Joint State Estimation Research Articles

Joint State and Fault Estimation of Complex Networks Under Measurement Saturations and Stochastic Nonlinearities

In this paper, the joint state and fault estimation problem is investigated for a class of discrete-time complex networks with measurement saturations and stochastic nonlinearities. The difference between the actual measurement and the saturated measurement is regarded as an unknown input and the system is thus re-organized as a singular system. An appropriate estimator is designed for each node which aims to estimate the system states and the loss of the actuator effectiveness simultaneously. In the presence of measurement saturations and stochastic nonlinearities, upper bounds of the error covariances of the fault estimates are recursively obtained and then minimized. Sufficient conditions are proposed to guarantee the existence, unbiasedness, and boundeness of the developed estimator. Our developed estimator design algorithm is distributed because it depends only on the local information and the information from the neighboring nodes, thereby avoiding the usage of a center estimator. Finally, simulation results are presented to show the performance of the proposed strategy in simultaneously estimating the states and faults.

Kalman Filter Estimation of Lithium Battery SOC Based on Model Capacity Updating

High-precision estimation of lithium battery SOC can effectively optimize vehicle energy management, improve lithium battery safety protection, extend lithium battery cycle life, and reduce new energy vehicle costs. Based on the forgetting factor recursive least square method (FFRLS), Thevenin equivalent circuit model and Singular Value Decomposition-Unscented Kalman Filter (SVD-UKF), the SVD-UKF combined lithium battery SOC estimation algorithm with model capacity update is proposed, aiming at further improving the SOC estimation accuracy of lithium battery. The parameter identification of Thevenin model is studied by using the forgetting factor recursive least square method. To overcoming the shortcomings of Kalman filter linearization error and non-positive definite covariance matrix, the singular value decomposition unscented Kalman filter algorithm is proposed. It is worth mentioning that in order to consider the impact of battery available capacity attenuation on the estimation of lithium battery SOC, the model capacity update algorithm is used to optimize the model parameters and state joint estimation algorithm based on FFRLS & SVD-UKF. Verified by simulation and lithium battery test, the results show that the SVD-UKF algorithm based on model capacity update can accurately estimate the SOC of lithium battery in real time with the available capacity of lithium battery continuous attenuation. The purpose of improving the accuracy of SOC estimation of lithium batteries is achieved.

Event-based joint state and fault estimation: The envelope-constrained [formula omitted] criterion

In this paper, the joint state and fault estimation problem is investigated for a class of discrete time-varying systems under the dynamic event-triggering mechanism. The actuator fault and the sensor fault are, respectively, considered in the state and measurement equations where only the changing rate of the actuator fault is needed. The dynamic event-triggering scheme is used to decrease unnecessary transmissions from the sensor to the estimator. To facilitate the joint estimator design, a novel descriptor system model is constructed by aggregating the system state and the sensor fault. The main aim of the addressed problem is to design a joint estimator to ensure that the estimation error dynamics simultaneously achieves the finite-horizon H∞ performance and the envelope constraint. Sufficient conditions are provided to obtain the desired joint estimator parameters by solving a series of recursive matrix inequalities. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed estimation method. The major novelty of this study is that we make one of the very first few attempts to deal with the multi-objective joint state and fault estimation issue under the dynamic event-trigging transmission mechanism.

Joint estimation of state of charge and state of health of lithium-ion battery based on fractional order model

Joint estimation of state of charge and state of health of lithium-ion battery based on fractional order model

A particle‐filtering framework for integrity risk of GNSS‐camera sensor fusion

<h3>Abstract</h3> Adopting a joint approach toward state estimation and integrity monitoring results in unbiased integrity monitoring unlike traditional approaches. So far, a joint approach was used in particle RAIM (Gupta &amp; Gao, 2019) for GNSS measurements only. In our work, we extend Particle RAIM to a GNSS-camera fused system for joint state estimation and integrity monitoring. To account for vision faults, we derived a probability distribution over position from camera images using map-matching. We formulated a Kullback-Leibler divergence (Kullback &amp; Leibler, 1951) metric to assess the consistency of GNSS and camera measurements and mitigate faults during sensor fusion. Experimental validation on a real-world data set shows that our algorithm produces less than 11 m position error and the integrity risk over bounds the probability of HMI with 0.11 failure rate for an 8 m alert limit in an urban scenario.

Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models.

