Extended Set-membership Filter Research Articles

A novel ESMF-based observer and control scheme for a type of tendon-sheath hysteresis system

Due to the backlash hysteresis, robust and accurate tracking control of a hysteresis system is a challenging problem. We propose in this paper an active observer based robust control scheme to reject the influence of hysteresis. Firstly, the normal piecewise C–H model of hysteresis plant was modified into a continuous form so that an active observer could be applied on. Secondly, an observer was designed based on the extended set-membership filter (ESMF). This intends to take the advantages of ESMF on the bound-guaranteed estimation and the unknown but bounded (UBB) noise tolerance. Thirdly, a robust controller was constructed using both the magnitude and the bounds of the hysteresis uncertainty estimated by the observer. The stability of the control scheme was theoretically proved. Experiments were conducted on a robotic flexible ureteroscope test-bed. The performance of the modified model, the ESMF-based observer, and the robust control were extensively verified, and the improvements benefited from this proposed scheme were demonstrated.

Automatic brain tumour diagnostic method based on a back propagation neural network and an extended set-membership filter

BackgroundDiagnosing brain tumours remains a challenging task in clinical practice. Despite their questionable accuracy, magnetic resonance image (MRI) scans are presently considered the optimal facility for assessing the growth of tumours. However, the efficiency of manual diagnosis is low, and high computational cost and poor convergence restrict the application of machine learning methods. This study aims to design a method that can reliably diagnose brain tumours from MRI scans. MethodsFirst, image pre-processing (which includes background removal, size standardization, noise removal, and contrast enhancement) is utilized to normalize the images. Then, grey level co-occurrence matrix features are selected as texture features of the brain MRI scans. Finally, a method combining a back propagation neural network (BPNN) and an extended set-membership filter (ESMF) is proposed to classify features and perform image classification. ResultsA total of 304 patient MRI series (247 images of brains with tumours and 57 images of normal brains) were included and assessed in this study. The results revealed that our proposed method can achieve an accuracy of 95.40% and has classification accuracies of 97.14% and 88.24% for brain tumour and normal brain, respectively. ConclusionThis study proposes an automatic brain tumour detection model constructed using a combination of BPNN and ESMF. The model is found to be able to accurately classify brain MRI scans as normal or tumour images.

Robust Estimation of Vehicle Motion States Utilizing an Extended Set-Membership Filter

Reliable vehicle motion states are critical for the precise control performed by vehicle active safety systems. This paper investigates a robust estimation strategy for vehicle motion states by feat of the application of the extended set-membership filter (ESMF). In this strategy, a system noise source is only limited as unknown but bounded, rather than the Gaussian white noise claimed in the stochastic filtering algorithms, such as the unscented Kalman filter (UKF). Moreover, as one part of this strategy, a calculation scheme with simple structure is proposed to acquire the longitudinal and lateral tire forces with acceptable accuracy. Numerical tests are carried out to verify the performance of the proposed strategy. The results indicate that as compared with the UKF-based one, it not only has higher accuracy, but also can provide a 100% hard boundary which contains the real values of the vehicle states, including the vehicle’s longitudinal velocity, lateral velocity, and sideslip angle. Therefore, the ESMF-based strategy can proffer a more guaranteed estimation with robustness for practical vehicle active safety control.

The iterated extended set membership filter applied to relative localization between autonomous vehicles based on GNSS and UWB ranging

AbstractThis paper presents a novel Iterated Extended Set Membership Filter (IESMF) with an application to relative localization. For safe operation of formations of automatic vehicles, consistent uncertainty estimates are of crucial importance. Here, a localization filter that provides ellipsoidal regions that are guaranteed to contain another vehicles position is presented. The proposed iterative update step can appreciably reduce the size of the a posteriori state ellipsoid. The idea of using SIVIA as a baseline to quantify conservativeness is introduced. Another novelty is that we take into account parametric uncertainty of the observation equation.The proposed filter is applied to a two unmanned aircraft systems (UAS) localization problem in simulation with observation noise obtained from real sensors. Simulation results illustrate the effective reduction of filter conservativeness by a small number of iterative updates.

Set value‐based dynamic model development for non‐linear manoeuvring target tracking problem in the presence of unknown but bounded disturbances

The stochastic models developed for the manoeuvring target tracking (MTT) problem do not exhibit good performance owing to the lack of sufficient information about uncertainties. Moreover, each of the MTT models can be used for limited target manoeuvres. An ‘unknown but bounded’ (UBB)-based non-linear dynamic model for modelling time-dependent acceleration and model uncertainties is proposed for addressing the aforementioned problems. In the UBB approach, uncertainties and target manoeuvre are modelled using information about their upper bounds only. The extended set membership filter can be used to estimate the target states and manoeuvre with this new dynamic model. In order to examine the stability of the proposed method, the input to state stability of the estimation error is analysed. Very good performance is achieved by the proposed dynamic model without precise information about the model uncertainties. The proposed MTT algorithm can be used to track both non-manoeuvring and manoeuvring targets. The theoretical development is verified using simulations and the results are compared with those of other MTT methods. These comparisons demonstrate that the performance of the proposed method is better.

