Joint State Estimation Research Articles

Selection of a stealthy and harmful attack function in discrete event systems

In this paper we consider the problem of joint state estimation under attack in partially-observed discrete event systems. An operator observes the evolution of the plant to evaluate its current states. The attacker may tamper with the sensor readings received by the operator inserting dummy events or erasing real events that have occurred in the plant with the goal of preventing the operator from computing the correct state estimation. An attack function is said to be harmful if the state estimation consistent with the correct observation and the state estimation consistent with the corrupted observation satisfy a given misleading relation. On the basis of an automaton called joint estimator, we show how to compute a supremal stealthy joint subestimator that allows the attacker to remain stealthy, no matter what the future evolution of the plant is. Finally, we show how to select a stealthy and harmful attack function based on such a subestimator.

Recursive zonotopic set-membership approach for system-level prognostics with application to linear parameter-varying systems

A robust recursive zonotopic set-membership approach for remaining useful life forecasting with application to linear parameter-varying systems is proposed in this paper. The proposed approach addresses systems with degraded components formulated as a system-level prognostics problem. Thus, the critical degraded components of the system are augmented to the states resulting a nonlinear system that is reformulated as a linear parameter-varying model. Hence, joint estimation of states and parameters is adopted in a zonotopic set-membership scheme with an optimal linear matrix inequality-based tuning and assuming unknown-but-bounded noises and uncertainties. As a result, a recursive zonotopic set-membership approach is proposed for remaining useful life forecasting based on the prediction of the failure precursors of degraded systems. Finally, this approach is tested on a DC–DC converter case study with unknown degradation behaviors, and the obtained results show the estimation and the forecasting accuracy of this methodology.

A Nonlinear Predictive Control Approach for Urban Drainage Networks Using Data-Driven Models and Moving Horizon Estimation

Real-time control (RTC) of urban drainage networks (UDNs) is a complex task where transport flows are non-pressurized and therefore impose flow-dependent time delays in the system. Unfortunately, the installation of flow sensors is economically out of reach at most utilities, although knowing volumes and flows are essential to optimize system operation. In this article, we formulate joint parameter and state estimation based on level sensors deployed inside manholes and basins in the network. We describe the flow dynamics on the main pipelines by the level variations inside manholes, characterized by a system of coupled partial differential equations (PDEs). These dynamics are approximated with kinematic waves where the network model is established with the water levels being the system states. Moving horizon estimation (MHE) is developed where the states and parameters are obtained via the levels and estimated flow data, utilizing the topological layout of the network. The obtained model complexity is kept within practically achievable limits, suitable for nonlinear predictive control. The effectiveness of the control and estimation method is demonstrated on a high-fidelity model of a drainage network, acting as virtual reality. We use real rain and wastewater flow data and test the controller against the uncertainty in the disturbance forecasts.

Joint state estimation of power battery based on UKPF

Accurate estimation of power battery state is an important function in battery management system. In order to accurately estimate power battery SOC and SOH and improve the performance of long-term estimation of battery SOC, a joint estimation method of power battery state based on UKPF was proposed in this paper. The particle filter algorithm was added on the basis of the unscented Kalman filter algorithm, and the particle filter algorithm was optimized by the unscented Kalman filter algorithm, which improved the particle degradation problem and improved the accuracy of battery state estimation. Based on the time scale transformation, the battery state estimation was completed, and the SOC and SOH were estimated at short and long time scales, respectively. The SOH estimation results were updated to the model parameters for SOC estimation. The results show that the joint estimation method can accurately estimate battery SOC and SOH with an error of less than 3%.

Joint state estimation of indoor thermal dynamics with unknown inputs using augmented fading memory Kalman filter

An intelligent and efficient utilization of a heating, ventilation, and air conditioning system can be instrumental to reduce the building energy consumption, which in turn, is expected to reduce the green-house gases. The energy profiling requires modelling and estimation of the building environment with uncertainties. This paper proposes a strategy to estimate indoor thermal dynamics at multiple walls using a forgetting factor-based fading memory Kalman filter (FMKF) in presence of unknown inputs. This work also proposes a joint state estimation scheme based on FMKF which considers augmentation of the unknown heating energy inputs along with the thermal parameters of the thermodynamic model developed for indoor environment. The contribution of unknown inputs in the process of state estimation have been studied in the context of measuring node distribution. The proposed scheme has been implemented for multiple real-life thermal scenarios and results outperformed the conventional Kalman filter-based estimation scheme.

