Kalman Filters

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Fanghui Liu - One of the best experts on this subject based on the ideXlab platform.

  • Kalman Filters for linear continuous time fractional order systems involving coloured noises using fractional order average derivative
    Iet Control Theory and Applications, 2018
    Co-Authors: Chao Yang, Zhe Gao, Fanghui Liu
    Abstract:

    In this study, Kalman Filters for continuous-time linear fractional-order systems are studied with fractional-order coloured process and measurement noise, respectively. By fractional-order average derivative, linear fractional-order systems with coloured fractional-order process or measurement noise are discretised. To deal with coloured noises, the authors construct an augmented system with respect to the state, the process noise and the measurement noise. Furthermore, fractional-order Kalman filter using the fractional-order average derivative is proposed. This filter improves the accuracy of the state estimation and the filtering effect for coloured process and measurement noises. Finally, they give two examples to verify the correctness and validity of the proposed algorithm.

Zhe Gao - One of the best experts on this subject based on the ideXlab platform.

  • reduced order Kalman filter for a continuous time fractional order system using fractional order average derivative
    Applied Mathematics and Computation, 2018
    Co-Authors: Zhe Gao
    Abstract:

    Abstract This paper investigates two kinds of reduced order Kalman Filters for a continuous-time fractional-order system with uncorrelated and correlated process and measurement noises. The fractional-order average derivative is adopted to enhance the discretization accuracy for the investigated continuous-time fractional-order system. The uncorrelated and correlated cases for the process and measurement noises are treated by the reduced order Kalman Filters to achieve the robust estimation for a part of states of a fractional-order system. The truncation issue is considered to implement the practical application of the proposed state estimation algorithm. Finally, two examples for uncorrelated and correlated noises are offered to verify the effectiveness of the proposed reduced order Kalman Filters.

  • Kalman Filters for linear continuous time fractional order systems involving coloured noises using fractional order average derivative
    Iet Control Theory and Applications, 2018
    Co-Authors: Chao Yang, Zhe Gao, Fanghui Liu
    Abstract:

    In this study, Kalman Filters for continuous-time linear fractional-order systems are studied with fractional-order coloured process and measurement noise, respectively. By fractional-order average derivative, linear fractional-order systems with coloured fractional-order process or measurement noise are discretised. To deal with coloured noises, the authors construct an augmented system with respect to the state, the process noise and the measurement noise. Furthermore, fractional-order Kalman filter using the fractional-order average derivative is proposed. This filter improves the accuracy of the state estimation and the filtering effect for coloured process and measurement noises. Finally, they give two examples to verify the correctness and validity of the proposed algorithm.

Waldemar Leite C Filho - One of the best experts on this subject based on the ideXlab platform.

  • on the error state selection for stationary sins alignment and calibration Kalman Filters part ii observability estimability analysis
    Sensors, 2017
    Co-Authors: Felipe O Silva, Elder M Hemerly, Waldemar Leite C Filho
    Abstract:

    This paper presents the second part of a study aiming at the error state selection in Kalman Filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

  • on the error state selection for stationary sins alignment and calibration Kalman Filters part i estimation algorithms
    Aerospace Science and Technology, 2017
    Co-Authors: Felipe O Silva, Elder M Hemerly, Waldemar Leite C Filho
    Abstract:

    Abstract This paper presents the first part of a study aiming at error state selection in Kalman Filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). Estimation algorithms are derived through the analytical manipulation of the full SINS error model, thereby enabling us to investigate the dynamic coupling existing between the state variables. As contributions of this work, we demonstrate that the vertical velocity error is very important for the estimation of almost all error states. Latitude and altitude errors, in turn, are shown to uniquely affect the inertial sensor bias estimates. Besides, the longitude error is found to be totally detached from the system. As straightforward consequence, Bar-Itzhack and Berman's error model turns out to be inadequate for real implementations, and a 12-state Kalman filter is shown to be the optimal error state selection for SSAC purposes. Simulated and experimental tests confirm the adequacy of the outlined conclusions.

Chao Yang - One of the best experts on this subject based on the ideXlab platform.

  • Kalman Filters for linear continuous time fractional order systems involving coloured noises using fractional order average derivative
    Iet Control Theory and Applications, 2018
    Co-Authors: Chao Yang, Zhe Gao, Fanghui Liu
    Abstract:

    In this study, Kalman Filters for continuous-time linear fractional-order systems are studied with fractional-order coloured process and measurement noise, respectively. By fractional-order average derivative, linear fractional-order systems with coloured fractional-order process or measurement noise are discretised. To deal with coloured noises, the authors construct an augmented system with respect to the state, the process noise and the measurement noise. Furthermore, fractional-order Kalman filter using the fractional-order average derivative is proposed. This filter improves the accuracy of the state estimation and the filtering effect for coloured process and measurement noises. Finally, they give two examples to verify the correctness and validity of the proposed algorithm.

