A new form of the smooth variable structure filter with a covariance derivation

A multilayered neural network is a multi-input, multi-output (MIMO) nonlinear system in which training can be regarded as a nonlinear parameter estimation problem by estimating the network weights. In this paper, the relatively new smooth variable structure filter (SVSF) is used for the training of a nonlinear multilayered feed forward network. The SVSF is a recursive sliding mode parameter and state estimator that has a predictor-corrector form. Using a switching gain, a corrective term is calculated to force the network weights to converge to within a neighbourhood of the optimal weight values. SVSF-based trained neural networks are used to classify engine faults on the basis of vibration data. Two faults are induced in a four-stroke, eight-cylinder engine. Furthermore, a comparative study between the popular back propagation method, the extended Kalman filter (EKF), and the SVSF is presented. Experimental results indicate that the SVSF is comparable with the EKF, and both methods outperform back propagation. © 2011 IEEE.

Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

As a new-style filter, the smooth variable structure filter (SVSF) has attracted significant interest. Based on the predictor-corrector method and sliding mode concept, the SVSF is more robust in the face of modeling errors and uncertainties compared to the Kalman filter. Since the estimation performance is usually insufficient in real cases where the measurement vector is of fewer dimensions than the state vector, an improved SVSF (ISVSF) is proposed by combining the existing SVSF with Bayesian theory. The ISVSF contains two steps: firstly, a preliminary estimation is performed by SVSF. Secondly, Bayesian formulas are adopted to improve the estimation for higher accuracy. The ISVSF shows high robustness in dealing with modeling uncertainties and noise. It is noticeable that ISVSF could deliver satisfying performance even if the state of the system is undergoing a sudden change. According to the simulation results of target tracking, the proposed ISVSF performance can be better than that obtained with existing filters.

ABSTRACTThe aim of this paper is to present a cooperative simultaneous localization and mapping (CSLAM) solution based on a laser telemeter. The proposed solution gives the opportunity to a group of unmanned ground vehicles (UGVs) to construct a large map and localize themselves without any human intervention. Many solutions proposed to solve this problem, most of them are based on the sequential probabilistic approach, based around Extended Kalman Filter (EKF) or the Rao-Blackwellized particle filter. In our work, we propose a new alternative to avoid these limitations, a novel alternative solution based on the smooth variable structure filter (SVSF) to solve the UGV SLAM problem is proposed. This version of SVSF-SLAM algorithm uses a boundary layer width vector and does not require covariance derivation. The new algorithm has been developed to implement the SVSF filter for CSLAM. Our contribution deals with adapting the SVSF to solve the CSLAM problem for multiple UGVs. The algorithms developed in this work were implemented using a swarm of mobile robots Pioneer 3–AT. Two mapping approaches, point-based and line-based, are implemented and validated experimentally using 2D laser telemeter sensors. Good results are obtained by the Cooperative SVSF-SLAM algorithm compared with the Cooperative EKF-SLAM.

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.

Signal processing techniques are prevalent in a wide range of fields: Control, target tracking, telecommunications, robotics, fault detection and diagnosis, and even stock market analysis, to name a few. Although first introduced in the 1950s, the most popular method used for signal processing and state estimation remains the Kalman filter (KF). The KF offers an optimal solution to the estimation problem under strict assumptions. Since this time, a number of other estimation strategies and filters were introduced to overcome robustness issues, such as the smooth variable structure filter (SVSF). In this paper, properties of the SVSF are explored in an effort to detect and diagnosis faults in an electromechanical system. The results are compared with the KF method, and future work is discussed.

In the design of vehicle stability control (VSC) systems for ground vehicles, sideslip angle plays a vital role and its estimation has long been an active research topic. Accurate estimation of sideslip angle is more difficult for lightweight vehicles (LWVs) because their parameters are prone to significant changes with loading conditions — the amount and position of the payload. In this paper, a robust sideslip angle estimator based on a recently emerging smooth variable structure filter (SVSF) is presented. This sideslip angle estimator is suitable for LWVs because it is almost non-sensitive to the changes of the system parameters. A four-state vehicle lateral dynamic model including a pseudo-Burckhardt tire model is employed in the filter design. Compared with the widely utilized extended Kalman filter (EKF), the SVSF shows much better robustness against modeling errors. It is also more favorable in terms of tuning effort and computational speed. Simulation studies were conducted based on a high-fidelity vehicle model in CarSim®, where the vehicle took the form of a lightweight electric ground vehicle with independent in-wheel motors. The performance of the SVSF was shown by comparisons against the EKF under different settings for model parameters.