A Review of Critical State Joint Estimation Methods of Lithium-Ion Batteries in Electric Vehicles

Battery state of charge (SOC), state of health (SOH), and state of power (SOP) are decisive factors that influence the energy-management system (EMS) performance of electric vehicles. However, the accurate estimation of SOC, SOH, and SOP remains a challenge due to the high nonlinearity of the battery dynamic characteristics and the strong coupling among the states. In this paper, different methods of single-state and two-state joint estimation are classified and discussed, including SOC/SOH and SOC/SOP joint estimation methods, and their advantages and limitations are analyzed. On this basis, key issues of joint multi-state estimation are discussed, and suggestions for future work are made.

Variational Learning Data Fusion With Unknown Correlation

This article proposes the problem of joint state estimation and correlation identification for data fusion with unknown and time-varying correlation under the Bayesian learning framework. The considered data correlation is represented by the randomly weighted sum of positive semi-definite matrices, where the random weights depict at least three kinds of unknown correlation across single-sensor measurement components, multisensor measurements, and local estimates. Based on the variational Bayesian mechanism, the joint posterior distribution of the state and weights is derived in a closed-form iterative manner, through minimizing the Kullback-Leibler divergence. The three-case simulation shows the superiority of the proposed method in the root-mean-square error of estimation and identification.

State, global, and local parameter estimation using local ensemble Kalman filters: Applications to online machine learning of chaotic dynamics

AbstractIn a recent methodological article, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we investigate more systematically the possibility of using a local ensemble Kalman filter with either covariance localisation or local domains, in order to retrieve the state and a mix of key global and local parameters. Global parameters are meant to represent the surrogate dynamical core, for instance through a neural network, which is reminiscent of data‐driven machine learning of dynamics, while the local parameters typically stand for the forcings of the model. Aiming at joint state and parameter estimation, a family of algorithms for covariance and local domain localisation is proposed. In particular, we show how to update global parameters rigorously using a local‐domain ensemble Kalman filter (EnKF) such as the local ensemble transform Kalman filter (LETKF), an inherently local method. The approach is tested with success on the 40‐variable Lorenz model using several of the local EnKF flavors. A two‐dimensional illustration based on a multilayer Lorenz model is finally provided. It uses radiance‐like nonlocal observations. It features both local domains and covariance localisation, in order to learn the chaotic dynamics and the local forcings. This article addresses more generally the key question of online estimation of both global and local model parameters.

Comparative study of state and unknown input estimation for continuous–discrete​ stochastic systems

Joint state and unknown input estimation for continuous–discrete stochastic systems can be classified into two types: with and without modeling of unknown inputs. This paper first proposes a recursive four-step Kalman filter for addressing the joint state and unknown input estimation of continuous–discrete stochastic systems and presents its stability conditions. Then, a theoretical analysis of the performances using the unknown input Kalman filters and an adaptive augmented Kalman filter is presented and validated using numerical simulations under different situations. Both the theory and simulation demonstrate that the adaptive augmented Kalman filters is a better option when addressing unknown inputs for continuous–discrete stochastic systems.

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

Robust three-phase state estimation for PV-Integrated unbalanced distribution systems

As the increasing penetration of renewable energy brings uncertainty and fluctuation into the operating conditions of distribution systems, distribution system state estimation (DSSE) needs to track not only the state of the network, but also the state of the renewable energy sources robustly and under unbalanced conditions. Aiming at delivering comprehensive situational awareness of distribution systems hosting solar photovoltaic (PV) power plants, this paper proposed a joint state estimation model for unbalanced distribution systems integrated with single-phase and three-phase PV power plants, as well as an extended weighted least absolute value (EWLAV) estimation algorithm for handling simultaneous measurement errors and control input errors. The proposed state estimation model considers various loss components of single-phase and three-phase power electronic converters, and is applicable to general unbalanced conditions including unbalanced phasing and parameters of distribution lines, PV power plants, and loads. The proposed EWLAV algorithm leverages sparse l1 optimization principles and can identify and suppress the gross errors in both measurements and converter control inputs. Simulation results show that the developed model can reliably reflect the characteristics of three-phase unbalanced distribution networks and PV plants, and the EWLAV algorithm produces unbiased results under simultaneous measurement errors and control input errors, which conventional estimators such as the weighted least squares (WLS) and weighted least absolute values (WLAV) cannot achieve.

