State Estimation Error Research Articles

Optimal design of Luenberger reduced-order observer with low sensitivity for linear multivariable systems

For the linear multivariable systems, by combining both merits of orthogonal-function approach and evolutionary optimization, in this paper, a new method is presented for designing a Luenberger reduced-order observer to solve the low-sensitivity design issue for physical system parameter deviation and simultaneously to minimize a measurement of the quadratic performance for reducing state transient estimation error. Two given examples illustrate the effectiveness of the presented new low-sensitivity design approach on state estimation performance. From the given examples, it shows that the estimated state errors are not sensitive to system parameter deviation and have the asymptotical convergence property. Besides, the performances are apparently superior to those without considering low-sensitivity design means.

Allocation of Eavesdropping Attacks for Multi-System Remote State Estimation

In recent years, the problem of cyber–physical systems’ remote state estimations under eavesdropping attacks have been a source of concern. Aiming at the existence of eavesdroppers in multi-system CPSs, the optimal attack energy allocation problem based on a SINR (signal-to-noise ratio) remote state estimation is studied. Assume that there are N sensors, and these sensors use a shared wireless communication channel to send their state measurements to the remote estimator. Due to the limited power, eavesdroppers can only attack M channels out of N channels at most. Our goal is to use the Markov decision processes (MDP) method to maximize the eavesdropper’s state estimation error, so as to determine the eavesdropper’s optimal attack allocation. We propose a backward induction algorithm which uses MDP to obtain the optimal attack energy allocation strategy. Compared with the traditional induction algorithm, this algorithm has lower computational cost. Finally, the numerical simulation results verify the correctness of the theoretical analysis.

Event-Triggered State Filter Estimation for Nonlinear Systems with Packet Dropout and Correlated Noise

This paper begins by exploring the challenge of event-triggered state estimations in nonlinear systems, grappling with packet dropout and correlated noise. A communication mechanism is introduced that determines whether to transmit measurement values based on whether event-triggered conditions are violated, thereby minimizing redundant communication data. In designing the filter, noise decorrelation is initially conducted, followed by the integration of the event-triggered mechanism and the unreliable network transmission system for state estimator development. Subsequently, by combining the three-degree spherical–radial cubature rule, the numerical implementation steps of the proposed state estimation framework are outlined. The performance estimation analysis highlights that by adjusting the event-triggered threshold appropriately, the estimation performance and transmission rate can be effectively balanced. It is established that when there is a lower bound on the packet dropout rate, the covariance matrix of the state estimation error remains bounded, and the stochastic stability of the state estimation error is also confirmed. Ultimately, the algorithm and conclusions that are proposed in this paper are validated through a simulation example of a target tracking system.

Prescribed-time fault-tolerant control for the formation of quadrotors based on fully-actuated system approaches

This paper investigates the problem of prescribed-time fault-tolerant control for the formation of quadrotors by utilising the fully-actuated system approach. Since not all quadrotors can directly access the virtual leader's state, a distributed prescribed-time observer is designed to estimate the state of a virtual leader. Leveraging this observer, a horizontal position controller that combines the fully-actuated system approach with the prescribed-time method, as well as altitude and attitude fault-tolerant controller, are proposed. In the design of control law, two distinct sets of controllers are designed: asymptotically stable controller and prescribed-time controller, each tailored to specific control objectives. The proposed distributed prescribed-time observer can ensure that the estimation error of the leader's state reaches zero within any specified time interval. Finally, the numerical simulation is conducted to demonstrate the effectiveness of the proposed fault-tolerant formation control algorithm.

Observed Fisher information for radar clutter modeled with sub-Gaussian α-stable distribution

It is well known that the clutter in such applications as synthetic aperture radar (SAR) follows heavy-tailed distributions. In such applications, knowledge of the exact statistical properties and/or errors in estimation of the clutter parameters plays an important role in successful implementation of the related applications like target tracking using SAR. In this study, the observed Fisher information (OFI) matrix will be derived for the received clutter assuming that the statistical behavior of clutter follows a sub-Gaussian α-stable (SGS) distribution along with a density function for an SGS distribution based on a newly proposed expansion. The new expansion is characterized with high speed computation in one hand, and avoids issues related to numerical computation of SGS density function, on the other. The minimum standard error of the clutter parameters, then, will be derived as the OFI matrix is inversely related to the Cramer-Rao lower bound (CRLB) of the clutter's estimated parameters. In order to compute the density function and OFI of the SGS distribution, the performance of the proposed methodology has been tested through numerical simulation where the implemented computer code of the proposed numerical method has been demonstrated to be fast and accurate. The R code is available at https://github.com/mahditeimouri/Sub-Gaussian/blob/main/OFI-sub-Gaussian.r.

