State Augmentation Method Research Articles

A zonotope-based fault detection method for switched systems with parameter uncertainties and multiple time delays

This paper studies fault detection for discrete-time switched systems with parameter uncertainties and time delays. First, a state augmentation method is presented to decouple the effect of time delays. Then, a novel residual generator structure based on priori state estimation is introduced, and the adaptive thresholds for residual evaluation are computed via zonotope techniques. Meanwhile, peak-to-peak performance and H− performance are adopted to design the residual generator, ensuring both uncertainty robustness and fault sensitivity. Finally, numerical simulation results are provided to demonstrate the effectiveness and superiority of the proposed method.

State augmentation method for non-stationary/non-Gaussian vibrations of multi degree-of-freedom linear systems

The basic assumptions of stationary/Gaussian excitations and temporal independence in linear systems are commonly employed in stochastic dynamic analyses, facilitating various engineering investigations. However, in certain scenarios such as wind-induced vibrations under non-synoptic extreme wind, these assumptions may lead to unreliable predictions. The excitations exhibit significant non-stationary/non-Gaussian features due to the inherent non-synopticity of the flow. Moreover, when accounting for motion-induced forces, the coupled aerodynamic-mechanical system is modeled as a linear time-varying system marked by time-dependent aerodynamic damping and stiffness. This study aims to introduce a state augmentation method for examining the multi-modal vibrations of a long-span bridge excited by non-synoptic winds. Both unsteady motion-induced forces and non-stationary/non-Gaussian turbulence-induced forces are considered to predict the buffeting response. Based on stochastic calculus theory and the stars and bars method, we derive equations governing the statistical moments of all orders for the response of a dynamic system with multiple degrees of freedom. A comprehensive buffeting analysis of the model bridge to all wind segments of Typhoon Hagupit is conducted by using the proposed method, showing potentially greater responses when considering the non-synoptic features of the wind.

Event-Triggered Robust Fusion Estimation for Multi-Sensor Time-Delay Systems with Packet Drops

This paper investigates the robust fusion estimation problem for multi-sensor systems with communication constraints, parameter uncertainty, d-step state delays, and deterministic control inputs. The multi-sensor system consists of a fusion center and some sensor nodes with computational capabilities, between which there are random packet drops. The state augmentation method is utilized to transform a time-delay system into a non-time-delay one. The robust state estimation algorithm is derived based on the sensitivity penalty for each sensor node to reduce the impact of modelling errors, and modelling errors here are not limited to a unique form, which implies that the fusion estimator applies to a wide range of situations. An event-triggered transmission strategy has been adopted to effectively alleviate the communication burden from the sensor node to the fusion center. Moreover, the fusion estimator handles packet drops arising from unreliable channels, and the corresponding pseudo-cross-covariance matrix is provided. Some conditions are given to ensure that the estimation error of the robust fusion estimator is uniformly bounded. Two sets of numerical simulations are provided to illustrate the effectiveness of the derived fusion estimator.

State augmentation method for buffeting responses of wind-sensitive structures in wind environments with large turbulence intensity

Recent studies have shown that wind fields with large turbulence intensity are frequently observed in non-synoptic winds such as typhoons and hurricanes. The quadratic terms of the fluctuating wind speed are important for calculating buffeting responses of wind-sensitive structures under high turbulence. In this study, a moment-based method, which is called the state augmentation method, is used to obtain high-order response moments and avoid the large computational cost of the high-order frequency domain method. First, the buffeting force formula with nonlinear velocity terms is established, and the Non-Gaussian buffeting force is further approximated as a polynomial of the Ornstein–Uhlenbeck (OU) process. Then, an augmented state vector is introduced to express the relationship between the statistical moments of each order, and the 1st to 4th response moments can be solved sequentially by a particular set of linear equations. Finally, the extreme responses of a single-degree-of-freedom (SDOF) tower and a long-span suspension bridge are calculated as engineering examples. By comparing the computation results with the frequency method, it is proven that this moment-based method has a sufficient accuracy in analysing quadratic terms. The calculation results also show that quadratic terms under high turbulence significantly amplify the non-Gaussian peak factor and extreme responses.

