A common problem for agents operating in real-world environments is that the response of an environment to their actions may be non-deterministic and observed through noise. This renders environmental state and progress towards completing a task latent. Despite recent impressive demonstrations of LLM's reasoning abilities on various benchmarks, whether LLMs can build estimates of latent state and leverage them for reasoning has not been explicitly studied. We investigate this problem in the real-world domain of autonomous UI agents. We establish that appropriately prompting LLMs in a zero-shot manner can be formally understood as forming point estimates of latent state in a textual space. In the context of autonomous UI agents we then show that LLMs used in this manner are more than $76\%$ accurate at inferring various aspects of latent state, such as performed (vs. commanded) actions and task progression. Using both public and internal benchmarks and three reasoning methods (zero-shot, CoT-SC & ReAct), we show that LLM-powered agents that explicitly estimate and reason about latent state are able to successfully complete up to 1.6x more tasks than those that do not.
This paper is concerned with the state estimation problem for two-dimensional systems with asynchronous multichannel delays and energy harvesting constraints. In the system, each smart sensor has a certain probability of harvesting energy from the external environment, the authorized transmission between the sensor and the remote filter is contingent upon the current energy level of the sensor, which results in intermittent transmission of observation information. Addressing the issue of incomplete observation information due to asynchronous multi-channel delays, a novel approach for observation partition reconstruction is proposed to convert the delayed activated observation sequences into equivalent delay-free activated observation sequences. Through generating spatial equivalency validation, it is found that the reconstructed delay-free activated observation sequences contain the same information as the original delayed activated observation sequences. Based on the reconstructed activated observation sequence and activated probability, a novel unbiased h+1-step recursive estimator is constructed. Then, the evolution of the probability distribution of the energy level is discussed. The estimation gains are obtained by minimizing the filtering error covariance. Subsequently, through parameter assumptions, a uniform lower bound and a recursive upper bound for the filtering error covariance are presented. And the monotonicity analysis of activated probability on estimation performance is given. Finally, the effectiveness of the proposed estimation scheme is verified through a numerical simulation example.
Distribution system state estimation (DSSE) plays a crucial role in the real-time monitoring, control, and operation of distribution networks. Besides intensive computational requirements, conventional DSSE methods need high-quality measurements to obtain accurate states, whereas missing values often occur due to sensor failures or communication delays. To address these challenging issues, a forecast-then-estimate framework of edge learning is proposed for DSSE, leveraging large language models (LLMs) to forecast missing measurements and provide pseudo-measurements. Firstly, natural language-based prompts and measurement sequences are integrated by the proposed LLM to learn patterns from historical data and provide accurate forecasting results. Secondly, a convolutional layer-based neural network model is introduced to improve the robustness of state estimation under missing measurement. Thirdly, to alleviate the overfitting of the deep learning-based DSSE, it is reformulated as a multi-task learning framework containing shared and task-specific layers. The uncertainty weighting algorithm is applied to find the optimal weights to balance different tasks. The numerical simulation on the Simbench case is used to demonstrate the effectiveness of the proposed forecast-then-estimate framework.
State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that satisfy all these factors. This study introduces a neuromorphic approach for robust filtering of nonlinear dynamical systems: SNN-EMSIF (spiking neural network-extended modified sliding innovation filter). SNN-EMSIF combines the computational efficiency and scalability of SNNs with the robustness of EMSIF, an estimation framework designed for nonlinear systems with zero-mean Gaussian noise. Notably, the weight matrices are designed according to the system model, eliminating the need for a learning process. The framework's efficacy is evaluated through comprehensive Monte Carlo simulations, comparing SNN-EMSIF with EKF and EMSIF. Additionally, it is compared with SNN-EKF in the presence of modeling uncertainties and neuron loss, using RMSEs as a metric. The results demonstrate the superior accuracy and robustness of SNN-EMSIF. Further analysis of runtimes and spiking patterns reveals an impressive reduction of 85% in emitted spikes compared to possible spikes, highlighting the computational efficiency of SNN-EMSIF. This framework offers a promising solution for robust estimation in nonlinear dynamical systems, opening new avenues for efficient and reliable estimation in various industries that can benefit from neuromorphic computing.
