S. A. Gadsden

Kalman and smooth variable structure filters for robust estimation

The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are among the most popular estimation methods. The smooth variable structure filter (SVSF) is a relatively new sliding mode estimator. In an effort to use the accuracy of the EKF and the UKF and the robustness of the SVSF, the filters have been combined, resulting in two new estimation strategies, called the EK-SVSF and the UK-SVSF, respectively. The algorithms were validated by testing them on a well-known target tracking computer experiment.

Combined cubature Kalman and smooth variable structure filtering: A robust nonlinear estimation strategy

In this paper, nonlinear state estimation problems with modeling uncertainties are considered. As demonstrated recently in literature, the cubature Kalman filter (CKF) provides the closest known approximation to the Bayesian filter in the sense of preserving second-order information contained in noisy measurements under the Gaussian assumption. The smooth variable structure filter (SVSF) has also been recently introduced and has been shown to be robust to modeling uncertainties. In an effort to utilize the accuracy of the CKF and the robustness of the SVSF, the CKF and SVSF have been combined resulting in an algorithm referred to as the CK-SVSF. The robustness and accuracy of the CK-SVSF was validated by testing it on two different computer problems, namely, a target tracking problem and the estimation of the effective bulk modulus in an electrohydrostatic actuator.

Kalman filtering strategies utilizing the chattering effects of the smooth variable structure filter

The Kalman filter (KF) remains the most popular method for linear state and parameter estimation. Various forms of the KF have been created to handle nonlinear estimation problems, including the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The robustness and stability of the EKF and UKF can be improved by combining it with the recently proposed smooth variable structure filter (SVSF) concept. The SVSF is a predictor-corrector method based on sliding mode concepts, where the gain is calculated based on a switching surface. A phenomenon known as chattering is present in the SVSF, which may be used to determine changes in the system. In this paper, the concept of SVSF chattering is introduced and explained, and is used to determine the presence of modeling uncertainties. This knowledge is used to create combined filtering strategies in an effort to improve the overall accuracy and stability of the estimates. Simulations are performed to compare and demonstrate the accuracy, robustness, and stability of the Kalman-based filters and their combinations with the SVSF.

A New Robust Filtering Strategy for Linear Systems

For linear and well-defined estimation problems with Gaussian white noise, the Kalman filter (KF) yields the best result in terms of estimation accuracy. However, the KF performance degrades and can fail in cases involving large uncertainties such as modeling errors in the estimation process. The smooth variable structure filter (SVSF) is a relatively new estimation strategy based on sliding mode theory and has been shown to be robust to modeling uncertainties. The SVSF makes use of an existence subspace and of a smoothing boundary layer to keep the estimates bounded within a region of the true state trajectory. Currently, the width of the smoothing boundary layer is chosen based on designer knowledge of the upper bound of modeling uncertainties, such as maximum noise levels and parametric errors. This is a conservative choice, as a more well-defined smoothing boundary layer will yield more accurate results. In this paper, the state error covariance matrix of the SVSF is used for the derivation of an optimal time-varying smoothing boundary layer. The robustness and accuracy of the new form of the SVSF was validated and compared with the KF and the standard SVSF by testing it on a linear electrohydrostatic actuator (EHA).

Comparison of Extended and Unscented Kalman, Particle, and Smooth Variable Structure Filters on a Bearing-Only Target Tracking Problem

In this paper, we study a nonlinear bearing-only target tracking problem using four different estimation strategies and compare their performances. This study is based on a classical ground surveillance problem, where a moving airborne platform with a sensor is used to track a moving target. The tracking scenario is set in two dimensions, with the measurement providing angle observations. Four nonlinear estimation strategies are used to track the target: the popular extended and unscented Kalman filters (EKF/UKF), the particle filter (PF), and the relatively new smooth variable structure filter (SVSF). The SVSF is a predictor-corrector method used for state and parameter estimation. It is a sliding mode estimator, where gain switching is used to ensure that the estimates converge to true state values. An internal model of the system, either linear or nonlinear, is used to predict an a priori state estimate. A corrective term is then applied to calculate the a posteriori state estimate, and the estimation process is repeated iteratively. The performances of these methods applied on a bearing-only target tracking problem are compared in terms of estimation accuracy and filter robustness.

