State Estimation Scheme Research Articles

Real-Time Adaptive Dynamics Based State Estimation Scheme for Unmanned Aircrafts

In this paper we present a state estimation scheme for Unmanned Aircrafts (UAs) utilizing dynamics based models and multi-sensor data fusion. Employing the UA dynamics in estimation can substantially enhance the estimator performance, but obtaining accurate dynamics parameters for each UA is computationally costly and complex. To eliminate these issues, we propose two decoupled Extended Kalman Filters (EKFs), namely the Rotational Decoupled Extended Kalman Filter (RDEKF) and the Translational Decoupled Extended Kalman Filter (TDEKF). The dynamics parameters in these filters are identified in real-time using the Deep Neural Network and the Modified Relay Feedback Test (DNN-MRFT) approach. This approach doesn’t demand prior knowledge of the UA physical parameters, requiring only an Inertial Measurement Unit (IMU) and a positioning system for model classification. Our estimation scheme provides position, velocity and attitude estimates, in addition to smooth lag-free inertial acceleration estimates. We show experimentally the advantages of our approach on trajectory tracking problems that uses low rate position sensors. We also demonstrate how utilizing the estimated acceleration in feedback control can reduce the tracking error of an optimally tuned system by 43%. Moreover, the proposed estimator produces smooth estimates that leads to a reduction of controller action by 6.6%, when compared to kinematic based estimators. We compare the achieved results against other methods that require full prior knowledge of the UA parameters or the noise models, and show advantages in performance and real-time capability.

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.

Cross‐layered distributed data‐driven framework for enhanced smart grid cyber‐physical security

Smart Grid (SG) research and development has drawn much attention from academia, industry and government due to the great impact it will have on society, economics and the environment. Securing the SG is a considerably significant challenge due the increased dependency on communication networks to assist in physical process control, exposing them to various cyber-threats. In addition to attacks that change measurement values using False Data Injection (FDI) techniques, attacks on the communication network may disrupt the power system's real-time operation by intercepting messages, or by flooding the communication channels with unnecessary data. Addressing these attacks requires a cross-layer approach. In this paper a cross-layered strategy is presented, called Cross-Layer Ensemble CorrDet with Adaptive Statistics(CECD-AS), which integrates the detection of faulty SG measurement data as well as inconsistent network inter-arrival times and transmission delays for more reliable and accurate anomaly detection and attack interpretation. Numerical results show that CECD-AS can detect multiple False Data Injections, Denial of Service (DoS) and Man In The Middle (MITM) attacks with a high F1-score compared to current approaches that only use SG measurement data for detection such as the traditional physics-based State Estimation, ECD-AS strategy and other machine learning classification-based detection schemes.

State Estimation and Application of the Hitch Angle of a Semitrailer Train Under Full Working Conditions Based on Multimodel Information Fusion

Considering that the traditional estimation method for the hitch angle of a semitrailer train easily fails in high-speed driving and reversing conditions, this study theoretically determines that the root cause is the nonlinear disturbance. Moreover, this study analyzes the difference in nonlinear disturbance produced by a state estimator under two conditions. The criteria for the nonlinear disturbance of the estimator are determined on the basis of the analysis. With such criteria and different types of nonlinear disturbance, an estimation strategy for multimodel information fusion under all working conditions is proposed to accurately estimate the classification of forward low-speed, high-speed, and reverse conditions. A genetic algorithm is used to optimize the proposed state estimation algorithm, which improves the accuracy at a low speed and the antinoise capability of high-speed driving and reversing. The estimation strategy for different speeds and ranges of the hitch angle is simulated and verified through the cosimulation of TruckSim and MATLAB/Simulink. Lastly, the state estimation strategy is used in the application layer to design a model predictive linear reversing controller for a semitrailer train to verify the improvement of the control effect of the estimation strategy. Simulation results show that the proposed multimodel information fusion estimation strategy can accurately estimate the hitch angle under all working conditions and greatly improve the control effect of linear reversing trajectory tracking of a semitrailer train in the application layer.

A Distributed Optimization Scheme for State Estimation of Nonlinear Networks With Norm-Bounded Uncertainties

This article investigates state estimation for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties, and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of mean-square estimation errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.