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

Iterative state and parameter estimation algorithms for bilinear state-space systems by using the block matrix inversion and the hierarchical principle

This paper is concerned with the identification of the bilinear systems in the state-space form. The parameters to be identified of the considered systems are coupled with the unknown states, which makes the identification problem difficult. To deal with such a difficulty, the iterative estimation theory is considered to derive the joint parameter and state estimation algorithm. Specifically, a moving data window least squares-based iterative (MDW-LSI) algorithm is derived to estimate the parameters of the systems by using the window data, and the unknown states are estimated by a bilinear state estimator. Furthermore, in order to improve the computational efficiency, a matrix decomposition-based MDW-LSI algorithm and a hierarchical MDW-LSI algorithm are developed according to the block matrix inversion lemma and the hierarchical identification principle. Finally, the computational efficiency is discussed and the numerical examples are employed to test the proposed approaches.

Joint State and Fault Estimation for Networked Interconnected PDE Systems With Semi-Markov Fault Coefficient via Conjunct Measurement

This paper interconnects N parabolic partial differential equations (PDEs) by a nonlinear coupling protocol to describe a class of large-scale distributed parameter systems, for which, based on the network communication, the issue of joint state and fault estimation is investigated. First, a generalized fault model, where the fault coefficient follows a semi-Markov switching law, is introduced into the system model. Then, to achieve joint state and fault estimation and ensure the estimation accuracy, a special augmented distributed estimator is designed with using associated information among subsystems. Note that the sampled-data and pointwise measurements are conjunctly employed, such that the network communication resources can be saved to a large extent. Moreover, based on the graph theory, a global Lyapunov-Krasovskii functional (LKF) is constructed to handle the nonlinear coupling function. As a result, an effective theorem is proposed to guarantee that both the state and fault estimation errors can converge to zero while satisfying a strictly (Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,Ξ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> )-λ- dissipative index. Finally, a numerical example and an application study on chemical non-isothermal tubular reactors are provided to illustrate the feasibility and practicality of this paper.

Online state and inputs identification for stochastic systems using recursive expectation-maximization algorithm

In this paper, an online joint state estimation and unknown inputs (UIs) identification approach for industrial processes represented by the state-space model is proposed. The UIs identification is achieved by applying the recursive expectation-maximization (REM) technique. In E-step, a recursively calculated Q-function is derived based on the maximum likelihood framework, and the Kalman filter (KF) is adopted to estimate the states. In M-step, analytical solutions for UIs are obtained via locally maximizing the recursive Q-function. A numerical example of a quadrupled water tank process and practice application to system modeling of a distillation tower are employed to illustrate the proposed REM-KF algorithm's effectiveness. It is also demonstrated that the REM-KF algorithm is more accurate than existing online solutions.

Reduced order modelling for spatial-temporal temperature and property estimation in a multi-stage hot sheet metal forming process

A concise approach is proposed to determine a reduced order control design oriented dynamical model of a multi-stage hot sheet metal forming process starting from a high-dimensional coupled thermo-mechanical model. The obtained reduced order nonlinear parametric model serves as basis for the design of an Extended Kalman filter to estimate the spatial-temporal temperature distribution in the sheet metal blank during the forming process based on sparse local temperature measurements. To address modeling and approximation errors and to capture physical effects neglected during the approximation such as phase transformation from austenite to martensite a disturbance model is integrated into the Kalman filter to achieve joint state and disturbance estimation. The extension to spatial-temporal property estimation is introduced. The approach is evaluated for a hole-flanging process using a thermo-mechanical simulation model evaluated using LS-DYNA. Here, the number of states is reduced from approximately 17 000 to 30 while preserving the relevant dynamics and the computational time is 1000 times shorter. The performance of the combined temperature and disturbance estimation is validated in different simulation scenarios with three spatially fixed temperature measurements.

An Ellipsoidal Set-Membership Approach to Distributed Joint State and Sensor Fault Estimation of Autonomous Ground Vehicles

This paper is concerned with the problem of distributed joint state and sensor fault estimation for autonomous ground vehicles subject to unknown-but-bounded (UBB) external disturbance and measurement noise. In order to improve the estimation reliability and performance in cases of poor data collection and potential communication interruption, a multi-sensor network configuration is presented to cooperatively measure the vehicular yaw rate, and further compute local state and fault estimates. Toward this aim, an augmented descriptor vehicle model is first established, where the unknown sensor fault is modeled as an auxiliary state of the system model. Then, a new distributed ellipsoidal set-membership estimation approach is developed so as to construct an optimized bounding ellipsoidal set which guarantees to contain the vehicle's true state and the sensor fault at each time step despite the existence of UBB disturbance and measurement noises. Furthermore, a convex optimization algorithm is put forward such that the gain matrix of each distributed estimator can be recursively obtained. Finally, simulation results are provided to validate the effectiveness of the proposed approach.