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 new 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.
For distributed estimations in a sensor network, the consistency and accuracy of an estimator are greatly affected by the unknown correlations between individual estimates. An inconsistent or too conservative estimate may degrade the estimation performance and even cause divergence of the estimator. Cooperative estimation methods based on Inverse Covariance Intersection (ICI) can utilize a network of sensors to provide a consistent and tight estimate of a target. In this paper, unlike most existing ICI-based estimators that only consider two-dimensional (2-D) target state estimation in the vector space, we address this problem in a 3-D environment by extending the ICI algorithm to the augmented quaternion space. In addition, the proposed algorithm is fully distributed, as each agent only uses the local information from itself and its communication neighbors, which is also robust to a time-varying communication topology. To evaluate the performance, we test the proposed algorithm in a camera network to track the pose of a target. Extensive Monte Carlo simulations have been performed to show the effectiveness of our approach.
We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with filtering methods such as the extended and ensemble Kalman filter. We use the former to show robustness and the latter to ensure computational efficiency in the case of nonlinear models. Our method matches or outperforms other robust filtering methods (such as those based on variational Bayes) at a much lower computational cost. We show this empirically on a range of filtering problems with outlier measurements, such as object tracking, state estimation in high-dimensional chaotic systems, and online learning of neural networks.
Tracking objects in three-dimensional space is critical for autonomous driving. To ensure safety while driving, the tracker must be able to reliably track objects across frames and accurately estimate their states such as velocity and acceleration in the present. Existing works frequently focus on the association task while either neglecting the model performance on state estimation or deploying complex heuristics to predict the states. In this paper, we propose STT, a Stateful Tracking model built with Transformers, that can consistently track objects in the scenes while also predicting their states accurately. STT consumes rich appearance, geometry, and motion signals through long term history of detections and is jointly optimized for both data association and state estimation tasks. Since the standard tracking metrics like MOTA and MOTP do not capture the combined performance of the two tasks in the wider spectrum of object states, we extend them with new metrics called S-MOTA and MOTPS that address this limitation. STT achieves competitive real-time performance on the Waymo Open Dataset.
The paper examines a scenario wherein sensors are deployed within an Industrial Networked Control System, aiming to construct a digital twin (DT) model for a remotely operated Autonomous Guided Vehicle (AGV). The DT model, situated on a cloud platform, estimates and predicts the system's state, subsequently formulating the optimal scheduling strategy for execution in the physical world. However, acquiring data crucial for efficient state estimation and control computation poses a significant challenge, primarily due to constraints such as limited network resources, partial observation, and the necessity to maintain a certain confidence level for DT estimation. We propose an algorithm based on Value of Information (VoI), seamlessly integrated with the Extended Kalman Filter to deliver a polynomial-time solution, selecting the most informative subset of sensing agents for data. Additionally, we put forth an alternative solution leveraging a Graph Neural Network to precisely ascertain the AGV's position with a remarkable accuracy of up to 5 cm. Our experimental validation in an industrial robotic laboratory environment yields promising results, underscoring the potential of high-accuracy DT models in practice.
State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in high-dimensional state spaces, these filters face challenges such as 'particle deprivation' which hinders accurate representation of the true posterior distribution. This paper introduces a novel resampling-free particle filter designed to mitigate particle deprivation by forgoing the traditional resampling step. This ensures a broader and more diverse particle set, especially vital in high-dimensional scenarios. Theoretically, our proposed filter is shown to offer a near-accurate representation of the desired posterior distribution in high-dimensional contexts. Empirically, the effectiveness of our approach is underscored through a high-dimensional synthetic state estimation task and a 6D pose estimation derived from videos. We posit that as robotic systems evolve with greater degrees of freedom, particle filters tailored for high-dimensional state spaces will be indispensable.