A detection and rerouting mechanism for platoon control of non‐linear autonomous vehicles under denial of service attacks

AbstractThis paper presents a novel detection and rerouting mechanism for distributed adaptive platoon control of non‐linear autonomous connected vehicles under denial of service (DoS) attacks. DoS attacks can cause delays or losses of data packets due to blocked communication channels, leading to reducing platoon performance or even collisions among vehicles. To tackle this issue, the proposed mechanism detects and reroutes communication topology depending on the real‐time topology and the number of link failures. Real‐time detection divides the scenario of DoS attacks into three parts. According to the different scenarios, rerouting mechanisms will be utilized. A controller adapted to real‐time variable communication topology is also designed in this scheme. The adjacency matrix of the real‐time communication topology generated by the rerouting mechanism is used to update the controller so that the platoon can remain in a stable state without being affected by DoS attacks. In addition, the sliding mode controller and the observer are designed by solving linear matrix inequalities, and the platoon stability and internal stability are proven. Numerical simulation studies demonstrate that the proposed mechanism and control design can reduce the vehicle state estimate error and platoon‐tracking error to ideal states under DoS attacks. The proposed method solves the problem that the existing methods have not considered the number of link failures and the inability to restore communication when the communication topology is paralyzed.

Joint State and Unknown Input Estimation for a Class of Artificial Neural Networks With Sensor Resolution: An Encoding-Decoding Mechanism.

This article is concerned with the joint state and unknown input (SUI) estimation for a class of artificial neural networks (ANNs) with sensor resolution (SR) under the encoding-decoding mechanisms. The consideration of SR, which is an important specification of sensors in the real world, caters to engineering practice. Furthermore, the implementation of the encoding-decoding mechanism in the communication network aims to accommodate the limited bandwidth. The objective of this study is to propose a set-membership estimation algorithm that accurately estimates the state of the ANN without being influenced by the unknown input while accounting for the SR and the encoding-decoding mechanism. First, a sufficient condition is derived to ensure an ellipsoidal constraint on the estimation error. Then, by addressing an optimization problem, the design of the estimator gains is accomplished, and the minimal ellipsoidal constraint on the state estimation error is obtained. Finally, an example is provided to confirm the validity of the proposed joint SUI estimation scheme.

Automatic lung segmentation of magnetic resonance images: A new approach applied to healthy volunteers undergoing enhanced Deep-Inspiration-Breath-Hold for motion-mitigated 4D proton therapy of lung tumors

Background and purposeRespiratory suppression techniques represent an effective motion mitigation strategy for 4D-irradiation of lung tumors with protons. A magnetic resonance imaging (MRI)-based study applied and analyzed methods for this purpose, including enhanced Deep-Inspiration-Breath-Hold (eDIBH). Twenty-one healthy volunteers (41–58 years) underwent thoracic MR scans in four imaging sessions containing two eDIBH-guided MRIs per session to simulate motion-dependent irradiation conditions. The automated MRI segmentation algorithm presented here was critical in determining the lung volumes (LVs) achieved during eDIBH. Materials and methodsThe study included 168 MRIs acquired under eDIBH conditions. The lung segmentation algorithm consisted of four analysis steps: (i) image preprocessing, (ii) MRI histogram analysis with thresholding, (iii) automatic segmentation, (iv) 3D-clustering. To validate the algorithm, 46 eDIBH-MRIs were manually contoured. Sørensen-Dice similarity coefficients (DSCs) and relative deviations of LVs were determined as similarity measures. Assessment of intrasessional and intersessional LV variations and their differences provided estimates of statistical and systematic errors. ResultsLung segmentation time for 100 2D-MRI planes was ∼ 10 s. Compared to manual lung contouring, the median DSC was 0.94 with a lower 95 % confidence level (CL) of 0.92. The relative volume deviations yielded a median value of 0.059 and 95 % CLs of −0.013 and 0.13. Artifact-based volume errors, mainly of the trachea, were estimated. Estimated statistical and systematic errors ranged between 6 and 8 %. ConclusionsThe presented analytical algorithm is fast, precise, and readily available. The results are comparable to time-consuming, manual segmentations and other automatic segmentation approaches. Post-processing to remove image artifacts is under development.