Gaussian filters for parameter and state estimation

Real-time control systems rely on reliable estimates of states and parameters in order to provide accurate and safe control of electro-mechanical systems. The task of extracting state and parametric values from systems partial measurements is referred to as state and parameter estimation. The main goal is minimizing the estimation error as well as maintaining robustness against the noise and modeling uncertainties. The development of estimation techniques spans over five centuries, and involves a large number of contributors from a variety of fields. This paper presents a tutorial on the main Gaussian filters that are used for state estimation of stochastic dynamic systems. The main concept of state estimation is firstly described based on the Bayesian paradigm and Gaussian assumption of the noise. The filters are then categorized into several groups based on their applications for state estimation. These groups involve linear optimal filtering, nonlinear filtering, adaptive filtering, and robust filtering. New advances and trends relevant to each technique are addressed and discussed in detail.

Estimation Strategies for the Condition Monitoring of a Battery System in a Hybrid Electric Vehicle

This paper discusses the application of condition monitoring to a battery system used in a hybrid electric vehicle (HEV). Battery condition management systems (BCMSs) are employed to ensure the safe, efficient, and reliable operation of a battery, ultimately to guarantee the availability of electric power. This is critical for the case of the HEV to ensure greater overall energy efficiency and the availability of reliable electrical supply. This paper considers the use of state and parameter estimation techniques for the condition monitoring of batteries. A comparative study is presented in which the Kalman and the extended Kalman filters (KF/EKF), the particle filter (PF), the quadrature Kalman filter (QKF), and the smooth variable structure filter (SVSF) are used for battery condition monitoring. These comparisons are made based on estimation error, robustness, sensitivity to noise, and computational time.

Model-based fault detection of a battery system in a hybrid electric vehicle

Recently, a new type of interacting multiple model (IMM) method was introduced based on the relatively new smooth variable structure filter (SVSF), and is referred to as the IMM-SVSF. The SVSF is a type of sliding mode estimator that is formulated in a predictor-corrector fashion. This strategy keeps the estimated state bounded within a region of the true state trajectory, thus creating a stable and robust estimation process. The IMM method may be utilized for fault detection and diagnosis, and is classified as a model-based method. In this paper, for the purposes of fault detection, the IMM-SVSF is applied through simulation on a simple battery system which is modeled from a hybrid electric vehicle.

Target Tracking Formulation of the SVSF With Data Association Techniques

An important area of study for aerospace and electronic systems involves target tracking applications. To successfully track a target, state and parameter estimation strategies are used in conjunction with data association techniques. Even after 50 years, the Kalman filter (KF) remains the most popular and well-studied estimation strategy in the field. However, the KF adheres to a number of strict assumptions that leads to instabilities in some cases. The smooth variable structure filter (SVSF) is a relatively new method, which is becoming increasingly popular due to its robustness to disturbances and uncertainties. This paper presents a new formulation of the SVSF. The probabilistic and joint probabilistic data association techniques are combined with the SVSF and applied on multitarget tracking scenarios. In addition, a new covariance formulation of the SVSF is presented based on improving the estimation results of nonmeasured states. The results are compared and discussed with the popular KF method.

State Estimation and Fault Detection of an Electrohydrostatic Actuator

The electrohydrostatic actuator (EHA) is an efficient type of linear actuator commonly found in aerospace applications. It consists of an external gear pump (fluid), an electric motor, a closed hydraulic circuit, a number of control valves and ports, and a linear actuator. An EHA, built for experimentation, is studied in this paper. Two types of estimation strategies, the popular Kalman filter (KF) and the smooth variable structure filter (SVSF), are applied to the EHA for kinematic state and parameter estimation. The KF strategy yields the statistical optimal solution to linear estimation problems. However, the KF becomes unstable when strict assumptions are violated. The SVSF is an estimation strategy based on sliding mode concepts, which brings an inherent amount of stability to the estimation process. Recent advances in SVSF theory include a time-varying smoothing boundary layer. This method, known as the SVSF-VBL, offers an optimal formulation of the SVSF as well as a method for detecting changes or faults in a system. In addition to the application of the KF and SVSF for state estimation, the SVSF-VBL is applied to the EHA for the purposes of fault detection. The EHA is operated under various operating conditions (normal, friction fault, leakage fault, and so on), and the experimental results are presented and discussed.Copyright