Application Of State Estimation Research Articles

Informationally overcomplete measurements from generalized equiangular tight frames

Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators are well known. In this paper, we introduce a more general class of informationally overcomplete positive, operator-valued measure (POVMs) that are generated by equiangular tight frames of arbitrary rank. This class provides a generalization of equiangular measurements to non-projective POVMs, which include rescaled mutually unbiased measurements and bases. We provide a method of their construction, analyze their symmetry properties, and provide examples for highly symmetric cases. In particular, we find a wide class of generalized equiangular measurements that are conical two-designs, which allows us to derive the index of coincidence. Our results show benefits of considering a single informationally overcomplete measurement over informationally complete collections of POVMs.

Comprehensive review on dynamic state estimation techniques with cybersecurity applications

AbstractThe role of cybersecurity in cyber‐physical power systems (CPPS) is reviewed, focusing on the applications of dynamic state estimation (DSE) techniques. These DSE techniques are particularly relevant with the integration of phasor measurement units (PMUs) and advanced communication infrastructure. A comprehensive review on DSE techniques and applications to efficiently protect CPPS against cyberattacks is classified into three cyber resilience phases including prevention, detection, and mitigation. The DSE techniques in the prevention phase are surveyed to improve the observability of the CPPS by the robust design of the Kalman filter and optimal protection of PMUs. The DSE techniques in the detection phase are surveyed to improve the adaptability of CPPS in various attack detection scenerios and optimise the detection accuracy. The DSE techniques in the mitigation phase are surveyed to enhance the flexibility of CPPS resource utilisation with compensation‐based, isolation‐based, and scheduling‐based strategies. Finally, the benefits and limitations of each DSE technique are summarised with potential suggestions on research directions for enhancing the cyber resilience of CPPS.

Infinity augmented state Kalman filter and its application in unknown input and state estimation

This paper investigates the infinity augmented state Kalman filter (IASKF) to obtain the unknown input and state estimation for systems with the rank-deficient matrix. With the aid of input model, which is described as the random walk process with finite covariance, the augmented state Kalman filter (ASKF) is established. Then in light of matrix limiting, the IASKF is deduced from the ASKF as the covariance of the input signal tends to infinity. It is shown that the previous unbiased minimum-variance (UMV) algorithm and recursive three-step filter (RTSF) are the special cases of the proposed IASKF algorithm. Moreover, the condition of existence of the IASKF is given. The present work gives a new insight into unknown input and state estimation. It indicates that the ASKF can also be used to estimate the unknown input and state by only choosing a proper covariance matrix of the input signal. A simulation example is given to illustrate the effectiveness of the proposed results.

Multi-scenario and multi-stage robust NMPC with state estimation application on the Tennessee-Eastman process

This study presents the implementation of two discrete robust approaches to Non-linear Model Predictive Control (NMPC), multi-scenario NMPC (MSc-NMPC) and multi-stage NMPC (MS-NMPC), to the benchmark Tennessee-Eastman (TE) challenge, with Extended Kalman Filter (EKF) and Moving Horizon Estimation (MHE) as state estimators. The robust NMPC formulation results in closed-loop responses that prevent constraint violation and closely track the process set-point under parameter uncertainty, even in scenarios where traditional NMPC results in an unstable response for this process. Additionally, unconstrained state estimators such as EKF are unsuitable because the parameter uncertainty may cause estimates to fall outside the feasible region of the process, which ultimately destabilizes the process. MHE was able to overcome this challenge because it considers process constraints in its formulation. The additional computational time required to solve the robust NMPC formulations and MHE does not cause significant delays for the sampling time considered, demonstrating their applicability to challenging large-scale industrial chemical processes.

Adaptive distributed multiple-model filter with uncertainty of process model

Target tracking is a critical application in multiple-sensor state estimation. However, it is subject to uncertainty in the process model due to target maneuvering, which includes motion model uncertainty and process noise uncertainty. In this paper, we present an adaptive distributed multiple-model filter for maneuvering target tracking that solves the two types of uncertainties by variational Bayesian. Initially, a centralized algorithm is developed over multiple-sensor. Using Categorical distribution and inverse Wishart distribution as the conjugate prior of motion model and process noise covariance respectively, the target state, model identity and noise parameters are jointly estimated by variational Bayesian. The algorithm is then extended to a distributed version where prior information and likelihood function achieve consensus through the Alternating Direction Method of Multipliers (ADMM). We also analyze the consensus and convergence of the proposed algorithm. The simulation results demonstrate the effectiveness of the proposed algorithm for maneuvering target tracking under process model uncertainty.

