Showing papers on "Invariant extended Kalman filter published in 2019"

Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function

Abstract: This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using th...

On constrained integrated total Kalman filter for integrated direct geo-referencing

Abstract: A constrained integrated total Kalman filter algorithm is developed. It considers a quadratic constraint which may appear in some problems of integrated direct geo-referencing in particular when IN...

A stochastic well-test analysis on transient pressure data using iterative ensemble Kalman filter

Abstract: Accurate estimation of the reservoir parameters is crucial to predict the future reservoir behavior. Well testing is a dynamic method used to estimate the petro-physical reservoir parameters through imposing a rate disturbance at the wellhead and recording the pressure data in the wellbore. However, an accurate estimation of the reservoir parameters from well-test data is vulnerable to the noise at the recorded data, the non-uniqueness of the obtained match, and the accuracy of the optimization algorithm. Different stochastic optimization methods have been applied to this address problem in the literature. In this study, we apply the recently developed iterative ensemble Kalman filter in the context of well-test analysis to infer reservoir parameters from the noisy recorded data. Since the introduction of the ensemble Kalman filter (EnKF) by Evensen in 1994 as a novel method for data assimilation, it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. While the objective of the standard EnKF approaches is to approximate the statistical properties of geological parameters conditioned to observation, via an ensemble, the objective of the iterative ensemble Kalman methods is to approximate the solution of inverse problems using a deterministic derivative-free iterative scheme. We conducted three case studies of the application of the iterative ensemble Kalman methods for a well-test analysis of a homogenous reservoir model, a dual-porosity heterogeneous system, and a faulted discontinuous reservoir. We demonstrated that the convergence occurs very rapidly almost at the first iterations contrary to the well-known particle swarm optimization algorithm. The maximum relative error for the simulated cases is below 15%, which belongs to the skin factor. Low relative error, narrowed uncertainty range over time, and excellent graphical match obtained between the simulated derivative data and the generated curve by using the iterative EnKF verify the robustness of the developed algorithm even in dealing with complex heterogeneous models.

Robust estimation of linear state space models

Abstract: The model parameters of linear state space models are typically estimated with maximum likelihood estimation, where the likelihood is computed analytically with the Kalman filter. Outliers ...

A higher-order robust correlation Kalman filter for satellite attitude estimation

Abstract: A higher-order robust correlation Kalman filtering approach is presented to achieve attitude estimation for satellites with unknown modeling errors. A robust correlation Kalman filter (RCKF) is preliminarily derived by using the sequence orthogonal principle. To improve its performance further, a higher-order sigma version of the RCKF is designed by incorporating a novel sigma point generation algorithm. This modified filter can capture the third and the fourth central moment's information of the system posteriori probability density function. It is proved that the proposed filter achieves better estimation accuracy and robustness. The effectiveness of the developed filter is demonstrated by simulation results with it applied to the satellite attitude estimation problem.

An Invariant Extended H ∞ Filter

Abstract: This paper presents an invariant extended ${\mathcal{H}_\infty }$ filter for position and attitude estimation on the matrix Lie group SE (2). Extended ${\mathcal{H}_\infty }$ filtering results are adapted to work directly within a matrix Lie group framework in an analogous way to how the invariant extended Kalman filter (IEKF) adapts the standard extended Kalman filter (EKF) to work within a matrix Lie group framework. The principal advantage of the invariant extended ${\mathcal{H}_\infty }$ filter over the extended ${\mathcal{H}_\infty }$ filter is that the linearization of the state and measurement models is independent of the current state estimate, leading to state-independent Jacobians at any linearization point. Moreover, for the SE (2) problem considered, the invariant extended ${\mathcal{H}_\infty }$ filter realizes a substantially lower minimum performance bound γ than the standard extended ${\mathcal{H}_\infty }$ filter.

Invariant Extended Kalman Filter Applied to Tracking for Air Traffic Control

Abstract: In this paper, a recent target model expressed in intrinsic coordinates and based on the Frenet-Serret frame is reviewed. The associated variant of the EKF suited to track the corresponding state, and called the Invariant Extended Kalman Filter (IEKF) is also reviewed. Our main contribution is to apply those recent tools to Air Traffic Control (ATC) situations. For ATC application, a good precision on the velocity vector is critical, especially its direction (i.e., the heading of the plane), to display a coherent view of the situation in the sky to the operator. This filter is implemented in a realistic ATC tracking chain to test the algorithm under realistic conditions, when inserted in the complete tracking pipeline. The new filter proposed is then compared to an Extended Kalman Filter (EKF) with a constant velocity target model, which is fairly simple but widely used in practice for ATC. We show the results are improved, especially during turns .