A Framework of High-precision State Estimation for Approaching, Orbiting, and Touching an Asteroid

High-precision state estimation lies at the core of asteroid exploration. This paper investigates the high-precision state estimation methods in asteroid approaching, orbiting, and touching phases. The system and measurement models are established, and state estimation strategies are designed respectively for each phase. In the approaching phase, the star image is used to directly determine the relative orbit of the spacecraft to the target asteroid. To improve the optical state estimation precision, a deceleration-orientation-deceleration strategy is developed. In the orbiting phase, coupled orbit-attitude estimation is realized based on the terrain features of the asteroid, and the effect of dynamic error on the accuracy of state estimation is analysed. Then, a decoupled orbit-attitude state estimation method is developed to avoid the affection of dynamic error. In the touching phase, lidar measurement is used to determine the relative orbit and attitude of the spacecraft with respect to the landing spot. Based on the triple-stage state estimation framework proposed in this paper, the relative state error of the spacecraft converges from 100km level to 1mm level.

Visual-Inertial Cross Fusion: A Fast and Accurate State Estimation Framework for Micro Flapping Wing Rotors

Real-time and drift-free state estimation is essential for the flight control of Micro Aerial Vehicles (MAVs). Due to the vibration caused by the particular flapping motion and the stringent constraints of scale, weight, and power, state estimation divergence actually becomes an open challenge for flapping wing platforms’ longterm stable flight. Unlike conventional MAVs, the direct adoption of mature state estimation strategies, such as inertial or vision-based methods, has difficulty obtaining satisfactory sensing performance on flapping wing platforms. Inertial sensors offer high sampling frequency but suffer from flapping-introduced oscillation and drift. External visual sensors, such as motion capture systems, can provide accurate feedback but come with a relatively low sampling rate and severe delay. This work proposes a novel state estimation framework to combine the merits from both to address such key sensing challenges of a special flapping wing platform—micro flapping wing rotors (FWRs). In particular, a cross-fusion scheme, which integrates two alternately updated Extended Kalman Filters based on a convex combination, is proposed to tightly fuse both onboard inertial and external visual information. Such a design leverages both the high sampling rate of the inertial feedback and the accuracy of the external vision-based feedback. To address the sensing delay of the visual feedback, a ring buffer is designed to cache historical states for online drift compensation. Experimental validations have been conducted on two sophisticated microFWRs with different actuation and control principles. Both of them show realtime and drift-free state estimation.

An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

For linear time-invariant dynamic systems with exactly known coefficients of their system matrices for which measurements with bounded errors are available at discrete time instants, an optimal polygonal state estimation scheme was recently published. This scheme allows for tightly enclosing all possible state trajectories in presence of uncertain, but bounded, system inputs which may be varying arbitrarily within in their bounds. Moreover, this approach is also capable of accounting for uncertainty related to the measurement time instants. However, the drawback of this polygonal technique is its rapidly increasing complexity for larger system dimensions. For that reason, the polygonal state enclosures are replaced by a computationally less expensive, but nearly optimal, ellipsoidal enclosure technique in this paper. Numerical simulations for representative benchmark examples focusing both on applications with precisely known and uncertain parameters conclude this contribution.

H ∞ state estimation for memristive neural networks with randomly occurring DoS attacks

This study deals with the problem of the state estimation for discrete-time memristive neural networks with time-varying delays, where the output is subject to randomly occurring denial-of-service attacks. The average dwell time is used to describe the attack rules, which makes the randomly occurring denial-of-service attack more universal. The main purpose of the addressed issue is to contribute with a state estimation method, so that the dynamics of the error system is exponentially mean-square stable and satisfies a prescribed disturbance attenuation level. Sufficient conditions for the solvability of such a problem are established by employing the Lyapunov function and stochastic analysis techniques. Estimator gain is described explicitly in terms of certain linear matrix inequalities. Finally, the effectiveness of the proposed state estimation scheme is proved by a numerical example.

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

AbstractIn this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two‐time‐scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time‐scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one‐directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.

Hybrid domain decomposition filters for advection–diffusion PDEs with mobile sensors

This paper examines one aspect of computational control, namely the reduction of computational load for the real-time estimation of distributed parameter systems over large spatial domains. One way to improve the performance of the state estimator is to employ a small number of mobile devices that are free to move within the spatial domain while collecting process information. Another way is to use numerical methods to reduce the computational load as dictated by the discretization index of the finite dimensional representation of the filter. This is done via the use of domain decomposition methods and the domain decomposition filter is presented here for the first time along with its well-posedness. In the subdomain surrounding the sensor a refined grid is used as it improves the spatial resolution, and in the subdomain excluding the vicinity of the sensing device, a naïve observer with coarse grid is used which results in a significant reduction of the computational cost. However, due to the transmission conditions that couple the information between the inner subdomain surrounding the sensor and the outer subdomain excluding the sensor, the filters in the two subdomains implement an information exchange protocol rendering them consensus filters. The two approaches are combined thus resulting in a state estimation scheme where the mobile sensor residing in the inner subdomain carries its own refined grid. Not only is the sensor mobile, but also the refined grid surrounding the sensor is moving along with the sensor. A further reduction in computational costs is presented in the form of a hybrid DD filter wherein the filter kernel is rendered sparse thus ensuring that no residual measurement signals enter as disturbance signals in the naïve observer defined over the outer subdomain. Extensive simulation studies of a 2D PDE with realistic parameters are included to demonstrate the proposed hybrid DD filter.