Research on the angular velocity estimation method based on the state augmentation method

In the maneuvering target tracking research due to the unpredictability of the target’s maneuvering, it makes it difficult to establish an accurate target motion model to reflect the real motion trajectory of the target. Based on the determination of the parametric maneuver model and the radar measurement conditions of the target, the joint estimation method of the motion state and the maneuver parameters is designed to obtain the optimal estimation of the motion state and the maneuver parameters based on the optimal evaluation criteria. Currently, in the descriptive category of the state space model, the state augmentation method is obtained to solve the joint estimation of the motion state and maneuver parameters based on the estimation criterion [1]. Therefore, the angular velocity estimation method of the state augmentation method is used to consider the estimated value of the target angular velocity and the estimated variance comprehensively to improve the convergence speed of target tracking, minimize the error between the filtered angular velocity and the real angular velocity of the maneuvering target, and finally achieve the purpose of improving the target tracking accuracy.

SA-HPMHT for Maritime Dim Targets Tracking With Sensor Location Uncertainty

To address the problem of tracking low signal-to-clutter ratio (SCR) maritime targets with sensor location uncertainty, an effective track-before-detect (TBD) method, called the state augmentation histogram probabilistic multihypothesis tracking (SA-HPMHT) algorithm, is proposed in this article. In this algorithm, the initialization of new tracks is realized based on the constant false alarm rate (CFAR) detector with a low threshold and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -means clustering algorithm. The target and sensor states are then simultaneously estimated in an iterative manner via a synthetic histogram and state augmentation (SA) method. In each iteration, we update the estimated sensor state and yield more accurate measured images, allowing for improved performance of detection and tracking targets. Finally, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}/{N}$ </tex-math></inline-formula> logic technology is invoked to confirm or terminate the tracks. The results of simulation and real dataset verification show that the SA-HPMHT algorithm has a better performance compared with the histogram probabilistic multihypothesis tracking (H-PMHT) algorithm and the sequential Monte Carlo probability hypothesis density (SMC-PHD) algorithm.

Robust state estimation for uncertain linear discrete systems with d‐step measurement delay and deterministic input signals

AbstractIn this study, the state estimation problems for linear discrete systems with uncertain parameters, deterministic input signals and d‐step measurement delay are investigated. A robust state estimator with a similar iterative form and comparable computational complexity to the Kalman filter is derived based on the state augmentation method and the sensitivity penalisation of the innovation process. It is discussed that the steady‐state properties such as boundedness and convergence of the robust state estimator under the assumptions that the system parameters are time invariant. Numerical simulation results show that compared with the Kalman filter, the obtained state estimator is more robust to modelling errors and has nice estimation accuracy.

Improved state augmentation method for buffeting analysis of structures subjected to non-stationary wind

Extreme winds such as hurricanes and thunderstorms often present non-stationary characteristics, having time-varying mean wind speeds and non-stationary wind fluctuations. When concerning the wind-induced vibrations under non-stationary wind, the excitation will be a non-stationary process, and the wind-structure coupled system can be represented by a linear time-varying (LTV) system. The aim of this study is to present a state augmentation method to investigate the non-stationary buffeting of a model bridge tower subjected to non-stationary wind with consideration of the aeroelastic damping. Based on the theory of stochastic differential equations and Itô’s lemma, the statistical moments of the non-stationary buffeting response are derived through solving a first-order ordinary differential equation system. The proposed method is validated by comparisons with the Monte Carlo method and the pseudo excitation method. The result shows that the state augmentation method has higher accuracy and efficiency than the well-accepted time–frequency techniques.

