposition yields intuitive costs terms associated to expected localization error and existence probability mismatch error for properly detected objects, expected missed and false detection error, and track switch error. The effectiveness of the proposed metric is demonstrated through a simulation study.
With the increasing presence of automated vehicles on open roads under driver supervision, disengagement cases are becoming more prevalent. While some data-driven planning systems attempt to directly utilize these disengagement cases for policy improvement, the inherent scarcity of disengagement data (often occurring as a single instances) restricts training effectiveness. Furthermore, some disengagement data should be excluded since the disengagement may not always come from the failure of driving policies, e.g. the driver may casually intervene for a while. To this end, this work proposes disengagement-reason-augmented reinforcement learning (DRARL), which enhances driving policy improvement process according to the reason of disengagement cases. Specifically, the reason of disengagement is identified by a out-of-distribution (OOD) state estimation model. When the reason doesn't exist, the case will be identified as a casual disengagement case, which doesn't require additional policy adjustment. Otherwise, the policy can be updated under a reason-augmented imagination environment, improving the policy performance of disengagement cases with similar reasons. The method is evaluated using real-world disengagement cases collected by autonomous driving robotaxi. Experimental results demonstrate that the method accurately identifies policy-related disengagement reasons, allowing the agent to handle both original and semantically similar cases through reason-augmented training. Furthermore, the approach prevents the agent from becoming overly conservative after policy adjustments. Overall, this work provides an efficient way to improve driving policy performance with disengagement cases.
This paper investigates the design of output-feedback schemes for systems described by a class of recurrent neural networks. We propose a procedure based on linear matrix inequalities for designing an observer and a static state-feedback controller. The algorithm leverages global and regional incremental input-to-state stability (incremental ISS) and enables the tracking of constant setpoints, ensuring robustness to disturbances and state estimation uncertainty. To address the potential limitations of regional incremental ISS, we introduce an alternative scheme in which the static law is replaced with a tube-based nonlinear model predictive controller (NMPC) that exploits regional incremental ISS properties. We show that these conditions enable the formulation of a robust NMPC law with guarantees of convergence and recursive feasibility, leading to an enlarged region of attraction. Theoretical results are validated through numerical simulations on the pH-neutralisation process benchmark, demonstrating the effectiveness of the proposed schemes.
Vision-Language-Action (VLA) models have recently made significant advance in multi-task, end-to-end robotic control, due to the strong generalization capabilities of Vision-Language Models (VLMs). A fundamental challenge in developing such models is effectively aligning the vision-language space with the robotic action space. Existing approaches typically rely on directly fine-tuning VLMs using expert demonstrations. However, this strategy suffers from a spatio-temporal gap, resulting in considerable data inefficiency and heavy reliance on human labor. Spatially, VLMs operate within a high-level semantic space, whereas robotic actions are grounded in low-level 3D physical space; temporally, VLMs primarily interpret the present, while VLA models anticipate future actions. To overcome these challenges, we propose a novel training paradigm, ROSA, which leverages robot state estimation to improve alignment between vision-language and action spaces. By integrating robot state estimation data obtained via an automated process, ROSA enables the VLA model to gain enhanced spatial understanding and self-awareness, thereby boosting performance and generalization. Extensive experiments in both simulated and real-world environments demonstrate the effectiveness of ROSA, particularly in low-data regimes.
In the field of multi-sensor fusion for simultaneous localization and mapping (SLAM), monocular cameras and IMUs are widely used to build simple and effective visual-inertial systems. However, limited research has explored the integration of motor-encoder devices to enhance SLAM performance. By incorporating such devices, it is possible to significantly improve active capability and field of view (FOV) with minimal additional cost and structural complexity. This paper proposes a novel visual-inertial-encoder tightly coupled odometry (VIEO) based on a ViDAR (Video Detection and Ranging) device. A ViDAR calibration method is introduced to ensure accurate initialization for VIEO. In addition, a platform motion decoupled active SLAM method based on deep reinforcement learning (DRL) is proposed. Experimental data demonstrate that the proposed ViDAR and the VIEO algorithm significantly increase cross-frame co-visibility relationships compared to its corresponding visual-inertial odometry (VIO) algorithm, improving state estimation accuracy. Additionally, the DRL-based active SLAM algorithm, with the ability to decouple from platform motion, can increase the diversity weight of the feature points and further enhance the VIEO algorithm's performance. The proposed methodology sheds fresh insights into both the updated platform design and decoupled approach of active SLAM systems in complex environments.
Vehicle state estimation presents a fundamental challenge for autonomous driving systems, requiring both physical interpretability and the ability to capture complex nonlinear behaviors across diverse operating conditions. Traditional methodologies often rely exclusively on either physics-based or data-driven models, each with complementary strengths and limitations that become most noticeable during critical scenarios. This paper presents a novel consensus multi-model Kalman filter framework that integrates heterogeneous model types to leverage their complementary strengths while minimizing individual weaknesses. We introduce two distinct methodologies for handling covariance propagation in data-driven models: a Koopman operator-based linearization approach enabling analytical covariance propagation, and an ensemble-based method providing unified uncertainty quantification across model types without requiring pretraining. Our approach implements an iterative consensus fusion procedure that dynamically weighs different models based on their demonstrated reliability in current operating conditions. The experimental results conducted on an electric all-wheel-drive Equinox vehicle demonstrate performance improvements over single-model techniques, with particularly significant advantages during challenging maneuvers and varying road conditions, confirming the effectiveness and robustness of the proposed methodology for safety-critical autonomous driving applications.