The background subtraction is a widely used approach for Detecting Moving Objects (DMO) by a static camera using a simple algorithm; however, it is very sensitive to the local gradual changes of illumination, shadows, non-rigid moving objects and partial or full target occlusion. In order to overcome these issues, and to bring more potential to the solution, we propose an effective method for object detection based on active contour with camera motion compensation. The principle of active contours is to evolve an initial curve towards the object of interest that corresponds to the boundaries of the moving objects. Once the object has been detected, then it can be tracked by the Kalman filter. This latter requires many preassumptions about models and noise characteristics. As an alternative, a new method based on the Smooth Variable Structure Filter (SVSF) is implemented. The SVSF was introduced in an effort to provide a more robust estimation strategy. Detection and tracking algorithms require stable images to recognize a real moving target position. Therefore, the captured image from cameras which are placed on the moving platform, have undesired jitters, shakes and blurs. Video stabilization becomes an indispensable technique which is focusing on removing unnecessary camera vibrations from image sequences using a homographic matrix by extracting features using FAST corner detector and FREAK feature descriptor. The proposed algorithm is validated in real-world and the obtained results confirm the efficiency and robustness of our approach.

Design of zonotopic space interpolation-based smooth variable structure filter for systems with unknown but bounded noise.

In this paper, a study of estimation strategies based on variable structure and sliding mode theory is performed. The smooth variable structure filter (SVSF) and the new sliding innovation filter (SIF) are based on similar sliding mode concepts but with some notable differences. The relevant literature and background are explored and the SVSF and SIF estimation algorithms are presented. For comparison purposes, the two estimation strategies are applied on a mechatronic system. The results indicate that although both the SVSF and SIF provide robust estimates to faults, the SIF formulation provides slightly more accurate estimates while maintaining robustness, and is less computationally complex.

Parameter estimation is an important concept that can be used for health and condition monitoring. Estimation or measurement of physically meaningful parameters and their evaluation against predetermined thresholds allows detection of gradual or abrupt deteriorations in the plant. This early detection of faults enables preventative unscheduled maintenance that is of benefit to industries concerned with reliability and safety. In this paper, a recently proposed state estimation strategy referred to as the smooth variable structure filter (SVSF) is reviewed and extended to parameter estimation. The SVSF is applied to a novel hydrostatic actuation system referred to as the electrohydraulic actuator (EHA). Condition monitoring of the EHA for preventative unscheduled maintenance would increase its safety in applications pertaining to aerospace and would reduce its operational and maintenance costs.

The most popular and well-studied estimation method is the Kalman filter (KF), which was introduced in the 1960s. It yields a statistically optimal solution for linear estimation problems. 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. This article discusses the application of two estimation strategies (the KF and the SVSF) on a multi-target tracking problem.

A nonlinear second-order filtering strategy for state estimation of uncertain systems

Unmanned Aerial Vehicles (UAVs) dynamics modeling and parameter estimation has recently occupied great interest due to their vast use in military, civilian, industrial and agricultural applications. Accurate Online UAV parameter estimation is essential for robust autonomous control design. This study presents two different online UAV parameter estimation methods; the smooth variable structure filter (SVSF) method and the recursive least squares (RLS) method. This work presents the application of the SVSF method; including chattering signal's information which previously was applied to linear models, over a nonlinear dynamics model. Moreover, the work presents a simulation study to assess the performance of the methods in terms of accuracy and speed of convergence when applied to estimate the parameters of a general Quadrotor dynamics model. The better method might be considered for deployment in an experimental UAV parameter estimation project under run by the authors.

The use of hybrid (HEVs) and electric vehicles(EVs) has become more prevalent around the world in the last decade. These vehicles commonly use lithium-ion batteries due to their high energy density. They also utilize battery management systems (BMSs), which rely on continuous real-time monitoring and control, to ensure safe operation. The BMS acquires accurate State Of Charge (SOC) and State Of Health (SOH) estimates. For these, battery models that are identified and updated at various states of life from new to aged are required. In this paper, a dual strategy for both parameter and SOC estimation is proposed using a third-order equivalent circuit-based battery model (OCVR-3RC). The strategy employs a square-root recursive least squares (SR-RLS) method to identify the parameters related to SOC. The smooth variable structure filter (SVSF) is then used as an estimation strategy for obtaining the battery SOC. The efficacy of the proposed algorithm is verified by applying it to experimental data from an extensive aging test.