Simultaneous Identification and Correction of Multiple Network Parameter Errors by Mixed-Effects Models

Accurate parameter values are essential for the secure and stable operation of power systems. Parameters may be erroneous in real power systems, while existing methods may provide false results in the case of multiple interacting parameter errors. This paper proposes an LME-HTI method for the simultaneous identification of multiple parameter errors based on a linear mixed-effects (LME) model and hypothesis testing identification (HTI). The residual equations from multiple-snapshot state estimation are used to formulate the LME model in which the parameter errors are considered as the fixed effects and the measurement errors are considered as the random effects. By solving the LME model, all the parameter errors and the variances of the measurement errors can be simultaneously estimated. Then, hypothesis testing is performed to infer whether each parameter error is zero. An extended state augmentation (ESA) method is proposed to further remove the misidentified but correct parameters from the suspicious parameter set while correcting the left erroneous parameters by constrained nonlinear optimization. In this way, only a limited number of parameters with strong evid

Robust State Estimation for Uncertain Discrete Linear Systems with Delayed Measurements

Measurement delays and model parametric uncertainties are meaningful issues in actual systems. Addressing the simultaneous existence of random model parametric uncertainties and constant measurement delay in the discrete-time linear systems, this study proposes a novel robust estimation method based on the combination of Kalman filter regularized least-squares (RLS) framework and state augmentation. The state augmentation method is elaborately designed, and the cost function is improved by considering the influence of modelling errors. A recursive program similar to the Kalman filter is derived. Meanwhile, the asymptotic stability conditions of the proposed estimator and the boundedness conditions of its error covariance are analyzed theoretically. Numerical simulation results show that the proposed method has a better processing capability for measurement delay and better robustness to model parametric uncertainties than the Kalman filter based on nominal parameters.

State Estimation With a Destination Constraint Imposed by Proportional Navigation Guidance Law

Proportional navigation (PN) guidance laws have been commonly applied to homing missile systems guiding the missile to its target. When the target is stationary and its location is known a priori, the state of the missile is subjected to a destination constraint, which contains extra information on missile state that can help increase tracking performance. This article concerns with the constraint modeling and the state estimation with a destination constraint imposed by PN guidance law in 3-D space. Constraint models corresponding to three representative PN guidance laws: pure PN, true PN, and generalized PN, are presented using the state augmentation method, which stacks the states at the previous and current time steps in one state vector to express the constraint relationships. For cases where the destination information is noisy and the parameters of the guidance law, i.e., the navigation constant and the bias angle, are not known a priori, the unknown parameters are estimated along with the missile state in the state vector in an augmentation way. Based on the formulations of constraint models, the construction of pseudomeasurements is carried out. A constrained state estimation method is proposed by incorporating the pseudomeasurements into the nonlinear filtering process. In this method, a sequential process framework is employed and the cubature Kalman filter is used to handle the high-dimensional filtering problem and the strong nonlinearity involved in pseudomeasurements. Numerical experiments in three scenarios are performed to demonstrate the validity of the proposed models along with the estimation method.

Non-Gaussian turbulence induced buffeting responses of long-span bridges based on state augmentation method

Traditionally, the structural turbulence-induced buffeting vibrations is analyzed along the famous Davenport chain through turbulence, wind loads and structural response based on one fundamental assumption: the random processes about the above three subsequent stages should be all Gaussian process. This assumption simplifies the mathematical derivation of turbulence-induced vibration, and were widely used in field of wind engineering for structures. However, several recent studies reveal that turbulence with non-Gaussian distribution is observed in the boundary-layer atmosphere during wind storm events, especially typhoons or hurricanes. For the turbulence-induced vibration, traditional Gaussian assumption may lead to non-conservative results, especially for non-Gaussian turbulence with positive skewness. Based on the state augmentation method, this paper derives formulations to calculate the moments of buffeting response. The non-Gaussian turbulence-induced buffeting forces are approximated by Hermite polynomials of the underlying Gaussian process, modeled as Ornstein–Uhlenbeck process in the state augmentation method. The state augmentation method is verified for bridge buffeting vibration caused by Gaussian turbulence, and the approximation of buffeting force by the Ornstein–Uhlenbeck process is also validated. Applying the state augmentation method on the bridge buffeting response excited by non-Gaussian turbulence, the corresponding bridge buffeting response RMS, skewness and kurtosis can be computed sequentially. The results show that the RMS of buffeting responses induced by non-Gaussian turbulence is slightly higher than Gaussian turbulence results. However, the extreme responses are greatly affected by the skewness of non-Gaussian turbulence.