Experimental Investigation for RUAV's Actuator Fault Detections with AESMF

The adaptive extended set-membership filter (AESMF) algorithm for robots' online modelling is today proposed for use in this field. Compared to the traditional ESMF, this novel filter method improves estimation accuracy under variable boundaries of unknown but bounded (UBB) process noise, which is often caused by the uncertainties of robotic dynamics. However, the applicability and stability of the AESMF method have not been tested in detail or demonstrated for real robotic systems. In this research, AESMF is applied for the actuator fault detections of a rotor-craft unmanned air vehicle (RUAV). The stability of AESMF is firstly analysed using mathematics and actuator healthy coefficients (AHC) are introduced for building the actuator failure model of RUAVs. AESMF is employed for the online boundary estimation of flight states and AHC parameters for fault tolerance control. Based on the proposed AESMF actuator fault estimation, flight experiments are conducted using a ServoHeli-40 RUAV platform and the flight results are compared with traditional ESMF and the adaptive extended Kalman filter (AEKF) in order to demonstrate its effectiveness, as well as for suggesting improvements for the actuator failure detection of RUAVs.

Simultaneous State and Parameter Estimation Based Actuator Fault Detection and Diagnosis for an Unmanned Helicopter

Abstract Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD) for single-rotor unmanned helicopters (UHs) is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs), which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed into a general nonlinear estimation one: given control inputs and the measured flight state contaminated by measurement noises, estimate both the flight state and AHCs recursively in each time-step, which is also known as the simultaneous state and parameter estimation problem. The estimated AHCs can further be used for fault tolerant control (FTC). Based on the existing widely used nonlinear estimation methods such as the unscented Kalman filter (UKF) and the extended set-membership filter (ESMF), three kinds of adaptive schemes (KF-UKF, MIT-UKF and MIT-ESMF) are proposed by our team to improve the actuator FDD performance. A comprehensive comparative study on these different estimation methods is given in detail to illustrate their advantages and disadvantages when applied to unmanned helicopter actuator FDD.

Extended set-membership filter for power system dynamic state estimation

A new method for power system dynamic state estimation is presented. It is based on the application of the extended set-membership filter (ESMF). The ESMF provides an on-line nonlinear guaranteed estimation that assumes that noise sources are unknown but bounded, rather than stochastic as in probabilistic estimation algorithms such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Thus, the ESMF provides 100% confidence to the estimated states for the safety and reliability of power systems. In this paper, the ESMF is derived and demonstrated by using two different single machine infinite bus (SMIB) systems. The performance of the ESMF is compared with the classical UKF by using one SMIB system modeled as a second-order nonlinear dynamic equation. The feasibility of the ESMF method with unknown inputs is also presented on the other SMIB system, in which the exciter output voltage may be unavailable but bounded. The ESMF method is also tested on a multi-machine system model to demonstrate its effectiveness.

A New Nonlinear Set Membership Filter Based on Guaranteed Bounding Ellipsoid Algorithm

The framework of set membership filter (SMF) with unknown-but-bounded noise assumption provides an attractive alternative for probabilistic filters. However, the potential computational burden and conservation consideration may seriously limit the usage of this filter in practical applications. In this paper, based on guaranteed bounding ellipsoid approximation, a new enhanced set membership filter with better real-time property and reduced conservation is proposed for state estimation problem of nonlinear systems. The nonlinear model is firstly linearized and the DC programming method is used to outer-bound the linearization error, which is incorporated to the model noise with ellipsoidal approximations. A classical two-step prediction-correction procedure consisting vector sum computation between ellipsoids and an iterative outer-bounding ellipsoid algorithm to intersect ellipsoid with strip is presented to compute the ellipsoidal feasible set of the estimated states. Simulation results with comparisons to the nonlinear extended set membership filter are given to demonstrate the effectiveness and improved performances of our proposed algorithm.

A MIT-Based Nonlinear Adaptive Set-Membership Filter for the Ellipsoidal Estimation of Mobile Robots' States

The adaptive extended set-membership filter (AESMF) for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method-based adaptive set-membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time-varying states and parameters. As a result of using the proposed MIT-AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.