Simulation and Evaluation of Distributed consensus Network for Multi-Agent Systems for Sybil Attacks

Distributed average consensus represents the amount of computing of inputs held by multiple agents that communicate through peer-to-peer networks. Collaboration among operators is essential for any distributed standard consensus protocol as every specialist needs to contribute to different operators, typically the adjacent (neighbouring) operators. Internet-of-Things (IoT) implementation is challenging because of its heterogeneous, massively distributed nature. The challenges of this challenge can be addressed with blockchain-based platforms and technologies. Testing and evaluation platforms are required for Blockchain deployments in IoT. A realistic and configurable network environment is presented in this paper to evaluate consensus algorithms. Many blockchainevaluation platforms do not provide a configurable and realistic network environment or are tied to a specific consensus protocol. With our simulator, practitioners can evaluate how consensus algorithms affect network events in congested or contested scenarios to determine the best consensus algorithm. It is proposed to achieve this task by generalizing consensus methods. The Blockchain simulator employs Discrete event network simulations for increased fidelity and scalability. In addition to evaluating the time, state block rate (%), estimation error, average throughput, and simulation time, we evaluate the performance of the proposed techniques based on the number of peer nodes. A comparison of the average transaction delivery rate with a traditional protocol is shown. The proposed protocol has a higher throughput average than the traditional one.

Split-spectrum based distributed state estimation for linear systems

This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator {comprising interconnected local estimators} is first described for estimating the state of a continuous and multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal. The estimator is guaranteed to solve the problem, provided a network-widely shared high gain condition achieving a form of spectrum separation is satisfied. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is also studied in which each agent adaptively adjusts a local gain, though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator based again on spectrum separation, but not high gain, is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that the state estimation errors in the local estimators all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network’s graph is strongly connected for all time. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.

Enhanced abnormal data detection hybrid strategy based on heuristic and stochastic approaches for efficient patients rehabilitation

Over the last few years, substantial research has been conducted towards developing efficient abnormal detection techniques while considering efficiency, accuracy, high-dimensional data, distributed environments, and others. Researchers increasingly deal with “abnormalities” in clinical patient data to derive relevant clinical knowledge for making informed decisions. However, data collection for clinically relevant research is often guided by patient conditions and administrative or clinical requirements rather than a regular schedule. Therefore, clinical data is frequently obtained in an unreliable form, characterized by data outliers and inconsistencies, incomplete information, and an unstructured format that varies based on patient types and data structures. In this research study, an enhanced hybrid AD strategy is developed based on heuristic and stochastic methods to cope with abnormalities in the clinical data of patients. The proposed hybrid strategy employs optimal k-means clustering as a heuristic method to cluster the clinical data based on the patient’s routine exercise characteristics to cope with abnormalities efficiently. Next, an interquartile range-based stochastic approach is employed as a statistical method to detect and eliminate abnormal data points by providing only reliable and effectual data to medical practitioners. The main objective of this research article is to facilitate healthcare and research practitioners by dealing with a high dimensional massive amount of inconsistent and incomplete clinical data of patients to detect and discard anomalous data points for providing only efficacious information. Furthermore, the AutoML paradigm is employed to develop an optimal regression model for analyzing the impact of the proposed hybrid strategy for abnormal pattern detection. In addition, different statistical error estimation measures are used to evaluate the empirical effectiveness of the proposed hybrid strategy using AutoML. The experiment results show a noteworthy improvement in terms of the R2 score for predicting healthcare indicators compared to the existing state-of-the-art regression models. Our optimal regression model performed efficiently regarding the R2 score and MAPE; it achieved an R2 score of 0.9855 and 0.9850 for predicting the Borg RPE and TUG, respectively. Similarly, our model achieved a low prediction error in terms of MAPE for predicting both health functional indicators; it achieved a MAPE of 6.57% and 5.19% for Borg RPE and TUG prediction. Our contribution signifies that the performance of the AutoML improves and outperforms traditional regression models while applying our proposed hybrid abnormal detection model to the patient’s rehabilitation data for accurately dealing with anomalous data.

Encryption-Decryption-Based State Estimation With Multirate Measurements Against Eavesdroppers: A Recursive Minimum-Variance Approach

This paper is concerned with the secure state estimation problem for a networked system with multi-rate measurements. The measurement data are transmitted to the estimator over a communication network, where an eavesdropper could intercept the transmitted information and generate the state estimates based on the overheard signals. In order to protect the privacy of the system state from information leakage, a novel encryptor is proposed to encrypt the measurement signals into codewords before being transmitted, and a decryptor is then adopted at the user side to decrypt the received codewords into the desired measurement signals, based on which a recursive state estimator is developed whose parameter is calculated by solving several coupled difference equations. Here, the secret key for decryption is available to the user but is unknown to the eavesdropper. The encryptor and the estimator are co-designed such that 1) at the user side, the estimation error covariance has an upper bound that is subsequently minimized in the sense of the matrix trace, where the uniform boundedness of the error covariance is also examined; and 2) at the eavesdropper side, the corresponding state estimation error is divergent. Two simulation examples are provided to demonstrate the effectiveness of our developed secure state estimation scheme.