Joint state and fault estimation for nonlinear complex networks with mixed time-delays and uncertain inner coupling: non-fragile recursive method

In this paper, the non-fragile joint state and fault estimation problem is investigated for a class of nonlinear time-varying complex networks (NTVCNs) with uncertain inner coupling and mixed time-delays. Compared with the constant inner coupling strength in the existing literature, the inner coupling strength is permitted to vary within certain intervals. A new non-fragile model is adopted to describe the parameter perturbations of the estimator gain matrix which is described by zero-mean multiplicative noises. The attention of this paper is focussed on the design of a locally optimal estimation method, which can estimate both the state and the fault at the same time. Then, by reasonably designing the estimator gain matrix, the minimized upper bound of the state estimation error covariance matrix (SEECM) can be obtained. In addition, the boundedness analysis is taken into account, and a sufficient condition is provided to ensure the boundedness of the upper bound of the SEECM by using the mathematical induction. Lastly, a simulation example is provided to testify the feasibility of the joint state and fault estimation scheme.

Joint state and parameter estimation based on constrained zonotopes

This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples.

Bayesian Filtering for Dynamic Anomaly Detection and Tracking

This article presents a Bayesian approach for sequential detection of anomalies in the motion of a target and joint tracking. The anomaly is modeled as a binary (on/off) switching unknown control input that goes into action (begins to exist, or “switches on”) thereby modifying the object dynamics; and by ceasing its activity (becoming nonexistent, or “switching off”) returns the dynamics to nominal. The developed Bayesian framework brings together random finite set (RFS) theory to represent the switching nature of the anomaly, and optimal joint input and state estimation to sequentially update a hybrid state that incorporates a random vector for the kinematic state and a Bernoulli RFS for the unknown control input. In addition, a closed-form solution, the Gaussian-mixture hybrid Bernoulli filter (GM-HBF), has been developed to provide a customized solution for dynamic anomaly detection in the maritime domain characterized by linear Gaussian target dynamics. Based on the Ornstein–Uhlenbeck dynamic model for vessels, where the evolution of the object velocity is governed by a piecewise mean-reverting stochastic process, the anomaly can be represented by a change in the long-run mean velocity (i.e., the unknown control input) from the nominal condition that forces the vessel to deviate from its standard route. We demonstrate the effectiveness of the proposed GM-HBF in both simulated and real-world maritime surveillance applications and test its performance in the face of false measurements, detection uncertainty, and sensor data gaps.

A Joint State Estimation Framework for Lithium-ion Batteries based on Hybrid Method

Accurate estimation of state of charge (SOC), state of health (SOH) and remaining useful life (RUL) of Lithium-ion batteries is of great importance. This paper proposes a estimation framework based on charging voltage segment and hybrid method combining with equivalent circuit model and data-driven algorithms to achieve the accurate estimation of SOC, SOH and RUL of the long life cycle of the battery. The charging voltage segment, with the merit of flexibility and available, which contains much information for battery degradation, is suitable for battery modeling and state estimation. The rising time of the optimal charging voltage segment which has the highest correlation with the present capacity is extracted as health feature (HF) to estimate the SOH with least squares support vector machine (LSSVM), and the identified resistance and capacitance parameters acquired by fitting the charging voltage segment with equivalent circuit model and estimated capacity acquired by LSSCM are used to estimate SOC with the unscented Kalman filter (UKF) algorithm in the discharge stage for this cycle; Gaussian process regression (GPR) is used to prediction the trend of HF, which are combined with established LSSVM model to estimate RUL. Experimental results show that the proposed method can estimate SOC, SOH and RUL jointly with high accuracy.