Invariant Sliding Window Filtering for Attitude and Bias Estimation

Abstract: This paper considers sliding window filtering in an invariant framework for estimation of attitude and rate gyro bias in a matrix Lie group formulation. The multiplicative extended Kalman filter (MEKF) and invariant extended Kalman filter (IEKF), variants of the extended Kalman filter well suited to estimation on matrix Lie groups, are discussed. The sliding window formulation of both the MEKF and IEKF is presented, leading to the sliding window filter (SWF), the invariant SWF (ISWF), and the imperfect ISWF for systems that are not group affine. Simulation results for an attitude and heading reference system with bias are presented, comparing the ISWF to the traditional $\mathbf{SWF,}$ MEKF, and IEKF.

Invariant observer design of attitude and heading reference system

Abstract: An attitude and heading reference system (AHRS) is a nonlinear state estimator unit for computing orientation in 3D space. This paper designs an AHRS using three approaches: an invariant observer, an invariant extended Kalman filter (IEKF), and a conventional extended Kalman filter (EKF). The three designs are validated in experiment versus a ground truth, demonstrating the practical interest of the invariant observer methodology and the advantage of the IEKF over the EKF under model uncertainty.

LQG/LTR procedure using reduced-order Kalman filters

Abstract: This paper discusses a linear-quadratic-Gaussian/loop transfer recovery (LQG/LTR) procedure using reduced-order Kalman filters by extending known exact-recovery result. The state-space realisation commonly used for reduced-order observer design is employed. The zero structure intrinsic to the realisation is revealed. Asymptotic recovery is achieved using a non-singular reduced-order Kalman filter with a parameterised set of covariance matrices. The proposed procedure provides a systematic method for directly designing reduced-order LQG controllers without additional coordinate transformations. A numerical design example for a simple multivariable plant is presented to compare the proposed design with the standard LQG/LTR design using a full-order Kalman filter.

A double laser filtering approach to vibration noise rejection for hot-rolled strip flatness measurement

Abstract: This paper proposes a new filtering method based on the Kalman filtering algorithm for hot-rolled strip flatness measurement system. The system involves processing slowly changing signal, which can be considered as a bounded random process, and its model parameters are completely unknown. The noise rejection strategy in double lasers can generate a compensation signal. Since the initial and accumulative error would lead to negative filter effect or even cause divergence, Kalman filter is integrated to effectively deal with the initial error and enhance convergence. In this setting, the noise rejection strategy is used as a prediction model to constitute a similar Kalman filter. The correlated error caused by measurement error is coped with by a compensation model based on the feature of correlated error to enhance the filter effect. Both theoretical analysis and simulations show that the new algorithm has a better filter effect than the traditional Kalman filtering algorithm for the system.

Inequality Constrained State-Space Models

Abstract: The standard Kalman filter cannot handle inequality constraints imposed on the state variables, as state truncation induces a nonlinear and non-Gaussian model. We propose a Rao-Blackwellized partic...

Invariant extended Kalman filter on matrix Lie groups

Abstract: We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. The proposed IEKF differs from existing techniques in literature on the account that it is derived using minimal tools from differential geometry that simplifies its representation and derivation to a large extent. The filter error dynamics is defined on the Lie algebra directly instead of identifying the Lie algebra with an Euclidean space or defining the error dynamics in local coordinates using exponential map, and the associated differential Riccati equations are described on the corresponding space of linear operators using tensor algebra. The proposed filter is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control, and its performance is compared against a conventional extended Kalman filter (EKF). Numerical experiments support that the IEKF is computationally less intensive and gives better performance than the EKF.

A fault tolerant attitude estimation architecture with GLR-based disturbance rejection

Abstract: This paper presents an architecture for fault tolerant attitude estimation systematically handling common attitude sensor faults and perturbations. The solution is posed as a filtering architecture composed of four distinct parts: The first stage serves to estimate the sensor outputs and provide fault sensitive residuals. The second stage is a fault detection and rejection stage based on $\chi^{2}$ - and Generalized Likelihood Ratio (GLR) tests. The third stage consolidates the measurements and activates or deactivates the attitude correction. The fourth and final stage is an Invariant Extended Kalman filter (IEKF) with a saturated bias model and local decoupling of the inclination and heading estimation. A series of flight tests with a multi-rotor drone subject to severe magnetic perturbations and inertial accelerations shows the resilience of the attitude estimation to sensor faults as compared to classical approaches.