SDE method for cosmic rays modulation in the heliosphere statistical error and solution uniqueness

The cosmic ray modulation in the heliosphere models comes to a new phase of their evolution, where the still higher number of models will be public with published source code. At the dawn of this period, we want to address two topics, the statistical error of their results and the uniqueness of their solutions.We present a method for the evaluation of statistical error for the numerical stochastic differential equation method, which is probably the most used method to numerically solve Parker's equation. We defined a limit of statistical error, for which we present a method to estimate the number of particles needed to be simulated to reach this limit. The estimation of statistical error from a scan of parametric space of two currently available models with public code, for the SOLARPROP model and Geliosphere 2D model, is presented.We present a test of the uniqueness of the solution of Parker's equation for 1D and 2D models of heliospheric modulation. Namely for the 1D B-p model and Geliosphere 2D model. The dependence of solution uniqueness on the selected model's input parameters is presented and discussed. Program summaryProgram Title: CudaHelioCommanderLightCPC Library link to program files:https://doi.org/10.17632/cptpkwphn4.1Developer's repository link:https://github.com/gladiatus55/CudaHelioCommanderLightLicensing provisions: GPLv3Programming language: C#, .NET 6.0Nature of problem: Despite the decades-long history of cosmic ray modulation in the heliosphere models, the topics of the statistical error of their results, and the uniqueness of their solutions were in published articles addressed only in a very limited way. A precise description of the method for statistical error evaluation, with examples applied to available models with published source code, is needed. The uniqueness of the solution of Parker's equation was not addressed in published literature.Solution method: The estimation of statistical error was evaluated for two currently available models with public code, the SOLARPROP model and Geliosphere 2D model, by a scan of their parametric space. The dependence of solution uniqueness on the selected model's input parameters was also done by scanning their parametric space.

Robust integration of fault estimation and sliding mode fault‐tolerant control for interconnected systems against sensor fault

AbstractThis paper provided a robust strategy for controlling nonlinear interconnected large‐scale systems subject to a sensor fault. The inherent challenge in controlling such systems is to sustain robust closed‐loop stability and performance in nonlinear interactions, faults, and exogenous inputs. A new closed‐loop structure has been devised to tackle this challenge by integrating the sliding mode controller with the unknown input observer. By exploiting the decoupling capability of the controller and observer, this integration ensures the robustness of the closed‐loop system against the simultaneous effect of interaction, fault, and disturbance. In this context, the unknown input observer has been constructed to supply the controller with an accurate sensor fault assessment despite additional unknown inputs. A novel approach is proposed for designing a decentralized fault‐tolerant control system that utilizes sliding mode control and proportional‐integral‐derivative controller tuning via a bacterial foraging optimization algorithm to compensate for the fault effect, leading to a robust output performance. The observer and controller gains are accomplished by utilizing the H∞ performance and linear matrix inequality formulation. The Lyapunov technique is used to demonstrate stability. A power system model emphasizes the proposed approach's robustness and effectiveness. The system performance with and without the proposed controller was compared, where the simulation results show a fast reaction to offset undesirable impacts, whereas the state estimation error approaches to zero in each subsystem.

Fault detection and identification for rolling mill main drive system based on integrated observer under iterative learning strategy

In this article, the problem of multiple fault detection, isolation and reconfiguration of the rolling mill main drive system containing external disturbances is investigated. Considering the nonlinear frictional damping between the rolls and the rolled parts, a nonlinear mathematical model of the main drive system of the mill is established. A comprehensive fault diagnosis scheme based on observer is addressed for this system subjected to unknown external interference. The proposed scheme is divided into two parts. In the first stage, a set of sliding mode observers is designed for system fault detection, and a fault isolation criterion is proposed based on observer redundancy and generalised residual set theory to reveal the fault source. In the second stage, combined with the iterative learning algorithm, an iterative learning-unknown input observer is constructed to realise the accurate estimation of the fault signal. Unlike the existing fault estimation methods, the iterative learning-unknown input observer designed in this article uses the state estimation error of the previous iteration to estimate the fault signal in the current iteration period. Using [Formula: see text] synthesis to design observers for the system will guarantee fault diagnosis robustness. The Lyapunov theory and linear matrix inequality are introduced to prove the convergence of the proposed observer. The simulation study of a 1780-mm hot strip mill evaluates the proposed scheme. Simulation results demonstrate that the sliding mode observer approach can detect faults in the main drive system and isolate faults accurately. In contrast, the iterative learning-unknown input observer method has the lowest fault reconfiguration error (99.87% smaller than the extended state observer, 99.77% smaller than the unknown input observer) and achieves accurate fault signal tracking.