Joint State and Parameter Estimation for Hypersonic Glide Vehicles Based on Moving Horizon Estimation via Carleman Linearization

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

Joint state and actuator fault estimation for networked systems under improved accumulation-based event-triggered mechanism

The joint state and actuator fault estimation problem is investigated in this paper for a type of networked systems subject to loss of the actuator effectiveness (LAE). A so-called improved accumulation-based event-triggered mechanism (ETM) is used to regulate the transmission of signals between the sensors and the estimator for the purpose of communication resource saving. Compared with the traditional ETM schemes, such accumulation-based ETM is robust against the “undesired” abrupt changes of signals (which would occur due to certain big noises). Different from the integral-based ETM for continuous-time systems, the improved accumulation-based ETM proposed in this paper is a “weighted” ETM, where a given weight coefficient is employed to “balance” the weights of output measurements in different time instants. The multiplicative LAE is described by an unknown diagonal matrix. The object of this paper is to design a remote estimator such that both the fault signals and system states can be simultaneously estimated in the sense of minimizing an upper bound of the corresponding estimation error covariance at each sampling instant. First, the upper bound of the estimation error covariance is given by means of the induction method. Then, the desired estimator gain is calculated recursively by solving two sets of coupled matrix equations. Finally, two simulation examples are given to verify the usefulness of the strategy we proposed subject to the LAE under the improved accumulation-based ETM.

Minimum-Variance State and Fault Estimation for Multirate Systems With Dynamical Bias

This brief is concerned with the joint state and fault estimation problem for a class of multi-rate systems with dynamical bias. To reflect real practice, the multi-rate sampling is considered which allows the sensor sampling rate and the state update rate to be different. The sensor is subject to the sensor fault that changes according to a dynamic equation. Instead of applying the traditional lifting technique, we introduce a time-varying delay into the measurement equation so as to transform the multi-rate systems into single-rate ones. The aim of this brief is to develop a joint state and fault estimation algorithm with minimized estimation error covariance. The recursion of the estimation error covariance is first derived, and appropriate estimator gains are then characterized that minimizes the estimation error covariance. A simulation example on the DC servo system is given to confirm the usefulness of the developed recursive state and fault estimation algorithm.

Nonlinear Reduced Models for State and Parameter Estimation

State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements when the parameter vector $y$ is unknown. Fast numerical recovery methods have been proposed in Maday et al. [Internat. J. Numer. Methods Engrg., 102 (2015), pp. 933--965] based on reduced models which are linear spaces of moderate dimension $n$ that are tailored to approximate the solution manifold ${\cal M}$ where the solution sits. These methods can be viewed as deterministic counterparts to Bayesian estimation approaches and are proved to be optimal when the prior is expressed by approximability of the solution with respect to the reduced model [P. Binev et al., SIAM/ASA J. Uncertain. Quantif., 5 (2017), pp. 1--29]. However, they are inherently limited by their linear nature, which bounds from below their best possible performance by the Kolmogorov width $d_m({\cal M})$ of the solution manifold. In this paper, we propose to break this barrier by using simple nonlinear reduced models that consist of a finite union of linear spaces $V_k$, each having dimension at most $m$ and leading to different estimators $u_k^*$. A model selection mechanism based on minimizing the PDE residual over the parameter space is used to select from this collection the final estimator $u^*$. Our analysis shows that $u^*$ meets optimal recovery benchmarks that are inherent to the solution manifold and not tied to its Kolmogorov width. The residual minimization procedure is computationally simple in the relevant case of affine parameter dependence in the PDE. In addition, it results in an estimator $y^*$ for the unknown parameter vector. In this setting, we also discuss an alternating minimization (coordinate descent) algorithm for joint state and parameter estimation that potentially improves the quality of both estimators.

Joint Communication and State Estimation Over a State-Dependent Fading Gaussian Channel

A joint message and state communication problem over a fading Gaussian channel with additive state is considered. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and known non-causally at the transmitter, while the instantaneous fading gain is assumed to be known at both the encoder and the decoder. The receiver not only has to decode the message from the transmitter, but also needs to estimate the state process to meet a prescribed distortion limit. A complete characterization of the optimal rate versus distortion performance is provided. Moreover, the converse proof presented here might be of independent interest, since it gives a simpler and more compact way of establishing the converse for settings with non-fading links studied in the literature – by virtue of relying only upon the differential entropy maximizing property of Gaussian random variables for a given variance.