Optimal H2 filtering for measurement‐delay systems with multiplicative noise and sampled data

AbstractThis paper is concerned with the optimal H2 filtering problem for continuous‐time systems with multiplicative noise and multiple sampled delay measurements. The reorganized observation technique is firstly applied for treating the sampled delay terms, and then an equivalent delay‐free sampled measurement is received. An optimal H2 filter is constructed by using a dynamic model with finite jumps, which can provide the state estimation of the measurement sampling interval as well as the measurement sampling moments. The filter gain is given in terms of the stabilizing solution to a set of specific Riccati differential equations. It should be pointed out that no state augmentation is required, and thus the Riccati equation developed in this paper remain the same dimension as that of the original system state. This is the clear distinction from the state augmentation method. A practical example is finally supplied to illustrate the efficiency of the proposed results.

Comparison of ensemble data assimilation methods for the estimation of time-varying soil hydraulic parameters

The hydraulic properties of the soil top layer may change during the growth period due to various factors such as wetting and drying cycles, tillage practices, and crop root growth. In this study, the potential of the assimilation method to estimate time-varying soil hydraulic parameters is explored. Four assimilation schemes, including the simultaneous update state augmentation method, the partitioned update state augmentation method, the simultaneous update parameter correction method, and the partitioned update parameter correction method, are compared. The performance of four assimilation schemes on parameter estimations and soil moisture simulations is tested first using the synthetic case. The influence of initial parameter values and a parameter update order on assimilation is also analyzed. Finally, the partitioned update parameter correction method is applied to a real case involving a field drip irrigation experiment. The results show that when the analyzed parameter has either a periodical or a linear variation, there is a time lag between the assimilation value and the true value. The assimilation method can respond immediately to an abrupt change of the parameter value. Using the simultaneous update method leads to an obvious parameter correlation problem. In contrast, the partitioned update method can relieve the parameter correlation problems, thereby improving the accuracy of parameter estimations and pressure head simulations. However, when the initial values of the parameters deviate from their true values to a certain extent, the partitioned update method cannot obtain accurate parameter estimations. Compared with the partitioned update state augmentation method, the partitioned update parameter correction method is not sensitive to the parameter update order. The partitioned update parameter correction method has higher computational efficiency and assimilation stability, and it can obtain more accurate parameter estimations and soil moisture predictions in comparison with the traditional state augmentation method. The partitioned update parameter correction method provides an assimilation tool for improving the predictions of soil moisture by considering the time-varying parameters.

A variational Bayesian approximation based adaptive single beacon navigation method with unknown ESV

The localization performance of single beacon navigation system is affected by the accuracy of effective sound velocity (ESV) which is difficult to precisely know. The state augmented method and expectation–maximization (EM) based method, the two existing state-of-the-art single beacon navigation methods which can deal with the unknown ESV, are sensitive to the noise statistic parameters and vehicle initial position offset, respectively. This paper proposes a variational Bayesian (VB) approximation based adaptive single beacon navigation method to deal with these deficiencies. The ESV is treated as a random variable with unknown statistic parameters, and the state vector, ESV and ESV uncertainty parameters are simultaneously estimated by VB approximation. Numerical studies indicate that the proposed VB approximation based navigation method can overcome the deficiencies of both state augmented and EM-based navigation methods, achieve better localization and ESV estimation performance than the existing state-of-the-art methods.

Distributed output feedback control for multi-unit system with delayed multirate measurements

The aim of this work is to analyze output feedback distributed control framework based on model predictive control (MPC) for multi-unit systems with multirate and delayed measurements. Primary controlled variable(s) is sampled infrequently, and the measurement is available after a delay. The distributed, unit-specific estimators and controllers communicate through selective information transfer based on process knowledge. The distributed state estimator is designed based on sampled state augmentation method to efficiently compute improved state estimates on arrival of the delayed infrequent measurements. The multirate estimators are appropriately modified to incorporate the disturbance model to handle model-plant mismatch (MPM). The proposed implementation is analyzed using two case studies. A linearized, reactor-separator system is used to demonstrate that multirate estimation is required for offset-free tracking. A more complex variant of the reactor-separator system with recycle demonstrates the ability of nonlinear distributed estimator-MPC framework to incorporate infrequent and delayed primary measurements.