A Review on Thermal Behaviors and Thermal Management Systems for Supercapacitors

As a representative electrochemical energy storage device, supercapacitors (SCs) feature higher energy density than traditional capacitors and better power density and cycle life compared to lithium-ion batteries, which explains why they are extensively applied in the field of energy storage. While the available reviews are mainly concerned with component materials, state estimation, and industrial applications, there is a shortage of understanding of thermal behaviors and thermal management systems of SCs, which makes this review a timely aide for fulfilling this gap. This review introduces the energy storage mechanisms of SCs, followed by descriptions of current investigations of thermal behaviors. This covers the aspects of heat generation rates for electric double-layer capacitors (EDLCs) and hybrid supercapacitors (HSCs), together with reviewing existing experimental methods to measure and estimate heat generation rates, as well as comparative assessments of multiple heat generation rate models and research on thermal runaway. In addition, there are also overviews of current efforts by researchers in air cooling systems, liquid cooling systems, phase change material cooling systems, and heat pipe cooling systems. Finally, an in-depth discussion is provided regarding the challenges and future work directions for SCs in thermal behaviors and thermal management systems.

Enhanced Fuzzy State Estimation of Discrete-Time Nonlinear Circuits via Two Relaxed Measures

This brief gives an enhanced result for fuzzy state estimation of discrete-time nonlinear circuits by developing two new technical measures of relaxations. Firstly, a novel balanced matrix method is proposed in which all the involved free matrices are with arbitrary variable orders, and thus a lot of freedom can be introduced into different switching modes for reducing the conservatism caused by existing those free matrices with fixed orders in the recent result. Secondly, an important property is employed in order to further relax the conservatism caused by the mismatch of adjacent normalized fuzzy weighting functions. Therefore, the scope of application of fuzzy state estimation can be enlarged by a large margin and much better estimation performance is obtained than before. Finally, the superiority of the developed approach is tested and verified based on the common benchmark example applied in the literature.

Hybrid State Estimation in a Semitrailer for Different Loading Conditions

For state and parameter estimation in vehicles, Kalman filters, especially nonlinear extensions like the extended Kalman filter (EKF) and unscented Kalman filter (UKF), are very common. However, the estimation accuracy is highly dependent on the quality of the model used in the process update of the Kalman filter. Model errors can result from non-modeled dynamics that are either unknown or very difficult to describe. In recent years data-driven approaches for state estimation are the subject of research with promising results in estimation accuracy and reduced implementation effort. In this work, both a model-based method with an UKF and a data-driven approach based on recurrent neural networks (RNN) are implemented and combined to two hybrid methods for the application of state and parameter estimation in a truck-semitrailer for three different loading conditions. Hybrid estimation architectures promise to combine the advantages of model-based and data-driven methods to achieve better estimation accuracy than their standalone components. To the best knowledge of the authors, this work is the first to extend the field of hybrid state estimation to semitrailers estimating the truck steering angle, articulation angle, and the trailer's lateral and vertical tire forces. Four estimation architectures (an UKF, one purely data-driven method, and two hybrid methods) are optimized and compared to each other regarding estimation accuracy. The UKF is optimized with a particle swarm optimization (PSO) while the hyperparameters of the data-driven method are tuned with the asynchronous successive halving algorithm (ASHA) to result in a fair comparison. All methods are developed and compared based on an experimental data set from a test vehicle.

A fast data-driven topology identification method for dynamic state estimation applications

This paper proposes a fast topology identification method to avoid estimation errors caused by network topology changes. The algorithm applies a deep neural network to determine the switching state of the branches that are relevant for the execution of a dynamic state estimator. The proposed technique only requires data from the phasor measurement units (PMUs) that are used by the dynamic state estimator. The proposed methodology is demonstrated working in conjunction with a frequency divider-based synchronous machine rotor speed estimator. A centralized and a decentralized approach are proposed using a modified version of the New England test system and the Institute of Electrical and Electronics Engineers (IEEE) 118-bus test system, respectively. The numerical results in both test systems show that the method demonstrate the reliability and the low computational burden of the proposed algorithm. The method achieves a satisfactory speed, the decentralized approach simplifies the training process and the algorithm proves to be robust in the face of wrong input data.

Application of Blockchain for Secure Data Transmission in Distributed State Estimation

The application of renewable energy sources in the power grid increases the necessity of tracking the system state, especially in smart grids, where there is a bidirectional transfer of data and power. The complexity of coupling between communication and the electrical infrastructure in a smart grid increases the risk of security breaches. Increasing the state estimation accuracy helps the smart grid operator efficiently manage the system. This article proposes an integration of distributed state estimation with a blockchain-designed communication platform. Additionally, the asynchronous data transmission, which is more likely to happen in the real world, is considered as the second task of this research. Finally, a detailed analysis of the blockchain-based application in distributed state estimation is provided. The numerical analysis shows that the proposed method meets real-world performance requirements and brings high security and reliability to the distributed state estimation process.