State estimation of a three-inline space tethered system with geometric constraints

Space tethered system (STS) has attracted wide attention recently because of its promising application potential. Accurate state estimation of the STS with topology reconfiguration is challenging because of the rigid-flexible coupling dynamics and large-amplitude tether librations. This paper proposes a novel state estimation scheme for the three-inline STS using only two low-cost GPS sensors. The proposed scheme is built on a new dynamics model, two low-cost GPS sensors, and the time-varying tether length constraints using pseudo measurements (PM). The use of geometric constraints helps enhance the filter performance and reduces the number of the needed sensors. Furthermore, the observability of the system is proved based on Lie derivatives and the feasibility of the proposed scheme is verified through the numerical simulations.

Distributed nonsynchronous event-triggered state estimation of genetic regulatory networks with hidden Markovian jumping parameters.

In this paper, the distributed state estimation problem of genetic regulatory networks (GRNs) with hidden Markovian jumping parameters (HMJPs) is explored. Furthermore, in order to improve the communication efficiency among state estimation sensors, the event-triggered strategy is employed in the distributed framework for sensor networks. Particularly, by considering the fact that the true modes are always unaccessible, a novel nonsynchronous state estimation (NSE) strategy is utilized based on observed hidden mode information. By means of Lyapunov-Krasovski method, sufficient stochastic state estimation analysis and synthesis results are established, such that the concentrations of mRNA and protein in GRNs can be both well estimated by convex optimization. Finally, an illustrative example with relevant simulations results is provided to validate the applicability and effectiveness of the developed state estimation approach.

Radix-Partition-Based Over-the-Air Aggregation and Low-Complexity State Estimation for IoT Systems Over Wireless Fading Channels

We consider remote state estimation for an internet-of-things (IoT) system, where a number of distributed IoT sensors monitor a dynamic plant and deliver the state measurements to a remote state estimator over an unreliable wireless network. We propose novel radix-partition-based over-the-air aggregation to coordinate the transmissions of the IoT sensors, which strongly enhances the spectral efficiency of radio resources and enables a smaller state estimation mean square error (MSE) at the remote state estimator, taking into consideration the quantization effect and radio resource allocation for the IoT sensors. We consider a fixed-filtering design at the remote state estimator, which significantly reduces the signal processing overhead at the remote state estimator compared to using the conventional Kalman-filtering-based state estimation approach. We show that the proposed low-complexity state estimation scheme enables state estimation stability via the linear matrix inequality (LMI) technique for on-off fading channels and via Lyapunov stability analysis for random fading channels. Based on this, we further propose efficient algorithms for the offline design of the filtering gain, connection topology and radix representation for IoT systems. Numerical results show that the proposed scheme has superior scalability performance and can achieve a smaller state estimation MSE compared to various state-of-the-art baselines.

Nonlinear Reduced DNN Models for State Estimation

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

Efficient state estimation strategies for stochastic optimal control of financial risk problems

<abstract><p>In this paper, a financial risk model, which is formulated from the risk management process of financial markets, is studied. By considering the presence of Gaussian white noise, the financial risk model is reformulated as a stochastic optimal control problem. On this basis, two efficient computational approaches for state estimation, which are the extended Kalman filter (EKF) and unscented Kalman filter (UKF) approaches, are applied. Later, based on the state estimate given by the EKF and UKF approaches, a linear feedback control policy is designed from the stationary condition. For illustration, some parameter values and the initial conditions of the financial risk model are used for the simulation of the stochastic optimal control problem. From the results, it is noticed that the UKF algorithm provides a better state estimate with a smaller value of the sum of squared errors (SSE) as compared to the SSE given by the EKF algorithm. Thus, the estimated output trajectory has a high accuracy that is close to the real output. Moreover, the control effort assists in estimating the state dynamics at the minimum cost. In conclusion, the efficiency of the computational approaches for optimal control of the financial risk model has been well presented.</p></abstract>

An MHE-based MPC strategy for simultaneous energy generation maximization and water level management in inland waterways

This paper proposes a combined control and state estimation strategy for inland waterways, aiming at simultaneously attaining the optimal water level management and maximizing hydroelectricity generation. The latter can be realized by turbines installed in canal locks that harness the energy generated during lock filling and draining operations. These two objectives are of opposed nature, as maximization of energy generation can be achieved by maximizing the number of lock operations, which in turn leads to unbalanced water levels upstream and downstream of the lock. To address this issue, the multi-objective optimization problem is formulated . Then, model predictive control (MPC) and moving horizon estimation (MHE) are designed to maintain navigation conditions in the canals while maximizing energy production. Finally, the proposed strategy is applied to a realistic case study based on part of the inland waterways in the north of France.

