Robust adaptive smooth variable structure Kalman filter for spacecraft attitude estimation

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.

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.

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.

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.

State and parameter estimation is important for the control of systems, particularly when not all of the system information is available for the designer. Filters are used to extract state information from measurements, which are typically corrupted by noise. A common measure of the performance of an estimate by a filter is through the use of a covariance matrix. This essentially provides a measure of the error in the estimate. Furthermore, knowledge of this covariance can lead to a more accurate derivation and greater number of applications for the filter. Introduced in 2007, the smooth variable structure filter (SVSF) is a relatively new filter. It is a predictor-correct estimator based on sliding mode control and estimation. In its current form, the SVSF is not a classical filter in the sense that it does not have a covariance matrix. This paper introduces the SVSF in a new form without affecting its original proof of stability, and outlines the derivation of a covariance matrix that can be used for comparative purposes as well as other applications. A linear mechanical system referred to as an electrohydrostatic actuator (EHA) is used to numerically demonstrate the new SVSF. The results are compared with the classical Kalman filter (KF), which is the most common and efficient filtering strategy for linear systems.

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

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

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.

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.

This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete‐time system with unknown disturbance, the AIEKF algorithm adopts the Gauss‐Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch‐mode combination technique is used to achieve the adaptive capability. The mean‐square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.

State estimation of river system includes the flow and stage estimation and used in the estimation of the final sensor's velocity which is proportional to the river velocity. The estimation process includes the system model and measurements. The measurements can be carried out using Eulerian sensor or Lagrangian sensor. The Lagrangian sensor is considered in this research since it able to observe the overall system compared to the Eulerian sensor that perform measurement in fixed position. Besides that, the estimation can be carried out using DA method such as Extended Kalman Filter (EKF) and Particle Filter (PF). The Smooth Variable Structure Filter (SVSF) is introduced to give better response in terms of error reduction by having convergence rate and the smoothing boundary layer width. The convergence analysis of SVSF shows the effectiveness of the proposed method in terms of mathematical representation. The simulation results proved the SVSF have better response compared to the forward simulation, EKF and PF. This shown by 25.6% for RMSE, 25.92% for SD, 15.34% for MAE and the computational time is reduced by 95.51 % if compared with PF.

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.

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.

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.