On the Active Vibration Control of Nonlinear Uncertain Structures

This study proposes an active nonlinear control strategy for effective vibration mitigation in nonlinear dynamical systems characterized by uncertainty. The proposed scheme relies on the coupling of a Bayesian nonlinear observer, namely the Unscented Kalman Filter (UKF) with a two-stage control process. The UKF is implemented for adaptive joint state and parameter estimation, with the estimated states and parameters passed onto the controller. The controller comprises a first task of feedback linearization, allowing for subsequent integration of any linear control strategy, such as addition of damping, LQR control, or other, which then operates on the linearized state equations. The proposed framework is validated on a Duffing oscillator characterized by light damping and an uncertain nonlinear parameter under harmonic and stochastic disturbance. The demonstrated performance suggests that the proposed Bayesian approach offers a competitive approach for active vibration suppression in nonlinear uncertain systems.

Set-valued mode recognition-based Bayesian estimation for nonlinear stochastic systems with unknown sensor mode

This paper proposes the problem of joint state estimation and mode recognition for nonlinear stochastic systems with unknown sensor mode. The considered sensor mode is represented by a random finite set, whose elements can be one specific mode or a set of certain modes. A set-valued mode recognition-based Bayesian estimation framework is proposed to propagate the posterior density of the state conditioned on sensor modes and measurements, where the mode is recognized based on the maximum correntropy criterion. Furthermore, a mode-separability metric is proposed to discern the reliability of mode recognition, and utilized to derive two distinct implementation schemes, including state estimation based on separable and inseparable modes. Simulation results of fault detection and target tracking are provided to demonstrate the superiority of the proposed method in terms of state estimation accuracy and mode recognition effectiveness.

Adaptive filtering-based soft sensor method for estimating total nitrogen in aquaponic systems

The aquaponic system can satisfy the different needs of aquatic products and plants by utilizing nutrient flow to improve the economic benefit. Nitrogen is a key nutrient element in such process. High nitrogen concentration can worsen water quality, which may further result in mass death of typical fish and/or shellfish. Therefore, it is particularly important to monitor the nitrogen concentration to manage aquatic products and plants growth in aquaponic systems. Sensors for measuring nitrogen concentration are commercially available, but they are often expensive and unreliable in service. At the same time, the research on the soft sensor of nitrogen concentration is very limited. Therefore, this paper proposes a new adaptive filtering-based soft sensor method for real-time estimation of total nitrogen concentration. This method provides accurate prediction by integrating mechanistic model, online measurements (e.g. fish biomass, temperature) and infrequent offline measurement of total nitrogen. A moving-horizon estimation (MHE) algorithm is used for joint state and parameter estimation, thus allowing correction of mismatch between model parameters and the real process. Furthermore, the appropriate frequency of offline nitrogen measurement is determined to balance between the soft sensor accuracy and cost. Through computer simulation study of an aquaponic system, the proposed approach is effective to provide promising real-time prediction performance. By applying the correction method, the RMSE (root-mean-square error) of nitrogen concentration estimation is reduced by 31.86% on average compared to the simulated practical situation. In conclusion, the proposed soft sensor method could provide useful monitoring of the total nitrogen in aquaponics, and such information could be used for optimizing the operations.

A Novel Fractional - Order Extended Kalman Filtering Method for on-line Joint State Estimation and Parameter Identification of the High Power Li-ion Batteries

To ensure the reliability and sustainability of the energy storage system, it is important to accurately estimate the state of charge of the battery management system. The Li-ion battery is established based on fractional-order model, and the model parameters are identified online using particle swarm optimization combined with the forgetting factor recursive least square method. On this basis, a novel fractional-order extended Kalman filter method for on-line joint state estimation and parameter identification is proposed. This method can update the parameter model of Li-ion battery in real-time, which not only improves the accuracy of the battery model but also improves the accuracy of SOC estimation. Finally, to verify the accuracy and superiority of the method, the integral order extended Kalman filter, fractional-order extended Kalman filter are compared with the proposed method under the BBDST test schedule. Experimental results show that the algorithm has the highest SOC estimation accuracy and the smallest estimation error (1.5 %.). The results indicate that the fractional-order model can better describe the dynamic characteristics of Li-ion battery, and the adaptive scheme can significantly suppress noise measurement errors and battery model errors. The algorithm realizes online parameter identification and can be used in engineering applications.

Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Joint Cramér-Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems.