Robust distributed Kalman filtering with event-triggered communication

We consider the problem of distributed Kalman filtering for sensor networks in the case there are constraints in data transmission, necessary to deal with the limitation of the channel capacity, and there is model uncertainty. More precisely, we propose two distributed filtering strategies with event-triggered communication where the state estimators are computed according to the least favorable model. The latter belongs to a ball about the nominal model. We also show that both the methods are stable in the sense that the mean-square of the state estimation error is bounded in all the nodes.

A deep learning model based on transformer structure for radar tracking of maneuvering targets

The motion complexity of maneuvering target causes the estimation uncertainty of target motion model, resulting in state estimation error. Especially for strong maneuvering target, the drastic change of target motion models makes the tracking methods hard to adapt and provide accurate state estimation promptly. To solve the state estimation problem of strong maneuvering targets, we propose a new transformer maneuvering target tracking model based on deep learning, named TrMTT model. The TrMTT model uses a new residual mapping between the observation trajectory and the real trajectory to estimate the target states, and is composed of the encoder and decoder branches while the two have the same input of observation trajectory. The encoder extracts the self-attention information for the input at each layer while the decoder implements cross-attention extraction and fusion between features in different layers, thus providing more correlation information between states for learning the transition law of rapidly changing states. Moreover, we propose an input module before the encoder–decoder structure to code the state features of the observation trajectory, and apply two kinds of normalization layers in the input module and the encoder–decoder structure, to project the input into a feature space which facilitates extracting the correlation information between states. Simulation results show that the proposed TrMTT model is superior in performance for maneuvering target tracking compared with other existing approaches.

Extended State Observer-Based Sliding Mode Control Design of Two-DOF Lower Limb Exoskeleton

Due to some model uncertainties and unknown friction disturbances that exist in the 2-DOF lower limb exoskeleton, a linear extended state observer (LESO) is proposed to estimate the unmeasurable angular velocity of two joints and the lumped uncertainties caused by friction disturbance and hydraulic parametric uncertainties. Meanwhile, by using the Lyapunov technique, a sliding mode controller is designed to improve the dynamic performance and the steady state accuracy of two joint angle responses in human–exoskeleton cooperative motion. By regulating the sliding mode controller gain, both the system state errors and estimation errors of the LESO are reduced in an arbitrary boundary of zero neighborhood. Finally, the effectiveness of the proposed control scheme is verified with both simulation and experimental results for one operator-wearable test, to guarantee that the joint position tracking performance and human–exoskeleton impedance torques are suppressed in a satisfactory boundary.

Sensor Scheduling for Remote State Estimation with Limited Communication Resources: A Time- and Event-Triggered Hybrid Approach.

This paper proposes a time- and event-triggered hybrid scheduling for remote state estimation with limited communication resources. A smart sensor observes a physical process and decides whether to send the local state estimate to a remote estimator via a wireless communication channel; the estimator computes the state estimate of the process according to the received data packets and the known scheduling mechanism. Based on the existing optimal time-triggered scheduling, we employ a stochastic event trigger to save precious communication chances and further improve the estimation performance. The minimum mean-squared error (MMSE) state estimate is derived since the Gaussian property is preserved. The estimation performance upper bound and communication rate are analyzed. The main results are illustrated by numerical examples.

Event-Based Optimal Stealthy False Data-Injection Attacks Against Remote State Estimation Systems.

Security is a crucial issue for cyber-physical systems, and has become a hot topic up to date. From the perspective of malicious attackers, this article aims to devise an efficient scheme on false data-injection (FDI) attacks such that the performance on remote state estimation is degraded as much as possible. First, an event-based stealthy FDI attack mechanism is introduced to selectively inject false data while evading a residual-based anomaly detector. Compared with some existing methods, the main advantage of this mechanism is that it decides when to launch the FDI attacks dynamically according to real-time residuals. Second, the state estimation error covariance of the compromised system is used to evaluate the performance degradation under FDI attacks, and the larger the state estimation error covariance, the more the performance degradation. Moreover, under attack stealthiness constraints, an optimal strategy is presented to maximize the trace of the state estimation error covariance. Finally, simulation experiments are carried out to illustrate the superiority of the proposed method compared with some existing ones.