Accurate localization is fundamental for autonomous underwater vehicles (AUVs) to carry out precise tasks, such as manipulation and construction. Vision-based solutions using fiducial marker are promising, but extremely challenging underwater because of harsh lighting condition underwater. This paper introduces a gradient-based active camera exposure control method to tackle sharp lighting variations during image acquisition, which can establish better foundation for subsequent image enhancement procedures. Considering a typical scenario for underwater operations where visual tags are used, we proposed several experiments comparing our method with other state-of-the-art exposure control method including Active Exposure Control (AEC) and Gradient-based Exposure Control (GEC). Results show a significant improvement in the accuracy of robot localization. This method is an important component that can be used in visual-based state estimation pipeline to improve the overall localization accuracy.
Recursive least squares (RLS) is derived as the recursive minimizer of the least-squares cost function. Moreover, it is well known that RLS is a special case of the Kalman filter. This work presents the Kalman filter least squares (KFLS) cost function, whose recursive minimizer gives the Kalman filter. KFLS is an extension of generalized forgetting recursive least squares (GF-RLS), a general framework which contains various extensions of RLS from the literature as special cases. This then implies that extensions of RLS are also special cases of the Kalman filter. Motivated by this connection, we propose an algorithm that combines extensions of RLS with the Kalman filter, resulting in a new class of adaptive Kalman filters. A numerical example shows that one such adaptive Kalman filter provides improved state estimation for a mass-spring-damper with intermittent, unmodeled collisions. This example suggests that such adaptive Kalman filtering may provide potential benefits for systems with non-classical disturbances.
AC State Estimation (ACSE) is widely recognized as a practical approach for determining the grid states in steady-state conditions. It serves as a fundamental analysis to ensure grid security and is a reference for market dispatch. As grid complexity increases with rapid electrification and decarbonization, there is a growing need for more accurate knowledge of the grid operating state. However, existing ACSE algorithms have technical gaps. Critically, current ACSE algorithms are susceptible to erroneous system parameters, which are assumed to be fixed in traditional approaches. In this paper, we build a novel circuit-theoretic joint parameter-state estimation algorithm to address this limitation. The innovative algorithm builds an analogous equivalent circuit of the grid with states and certain parameters unknown. It solves a circuit-constrained optimization to estimate the most likely grid states and parameters given a set of measurements. Further, it quantifies the goodness of the estimated output by formulating tight convex envelopes around the original non-convex problem to quantify the quality of estimates. We compare the various proposed approaches on systems with up to 2869 nodes while demonstrating a tradeoff between solution optimality and model fidelity.
This paper studies the traffic state estimation problem at signalized intersections with low penetration rate vehicle trajectory data. While many existing studies have proposed different methods to estimate unknown traffic states and parameters (e.g., penetration rate, queue length) with this data, most of them only provide a point estimation without knowing the uncertainty of these estimated values. It is important to quantify the estimation uncertainty caused by limited available data since it can explicitly inform us whether the available data is sufficient to satisfy the desired estimation accuracy. To fill this gap, we formulate the partially observable system as a hidden Markov model (HMM) based on the recently developed probabilistic time-space (PTS) model. The PTS model is a stochastic traffic flow model that is designed for modeling traffic flow dynamics near signalized intersections. Based on the HMM formulation, a single recursive program is developed for the Bayesian estimation of both traffic states and parameters. As a Bayesian approach, the proposed method provides the distributional estimation outcomes and directly quantifies the estimation uncertainty. We validate the proposed method with simulation studies and showcase its applicability to real-world vehicle trajectory data.
The Industrial Internet of Things (IIoT) is reshaping manufacturing, industrial processes, and infrastructure management. By fostering new levels of automation, efficiency, and predictive maintenance, IIoT is transforming traditional industries into intelligent, seamlessly interconnected ecosystems. However, achieving highly reliable IIoT can be hindered by factors such as the cost of installing large numbers of sensors, limitations in retrofitting existing systems with sensors, or harsh environmental conditions that may make sensor installation impractical. Soft (virtual) sensing leverages mathematical models to estimate variables from physical sensor data, offering a solution to these challenges. Data-driven and physics-based modeling are the two main methodologies widely used for soft sensing. The choice between these strategies depends on the complexity of the underlying system, with the data-driven approach often being preferred when the physics-based inference models are intricate and present challenges for state estimation. However, conventional deep learning models are typically hindered by their inability to explicitly represent the complex interactions among various sensors. To address this limitation, we adopt Graph Neural Networks (GNNs), renowned for their ability to effectively capture the complex relationships between sensor measurements. In this research, we propose physics-enhanced GNNs, which integrate principles of physics into graph-based methodologies. This is achieved by augmenting additional nodes in the input graph derived from the underlying characteristics of the physical processes. Our evaluation of the proposed methodology on the case study of district heating networks reveals significant improvements over purely data-driven GNNs, even in the presence of noise and parameter inaccuracies.