An Active Cooperative Observation Method for Multi-robots in Three Dimensional Environments

The solution to multiple mobile robot systems actively and cooperatively observing a moving target (MACO) means the algorithm that tries to pursuit optimal (sub-optimal) observations of the moving target by simultaneously fusing the observational data from multiple robot systems and regulating their behaviors cooperatively. In this paper, the 3D MACO method with two robots is studied. First, at the basis of extended set-membership filter (ESMF), a high precise observation fuse method is presented through combining the information fuse process and the set operations in ESMF algorithm. The new algorithm is as fast as the single ESMF algorithm since it has almost the same computational burden. Second, a coordinate behavior optimization method is given by combining the concept of optimal observational angle and the relative velocity coordinates (RVC) planning method. By using the RVC method, the coordinate behavior optimization can be transferred into a linear planning (LP) problem, which makes its real time application possible. Finally, 3D moving target observational simulations are conducted to verify the feasibility and validity of the proposed algorithm.

Least trace extended set-membership filter

To improve the consistency of estimation result, a least-trace extended set-membership filter (LTESMF) is presented for a class of nonlinear stochastic systems, which has linear output and unknown-but-bounded noise. Feedback technique is used instead of the intersection of ellipsoid-sets in the measurement update. The feedback parameter is optimized in order to minimize the trace of error bounded ellipsoid’s envelop matrix. A new stability analysis method was developed to prove the stochastic system’s stability by using the convergence of some measurement of the error bounded ellipsoid. Analysis result shows that the estimation error of LTESMF will converge to a bounded area. A simulation of SINS/GPS integrated alignment with large misalignment angles is conducted. The results demonstrate that the convergence speed and the consistency of LTESMF are much better than those of extended Kalman filter (EKF), in addition the steady estimation precision and computational complexity are close to that of EKF.

A UD Factorization-based Adaptive Extended Set-membership Filter

The extended set-membership filter for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity,as well as the difficulty in filter parameter selection.In this paper,a UD factorization-based adaptive set-membership filter is developed and applied to nonlinear joint estimation of both time-varying states and parameters.As a result of using the proposed UD factorization combined with a new sequential and selective measurement update strategy,the numerical stability and real-time applicability of conventional ESMF are substantially improved. Furthermore,an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub-optimal estimation.Simulation results have shown the efficiency and robustness of the proposed method.

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

AbstractThe extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

Simulation and Flight Test of Autonomous Aircraft Estimation, Planning, and Control Algorithms

The development, summary, and validation of real time autonomous estimation, planning, and control algorithms for nonlinear aircraft are presented. Two square root estimation algorithms are developed and used to estimate the state dynamics, parameters, and uncertainty bounds of a nonlinear aircraft in real time. A square root sigma point filter approximates the uncertain state using a finite set of points, while a square root extended set-membership filter bounds the states and parameters of the nonlinear system using ellipsoidal sets. The estimation methods are integrated into online optimized model predictive control methodology for fast reconfigurable control, and a path planner based on streamlines for fast path planning around obstacles and for target pursuit. The performances of the estimation, planning, and control techniques are tested in flight using the SeaScan autonomous aircraft. The SeaScan platform is briefly described, and real time hardware in the loop and flight data are presented for a variety of applications using each of the algorithms.

Bounded Switched Linear Estimator for Smooth Nonlinear Systems

The problem of establishing hard bounds on the state estimate of a nonlinear system using a switching piecewise linear hybrid estimator is addressed. Within an operating region, the proposed hybrid estimator uses a variant of the extended set-membership filter to select piecewise linear models based on minimizing uncertainty. Under certain conditions, analysis shows that the error between the center of the estimated set and the true value is bounded. A priori selection of the base piecewise linear models to guarantee a level of uncertainty is achieved by optimizing the placement of operating points over the operating region. The proposed methods are applied to a complex aircraft example to show its applicability

On‐line estimation and path planning for multiple vehicles in an uncertain environment

AbstractA unified approach to cooperative target tracking and path planning for multiple vehicles is presented. All vehicles, friendly and adversarial, are assumed to be aircraft. Unlike the typical target tracking problem that uses the linear state and nonlinear output dynamics, a set of aircraft nonlinear dynamics is used in this work. Target state information is estimated in order to integrate into a path planning framework. The objective is to fly from a start point to a goal in a highly dynamic, uncertain environment with multiple friendly and adversarial vehicles, without collision. The estimation architecture proposed is consistent with most path planning methods. Here, the path planning approach is based on evolutionary computation technique which is then combined with a nonlinear extended set membership filter in order to demonstrate a unified approach. A cooperative estimation approach among friendly vehicles is shown to improve speed and routing of the path. Copyright © 2004 John Wiley & Sons, Ltd.