State estimation of a lithium-ion battery based on multi-feature indicators of ultrasonic guided waves

Ultrasonic non-destructive testing technology has been applied to battery state estimation applications to ensure the safety of the energy storage system. However, the accuracy and robustness of battery state estimation should be improved. In this paper, the state estimation of a lithium-ion battery based on multi-feature indicators of ultrasonic guided waves is studied. Piezoelectric ceramic ultrasonic probes with a fixed angle are used as the transducers. Eleven feature indicators of ultrasonic signals are analyzed. The appropriate feature indicators for battery state estimation are determined based on sensitivity analysis and correlation analysis. Considering the frequency response characteristics of the probe and the battery, the multi-frequency response characteristics of the battery are analyzed. Finally, seven feature indicators with multi-frequency excitation are selected. Subsequently, an adaptive machine learning model is designed to estimate the battery state. Based on the experimental results, the root mean square error (RMSE) of the battery state of charge (SOC) estimation result is less than 2.36 %. The applicability of the proposed method is verified by battery fully charged and non-fully charged experiments. Meanwhile, the method can quickly diagnose the side reaction process under abuse conditions such as overcharge and overdischarge, which provides a new method for non-destructive battery state evaluation.

Maximum Correntropy with Variable Center Unscented Kalman Filter for Robust Power System State Estimation.

The robust Kalman filter with correntropy loss has received much attention in recent years for forecasting-aided state estimation in power systems, since it efficiently reduces the negative influence of various abnormal situations, such as non-Gaussian communication, changing environment, and instrument failures, and obviously improves the stability of power systems. However, the existing correntropy-based robust Kalman filters usually use the Gaussian function with a fixed center as the kernel function in correntropy, which may not be a suitable choice in practical applications of power system forecasting-aided state estimation (PSSE). To address this issue, a new and robust unscented Kalman filter, called the maximum correntropy with variable center unscented Kalman filter (MCVUKF), is proposed in this paper for PSSE. Specifically, MCVUKF adopts an extended version of correntropy, whose center can be located at any position, to replace the original correntropy in an unscented Kalman filter to improve the performance in PSSE. Moreover, by using an exponential function of the innovation vector to adjust a covariance matrix, an enhanced MCVUKF (En-MCVUKF) method is also developed for suppressing the influence of bad data to the innovation vector and further improving the accuracy of PSSE. Finally, extensive simulations have been conducted on IEEE 14-bus, 30-bus, and 57-bus test power systems, and the simulation results have shown the superiority of the proposed MCVUKF and En-MCVUKF methods compared with several related state-of-the-art Kalman filter methods.

Physics-Based Equivalent Circuit Model for Lithium-Ion Cells via Reduction and Approximation of Electrochemical Model

<div class="section abstract"><div class="htmlview paragraph">Physics-based electrochemical models and empirical Equivalent Circuit Models (ECMs) are well-established and widely used modeling techniques to predict the voltage behavior of lithium-ion cells. Electrochemical models are typically very accurate and require relatively little experimental data to calibrate, but present high mathematical and computational complexity. Conversely, ECMs are more computationally efficient and mathematically simpler, making them well-suited for applications in controls, diagnosis, and state estimation of lithium-ion battery packs. However, the calibration process requires extensive testing to calibrate the parameters of the model over a wide range of operating conditions.</div><div class="htmlview paragraph">This paper bridges the gap between these two classes of models by developing a method to analytically define the ECM parameters starting from an already-calibrated Extended Single-Particle Model (ESPM). The governing equations of the ESPM were reduced via model order reduction, linearization and by introducing approximations to yield the mathematical structure of a second order ECM. This allowed for analytically defining the parameters of the resulting ECM, without resorting to complex lookup tables and related extensive testing for calibration. The newly defined electrochemistry-based ECM (E-ECM) saw less than 1 mV RMS error increase compared to the ESPM voltage prediction across several test profiles.</div></div>

State Estimators in Soft Sensing and Sensor Fusion for Sustainable Manufacturing

State estimators, including observers and Bayesian filters, are a class of model-based algorithms for estimating variables in a dynamical system given the sensor measurements of related system states. They can be used to derive fast and accurate estimates of system variables that cannot be measured directly (‘soft sensing’) or for which only noisy, intermittent, delayed, indirect, or unreliable measurements are available, perhaps from multiple sources (‘sensor fusion’). In this paper, we introduce the concepts and main methods of state estimation and review recent applications in improving the sustainability of manufacturing processes across sectors including industrial robotics, material synthesis and processing, semiconductor, and additive manufacturing. It is shown that state estimation algorithms can play a key role in manufacturing systems for accurately monitoring and controlling processes to improve efficiencies, lower environmental impact, enhance product quality, improve the feasibility of processing more sustainable raw materials, and ensure safer working environments for humans. We discuss current and emerging trends in using state estimation as a framework for combining physical knowledge with other sources of data for monitoring and controlling distributed manufacturing systems.