Henrique M. T. Menegaz - One of the best experts on this subject based on the ideXlab platform.

  • unscented Kalman Filters for riemannian state space systems
    IEEE Transactions on Automatic Control, 2019
    Co-Authors: Henrique M. T. Menegaz, Joao Y. Ishihara, Hugo T M Kussaba
    Abstract:

    Unscented Kalman Filters (UKFs) have become popular in the research community. Most UKFs work only with Euclidean systems, but in many scenarios it is advantageous to consider systems with state-variables taking values on Riemannian manifolds . However, we can still find some gaps in the literature's theory of UKFs for Riemannian systems: for instance, the literature has not yet developed first, Riemannian extensions of some fundamental concepts of the UKF theory (e.g., extensions of $\sigma$ -representation, unscented transformation, additive UKF, augmented UKF, additive-noise system), second, proofs of some steps in their UKFs for Riemannian systems (e.g., proof of sigma points parameterization by vectors, state correction equations, noise statistics inclusion), and third, relations between their UKFs for Riemannian systems. In this paper, we attempt to develop a theory capable of filling these gaps. Among other results, we propose Riemannian extensions of the main concepts in the UKF theory (including closed forms), justify all steps of the proposed UKFs, and provide a framework able to relate UKFs for particular manifolds among themselves and with UKFs for Euclidean spaces. Compared with UKFs for Riemannian manifolds of the literature, the proposed Filters are more consistent, formally principled, and general. An example of satellite attitude tracking illustrates the proposed theory.

  • unscented Kalman Filters for riemannian state space systems
    arXiv: Optimization and Control, 2018
    Co-Authors: Henrique M. T. Menegaz, Joao Y. Ishihara, Hugo T M Kussaba
    Abstract:

    Unscented Kalman Filters (UKFs) have become popular in the research community. Most UKFs work only with Euclidean systems, but in many scenarios it is advantageous to consider systems with state-variables taking values on Riemannian manifolds. However, we can still find some gaps in the literature's theory of UKFs for Riemannian systems: for instance, the literature has not yet i) developed Riemannian extensions of some fundamental concepts of the UKF theory (e.g., extensions of $\sigma$-representation, Unscented Transformation, Additive UKF, Augmented UKF, additive-noise system), ii) proofs of some steps in their UKFs for Riemannian systems (e.g., proof of sigma points parameterization by vectors, state correction equations, noise statistics inclusion), and iii) relations between their UKFs for Riemannian systems. In this work, we attempt to develop a theory capable of filling these gaps. Among other results, we propose Riemannian extensions of the main concepts in the UKF theory (including closed forms), justify all steps of the proposed UKFs, and provide a framework able to relate UKFs for particular manifolds among themselves and with UKFs for Euclidean spaces. Compared with UKFs for Riemannian manifolds of the literature, the proposed Filters are more consistent, formally-principled, and general. An example of satellite attitude tracking illustrates the proposed theory.

  • Unscented Kalman Filters for Estimating the Position of an Automotive Electronic Throttle Valve
    IEEE Transactions on Vehicular Technology, 2016
    Co-Authors: Alessandro N. Vargas, Henrique M. T. Menegaz, Joao Y. Ishihara, Leonardo Acho
    Abstract:

    This paper presents an application of unscented Kalman Filters (UKFs) to an automotive electronic throttle device. The motivation of this study is on estimating the position of the throttle device when measurements of the position are inaccessible, e.g., due to failures in the sensor of position. In this case, an external wattmeter is connected in the circuitry to measure the power consumed by the throttle, and this information feeds UKFs to produce the estimation for the position. Experimental data support the findings of this paper. Almost all of the brand-new vehicles based on spark-ignition combustion engines have an electronic throttle valve to control the power produced by the engine. The electronic throttle has a unique sensor for measuring the position of the throttle valve, and this feature can represent a serious problem when the sensor of position fails. As an attempt to prevent the effects of a failure from such a sensor, we present an algorithm (UKF) combined with the use of an additional sensor, i.e., a wattmeter. The wattmeter is detached from the throttle's structure but is arranged to measure the electric power consumed by the throttle. Measurements of the power consumption then feed the UKF. This filter then produces an estimation of the position of the throttle valve. Experimental data illustrate the practical benefits of our approach.