Joint estimation of state of charge and state of health for lithium‐ion battery based on dual adaptive extended Kalman filter

Lithium-ion batteries (LIBs) are widely used in electric vehicles due to its high energy density and low pollution. As the key monitoring parameters of battery management system (BMS), accurate estimation of the state of charge (SOC) and state of health (SOH) can promote the utilization rate of battery, which is of great significance to ensure the safe use of LIBs. In this paper, a novel dual Kalman filter method is proposed to achieve simultaneous SOC and SOH estimation. This paper improves the estimation accuracy of SOC and SOH from the following four aspects. Firstly, the widely used equivalent circuit model is established as the battery model in this paper, and the forgetting factor recursive least squares (FFRLS) method is applied to identify the model parameters. Secondly, two kinds of single-variable battery states are established to analyze the influence of OCV-SOC curve and battery capacity on SOC estimation. Based on this, an error model is proposed combined with Kalman filter to achieve better estimation results of SOC and SOH. Besides, to promote the accuracy of SOC estimation, based on the error innovation sequence (EIS) and residual innovation sequence (RIS), the improved dual adaptive extended Kalman filter (IDAEKF) algorithm based on dynamic window is proposed. Finally, the superiority of the proposed model is verified under different cycles. Experimental results show that the estimation error of SOC and SOH is controlled within 1%.

Joint Sensor Node Selection and State Estimation for Nonlinear Networks and Systems

State estimation and sensor selection problems for nonlinear networks and systems are ubiquitous problems that are important for the control, monitoring, analysis, and prediction of a large number of engineered and physical systems. Sensor selection problems are extensively studied for linear networks. However, less attention has been dedicated to networks with nonlinear dynamics. Furthermore, widely used sensor selection methods relying on structural (graph-based) observability approaches might produce far from optimal results when applied to nonlinear network dynamics. In addition, state estimation and sensor selection problems are often treated separately, and this might decrease the overall estimation performance. To address these challenges, we develop a novel methodology for selecting sensor nodes for networks with nonlinear dynamics. Our main idea is to incorporate the sensor selection problem into an initial state estimation problem. The resulting mixed-integer nonlinear optimization problem is approximately solved using three methods. The good numerical performance of our approach is demonstrated by testing the algorithms on prototypical Duffing oscillator, associative memory, and chemical reaction networks. The developed codes are available online.

Prognosis based on the Joint Parameter/State Estimation Using Zonotopic LPV Set-Membership Approach

Abstract This paper addresses the problem of prognostics based on Joint Estimation of States and Parameters (JESP) using a zonotopic Linear Parameter-Varying (LPV) set-membership approach. The aim of the prognostics is to forecast the Remaining Useful Life (RUL) of systems with degraded components. Thus, this paper suggests transforming such systems with nonlinear dynamical models into an LPV representation. Hence, a Zonotopic Set-Membership (ZSM) observer has been proposed to carry out the JESP for degradation assessment with a considerable focus on multiple-output systems. Despite the existence of different geometrical shapes, zonotopes have gained recently a lot of popularity due to their low computational complexity, in addition to the possibility of relating them with stochastic approaches. Moreover, an optimal correcting gain has been designed based on Linear Matrix Inequality (LMI) for robust observer tuning. Additionally, the LMI-based tuning can be solved offline with reduced computational effort while coping with a polytopic LPV representation of the model. Consequently, a Recursive ZSM (RZSM) approach has been employed for degradation prediction and guaranteed zonotopic RUL forecasting. Finally, the proposed approach is assessed using a degraded power electronics system, and the results are illustrated.

Joint State Estimation Under Attack of Discrete Event Systems

The problem of state estimation in the setting of partially-observed discrete event systems subject to cyber attacks is considered. An operator observes a plant through a natural projection that hides the occurrence of certain events. The objective of the operator is that of estimating the current state of the system. The observation is corrupted by an attacker which can tamper with the readings of a set of sensors thus inserting some fake events or erasing some observations. The aim of the attacker is that of altering the state estimation of the operator. An automaton, called joint estimator, is defined to describe the set of all possible attacks. In more details, an unbounded joint estimator is obtained by concurrent composition of two state observers, the attacker observer and the operator observer. The joint estimator shows, for each possible corrupted observation, the joint state estimation, i.e., the set of states consistent with the uncorrupted observation and the set of states consistent with the corrupted observation. Such a structure can be used to establish if an attack function is harmful w.r.t. a misleading relation. Our approach is also extended to the case in which the attacker may insert at most n events between two consecutive observations.