Estimating key traffic state parameters through parsimonious spatial queue models

As an active performance evaluation method, the fluid-based queueing model plays an important role in traffic flow modeling and traffic state estimation problems. A critical challenge in the application of traffic state estimation is how to utilize heterogeneous data sources in identifying key interpretable model parameters of freeway bottlenecks, such as queue discharge rates, system-level bottleneck-oriented arrival rates, and congestion duration. Inspired by Newell’s deterministic fluid approximation model, this paper proposes a spatial queue model for oversaturated traffic systems with time-dependent arrival rates. The oversaturated system dynamics can be described by parsimonious analytical formulations based on polynomial functional approximation for virtual arrival flow rates. With available flow, density and end-to-end travel time data along traffic bottlenecks, the proposed modeling framework for estimating the key traffic queueing state parameters is able to systematically map various measurements to the bottleneck-level dynamics and queue evolution process. The effectiveness of the developed method is demonstrated based on three case studies with empirical data in different metropolitan areas, including New York, Los Angeles, and Beijing.

Injection-Constrained State Estimation

In applications of state estimation involving data assimilation over a spatial region, it is often convenient, and sometimes necessary, to confine the state correction to a prescribed subspace of the state space that corresponds to the measurement location. This is the injection-constrained state-estimation problem, where the injection of the output error is constrained to a specified subspace of the state space. Unlike full-state output-error injection, which is the dual of static full-state feedback, constrained output-error injection is the dual of static output feedback. To address the injection-constrained state-estimation problem, this paper develops the injection-constrained unscented Kalman filter (IC-UKF) and the injection-constrained retrospective cost filter (IC-RCF). The performance of these filters is evaluated numerically for linear and nonlinear state-estimation problems in order to compare their accuracy and determine their suboptimality relative to full-state output-error injection. As a benchmark test case, IC-UKF and IC-RCF are applied to the viscous Burgers equation for state and parameter estimation.

Application of State Estimation in Distribution Systems with Embedded Microgrids

In this paper, a weighted least square (WLS) state estimation algorithm with equality constraints is proposed for smart distribution networks embedded with microgrids. Since only a limited number of real-time measurements are available at the primary or secondary substations and distributed generation sites, load estimates at unmeasured buses remote from the substations are needed to execute state estimation. The load information can be obtained by forecasted and historical data or smart real-time meters. The proposed algorithms can be applied in either grid-connected or islanded operation mode and can efficiently identify breaker status errors at the main substations and feeders, where sufficient measurement redundancy exists. The impact of the accuracy of real and pseudo-measurements on the estimated bus voltages is tested with a 55-bus distribution network including distributed generation.

Ensemble kalman filter and particle filter-based state estimation on electrical power systems

In this article, a referential study of the sequential importance sampling particle filter with a systematic resampling and the ensemble Kalman filter is provided to estimate the dynamic states of several synchronous machines connected to a modified 14-bus test case, when a balanced three-phase fault is applied at a bus bar near one of the generators. Both are supported by Monte Carlo simulations with practical noise and model uncertainty considerations. Such simulations were carried out in MATLAB by the Power System Toolbox, whereas the evaluation of the Particle Filter and the Ensemble Kalman Filter by script files developed inside the toolbox. The results obtained show that the particle filter has higher accuracy and more robustness to measurement and model noise than the ensemble Kalman filter, which helps support the feasibility of the method for dynamic state estimation applications.

State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing.

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.

Architectural Exploration for Energy-Efficient Fixed-Point Kalman Filter VLSI Design

Efficient Kalman filter (KF) designs for real-time mobile applications, such as nano-drones navigation, robots localization, spacecraft orbit control, GPS positioning, image recognition, and multisensor data fusion for wearable systems, are key technology goals. The KF is a compute-intensive kernel composed of consecutive complex matrix operations, like multiplications and matrix inversions. The most complex block in the KF is the Kalman gain (KG) function, which involves matrices inversion at each iteration, applying the determinant matrix calculation and division operations. In this article, we combine architectural solutions of different types, for which balancing conflicting low-power and high-performance requirements aiming at real-time KF processing is a key design issue. The key finding in our architectural exploration herein presented is that the KF architectures in semiparallel and sequential forms offer the best balance of circuit area size, power dissipation, and processing speed. Compared to the state-of-the-art solutions, our KF architecture is more efficient, with 2.8 times fewer arithmetic operators, requiring 3.3 times fewer clock cycles. The usefulness of the developed KF in digital signal processing (DSP) is shown herein by simulations of system identification, noise elimination, and state estimation applications. These figures highlight the results of the KF architecture: the speed of adaptation for the system identification applications with root mean square error (RMSE) of 0.01 after 12 samples, precision level in noise elimination applications with RMSE of 0.13, and reliability in state estimation processes with RMSE less than 10% of system peak response.