A Flexible Top-Down Data-Driven Stochastic Model for Synthetic Load Profiles Generation

The study of the behavior of smart distribution systems under increasingly dynamic operating conditions requires realistic and time-varying load profiles to run comprehensive and accurate simulations of power flow analysis, system state estimation and optimal control strategies. However, due to the limited availability of experimental data, synthetic load profiles with flexible duration and time resolution are often needed to this purpose. In this paper, a top-down stochastic model is proposed to generate an arbitrary amount of synthetic load profiles associated with different kinds of users exhibiting a common average daily pattern. The groups of users are identified through a preliminary Ward’s hierarchical clustering. For each cluster and each season of the year, a time-inhomogeneous Markov chain is built, and its parameters are estimated by using the available data. The states of the chain correspond to equiprobable intervals, which are then mapped to a time-varying power consumption range, depending on the statistical distribution of the load profiles at different times of the day. Such distributions are regarded as Gaussian Mixture Models (GMM). Compared with other top-down approaches reported in the scientific literature, the joint use of GMM models and time-inhomogeneous Markov chains is rather novel. Furthermore, it is flexible enough to be used in different contexts and with different temporal resolution, while keeping the number of states and the computational burden reasonable. The good agreement between synthetic and original load profiles in terms of both time series similarity and consistency of the respective probability density functions was validated by using three different data sets with different characteristics. In most cases, the median values of synthetic profiles’ mean and standard deviation differ from those of the original reference distributions by no more than ±10% both within a typical day of each season and within the population of a given cluster, although with some significant outliers.

Simultaneous and sequential state and parameter estimation using receding-horizon nonlinear Kalman filter

Online estimation of internal states and parameters is often required for process monitoring, fault diagnosis and real time optimization. The conventional approach to tracking drifting parameters is to model their variations as a random walk process and estimate them simultaneously with the states. However, tuning of the random walk model is not a trivial exercise. Recently, moving window based simultaneous state and parameter estimation schemes have been proposed under the assumption that the parameters change slowly and remain constant within the window. These formulations make use of the conventional recursive Bayesian estimators or moving horizon estimator (MHE) for state estimation. While simultaneous smoothing of states along with filtering gives an edge to MHE over the conventional recursive estimators, MHE is computation intensive scheme. Recently, developed Receding-horizon Nonlinear Kalman (RNK) filter combines advantages of MHE (simultaneous smoothing) and recursive estimators (less computation time). In this work, we extend the RNK formulation to carry out simultaneous state and parameter estimation schemes under the assumption that parameters change at a slow rate and remain constant within the RNK window. Two maximum likelihood (ML) based parameter estimation schemes are developed by constructing partial likelihood and complete likelihood functions. Both formulations are further extended under the Bayesian framework to derive their maximum a-posteriori (MAP) versions by incorporating prior information of the parameters. The only tuning parameter in the proposed parameter estimation schemes is the window size, which is relatively easy to select. The efficacies of the proposed formulations are evaluated using simulation studies on two reactor systems and experimental data obtained from the benchmark quadruple tank system. Simulation studies reveal that the complete likelihood based estimation schemes have an edge over the partial likelihood based estimation schemes. Also, the proposed estimation schemes generate reasonably accurate state and parameter estimates with a significant reduction in the average computation time.

Set-membership-based distributed moving horizon estimation of large-scale systems

This work is concerned with the design of a two-step distributed state estimation scheme for large-scale systems in the presence of unknown-but-bounded disturbances and noise. The set-membership approach is employed to construct a compact set containing the states consistent with system measurements and bounded noise and disturbances. The tightened feasible region is then provided to a moving horizon estimator that determines the optimal state estimates. Partitioning of the overall problem and coordination of the resulting subproblems are achieved using decomposition of the optimality conditions and community detection. The proposed strategy is tested on a case study based on a reactor–separator system widely used in the literature. Its performance is compared to those of centralized and distributed (without set-membership) implementations, allowing to highlight its effectiveness.