A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are addressed within a distributed framework. By leveraging the Koopman operator concept, a parallel subsystem modeling approach is proposed to establish interactive linear subsystem process models in higher-dimensional subspaces, each of which correlates with the original nonlinear subspace of the corresponding process subsystem via a nonlinear mapping. The data-driven linear subsystem models can be used to collaboratively characterize and predict the dynamical behaviors of the entire nonlinear process. Based on the established subsystem models, local state estimators that can explicitly handle process operation constraints are designed using moving horizon estimation. The local estimators are integrated via information exchange to form a distributed estimation scheme, which provides estimates of the unmeasured/unmeasurable state variables of the original nonlinear process in a linear manner. The proposed framework is applied to a chemical process and an agro-hydrological process to illustrate its effectiveness and applicability. Good open-loop predictability of the linear subsystem models is confirmed, and accurate estimates of the process states are obtained without requiring a first-principles process model.
In this paper, we address a partition-based distributed state estimation problem for large-scale general nonlinear processes by proposing a Kalman-based approach. First, we formulate a linear full-information estimation design within a distributed framework as the basis for developing our approach. Second, the analytical solution to the local optimization problems associated with the formulated distributed full-information design is established, in the form of a recursive distributed Kalman filter algorithm. Then, the linear distributed Kalman filter is extended to the nonlinear context by incorporating successive linearization of nonlinear subsystem models, and the proposed distributed extended Kalman filter approach is formulated. We conduct rigorous analysis and prove the stability of the estimation error dynamics provided by the proposed method for general nonlinear processes consisting of interconnected subsystems. A chemical process example is used to illustrate the effectiveness of the proposed method and to justify the validity of the theoretical findings. In addition, the proposed method is applied to a wastewater treatment process for estimating the full state of the process with 145 state variables.
In this paper, partition-based distributed state estimation of general linear systems is considered. A distributed moving horizon state estimation scheme is developed via decomposing the entire system model into subsystem models and partitioning the global objective function of centralized moving horizon estimation (MHE) into local objective functions. The subsystem estimators of the distributed scheme that are required to be executed iteratively within each sampling period are designed based on MHE. Two distributed MHE algorithms are proposed to handle the unconstrained case and the case when hard constraints on states and disturbances, respectively. Sufficient conditions on the convergence of the estimates and the stability of the estimation error dynamics for the entire system are derived for both cases. A benchmark reactor-separator process example is introduced to illustrate the proposed distributed state estimation approach.
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is critical to state distribution inference. Previously, the conditional probability is assumed to be exactly known, which represents a measure of the occurrence probability of one event, given the second event. In this paper, we find that by adding an additional event that stipulates an inequality condition, we can transform the conditional probability into a special integration that is analogous to convolution. Based on this transformation, we show that both transition probability and output probability can be generalized to convolutional forms, resulting in a more general filtering framework that we call convolutional Bayesian filtering. This new framework encompasses standard Bayesian filtering as a special case when the distance metric of the inequality condition is selected as Dirac delta function. It also allows for a more nuanced consideration of model mismatch by choosing different types of inequality conditions. For instance, when the distance metric is defined in a distributional sense, the transition probability and output probability can be approximated by simply rescaling them into fractional powers. Under this framework, a robust version of Kalman filter can be constructed by only altering the noise covariance matrix, while maintaining the conjugate nature of Gaussian distributions. Finally, we exemplify the effectiveness of our approach by reshaping classic filtering algorithms into convolutional versions, including Kalman filter, extended Kalman filter, unscented Kalman filter and particle filter.