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propagates error covariance using the recursive Joseph's formula and optimizes the Gaussian negative log-likelihood. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.
The invariant filtering theory based on the group theory has been successful in statistical filtering methods. However, there exists a class of state estimation problems with unknown statistical properties of noise disturbances, and it is worth discussing whether the invariant observer still has performance advantages. In this paper, considering the problem of state estimation with unknown but bounded noise disturbances, an Invariant Zonotopic Set-Membership Filter (InZSMF) method on groups is innovatively proposed, which extends the invariant filtering theory to the field of non-statistical filtering represented by set-membership filtering. Firstly, the InZSMF method transforms the state space from the traditional Euclidean vector space to the Lie group space to construct group affine discrete systems with unknown but bounded noise uncertainty defined by the zonotope on groups. Secondly, the nonlinear observer on the group is defined and the corresponding linearized estimation error is derived. Then, two observer gain tuning algorithms under the InZSMF method are proposed, respectively, the pole configuration method and the F-radius optimization method. Finally, through simulation experiments, it is shown that the InZSMF state estimation method is generally superior to the traditional Zonotopic Set-Membership Filter (ZSMF) state estimation method. Especially, when the initial estimations are imprecise, the convergence speed of state estimation, the accuracy of set-membership center estimation, and the average interval area of zonotopic estimation of the InZSMF method are significantly better than those of the ZSMF method.
This paper presents a real-time capable algorithm for the learning of Gaussian Processes (GP) for submodels. It extends an existing recursive Gaussian Process (RGP) algorithm which requires a measurable output. In many applications, however, an envisaged GP output is not directly measurable. Therefore, we present the integration of an RGP into an Extended Kalman Filter (EKF) for the combined state estimation and GP learning. The algorithm is successfully tested in simulation studies and outperforms two alternative implementations -- especially if high measurement noise is present. We conclude the paper with an experimental validation within the control structure of a Vapor Compression Cycle typically used in refrigeration and heat pumps. In this application, the algorithm is used to learn a GP model for the heat-transfer values in dependency of several process parameters. The GP model significantly improves the tracking performance of a previously published model-based controller.
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design methodology is regularly applied to systems on smooth manifolds by choosing local coordinates, however, it is well known that this approach is not intrinsic to the manifold and performance depends heavily on choosing 'good' coordinates. In this paper, we propose an extended Kalman filter that is adapted to the specific geometry of the manifold in question. We show that an affine connection and the concepts of parallel transport, torsion, and curvature are the key geometric structures that allow the formulation of a suitable family of intrinsic Gaussian-like distributions and provide the tools to understand how to propagate state estimates and fuse measurements. This leads us to propose novel geometric modifications to the propagation and update steps of the EKF and revisit recent work on the geometry of the reset step. The relative performance of the proposed geometric modifications are benchmarked against classical EKF and iterated EKF algorithms on a simplified inertial navigation system with direct pose measurements and no bias.
Traditional optimization-based techniques for time-synchronized state estimation (SE) often suffer from high online computational burden, limited phasor measurement unit (PMU) coverage, and presence of non-Gaussian measurement noise. Although conventional learning-based models have been developed to overcome these challenges, they are negatively impacted by topology changes and real-time data loss. This paper proposes a novel deep geometric learning approach based on graph neural networks (GNNs) to estimate the states of PMU-unobservable power systems. The proposed approach combines graph convolution and multi-head graph attention layers inside a customized end-to-end learning framework to handle topology changes and real-time data loss. An upper bound on SE error as a function of topology change is also derived. Experimental results for different test systems demonstrate superiority of the proposed customized GNN-SE (CGNN-SE) over traditional optimization-based techniques as well as conventional learning-based models in presence of topology changes, PMU failures, bad data, non-Gaussian measurement noise, and large system implementation.
In industrial applications, the presence of moving machinery, vehicles, and personnel, contributes to the dynamic nature of the wireless channel. This time variability induces channel fading, which can be effectively modeled using a Markov fading channel (MFC). In this paper, we investigate the problem of secure state estimation for systems that communicate over a MFC in the presence of an eavesdropper. The objective is to enable a remote authorized user to accurately estimate the states of a dynamic system, while considering the potential interception of the sensor's packet through a wiretap channel. To prevent information leakage, a novel co-design strategy is established, which combines a privacy-preserving mechanism with a state estimator. To implement our encoding scheme, a nonlinear mapping of the innovation is introduced based on the weighted reconstructed innovation previously received by the legitimate user. Corresponding to this encoding scheme, we design a recursive privacy-preserving filtering algorithm to achieve accurate estimation. The boundedness of estimation error dynamics at the legitimate user's side is discussed and the divergence of the eavesdropper's estimation error is analyzed, which demonstrates the effectiveness of our co-design strategy in ensuring secrecy. Furthermore, a simulation example of a three-tank system is provided to demonstrate the effectiveness and feasibility of our privacy-preserving estimation method.