Method for joint estimation for states and parameters concerning non‐linear systems with time‐correlated measurement noise

A dimensionality-reduction-augmented non-linear state–space representation has been proposed to reduce the optimisation space for maximum-likelihood estimation. Based on the above representation, an expectation–maximisation algorithm has been derived to realise joint estimation of states and parameters. During the expectation step, the system state was estimated via the use of a fifth-order cubature Kalman filter and Rauch–Tung–Striebel smoother based on the state-augmented method. During the maximisation step, unknown parameters within iterations were estimated using the Newton method. Subsequently, two joint-estimation methods – one containing all measurements and the other involving a sliding window – were developed to estimate the invariants and step parameters, respectively. An example concerning manoeuvring-target tracking has been discussed to demonstrate the performance of proposed algorithms.

A Fast-Initial Alignment Method With Angular Rate Aiding Based on Robust Kalman Filter

In this paper, a fast-initial alignment method with angular rate aiding based on robust Kalman filter is proposed. First, the traditional system model of the initial alignment is derived, and the angular rate aiding method in the navigation frame is studied. To address the defects of the traditional angular rate aiding alignment method, the angular rate aiding method in body frame is derived. Then, a state augmentation method is employed to address the correlation between process noise and the measurement noise, which exists in the angular rate aiding methods. Considering the practical application, it is hard to keep completely still when the initial alignment is carried out on the vehicle. Therefore, a Huber's M-estimation has been adopted to eliminate the external interferences, and the robustness of the proposed method has been improved. Then, an analytical method for the observability of the proposed method is studied. The reason why the proposed method is faster than the traditional method is analyzed in detail. Finally, simulated and field tests are designed to validate the performance of the proposed method. The results show that the proposed method can finish the initial alignment when it is carried on the vehicle.

Research on Measurement Error Model of GNSS/INS Integration Based on Consistency Analysis

Kalman filter is widely taken as an optimal fusion algorithm in GNSS/INS integration, and GNSS positioning error is often simply modeled as white noise in a loosely-coupled system. But many research results have shown that GNSS positioning error has the characteristic of temporal correlation. Correct error model of Kalman filter can ensure that the level of estimated accuracy is equal to that of actual accuracy. Inaccurate model will influence the consistency between estimated accuracy and actual integrated accuracy. Moreover, quality control method based on variance-covariance with inconsistency is not reliable and not utilized to detect gross errors. So, this paper mainly researches on GNSS positioning and velocity error model and its impact on quality control in GNSS/INS integration. In this paper, state-augmentation method is applied to solve the problems of GNSS colored noise to ensure the navigation accuracy consistency, and the rationality of the improved model is verified by the effect of quality control. Simulation and field test results show that state-augmentation method can improve the consistency between actual error and estimation standard deviation, and satisfy the requirement of quality control based on variance-covariance to improve the integration reliability.

Underwater localization using single beacon measurements: Observability analysis for a double integrator system

This paper addresses the observability analysis for the single beacon localization problem of an Autonomous Underwater Vehicle (AUV) modeled as a double integrator where its input is the acceleration in an inertial reference frame and its output (measurement) is its range to a stationary beacon. The nonlinear map between range and position makes the range-based observability problem inherently nonlinear. The observability analysis here proposed addresses two complementary issues: the local weak observability for the nonlinear system, and the global observability for a linear time varying representation of the system derived through a state augmentation method. The proposed methods for observability analysis are discussed in different case studies (e.g. 2D/3D, absence/presence of current, and presence of additional sensors like a Doppler Velocity Logger or a depth gauge). Two different state observers, i.e., an Extended Kalman Filter for the nonlinear system, and a Kalman Filter for the system with augmented state are designed: their performances are analyzed through numerical simulations while validating the derived observability properties.