Decomposition of the extended Kalman filter

Sastry, V. A.

doi:10.1109/tac.1971.1099709

Cited by 21 publications

(3 citation statements)

References 3 publications

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“…As a linearized approximation method, extended Kalman filtering ( Sastry, 1971 ) is a class of extended form of standard Kalman filtering in nonlinear systems.…”

Section: Extended Kalman Filtering and Multi-sensor Fusion Reviewmentioning

confidence: 99%

A Loosely Coupled Extended Kalman Filter Algorithm for Agricultural Scene-Based Multi-Sensor Fusion

Wei

et al. 2022

Front. Plant Sci.

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With the arrival of aging society and the development of modern agriculture, the use of agricultural robots for large-scale agricultural production activities will become a major trend in the future. Therefore, it is necessary to develop suitable robots and autonomous navigation technology for agricultural production. However, there is still a problem of external noise and other factors causing the failure of the navigation system. To solve this problem, we propose an agricultural scene-based multi-sensor fusion method via a loosely coupled extended Kalman filter algorithm to reduce interference from external environment. Specifically, the proposed method fuses inertial measurement unit (IMU), robot odometer (ODOM), global navigation and positioning system (GPS), and visual inertial odometry (VIO), and uses visualization tools to simulate and analyze the robot trajectory and error. In experiments, we verify the high accuracy and the robustness of the proposed algorithm when sensors fail. The experimental results show that the proposed algorithm has better accuracy and robustness on the agricultural dataset than other algorithms.

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“…As a linearized approximation method, extended Kalman filtering ( Sastry, 1971 ) is a class of extended form of standard Kalman filtering in nonlinear systems.…”

Section: Extended Kalman Filtering and Multi-sensor Fusion Reviewmentioning

confidence: 99%

A Loosely Coupled Extended Kalman Filter Algorithm for Agricultural Scene-Based Multi-Sensor Fusion

Wei

et al. 2022

Front. Plant Sci.

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“…While in reality, the system is usually nonlinear, e.g., robot pose estimation is nonlinear as rotation incorporated. Extended Kalman filter (EKF) [32] approximates the nonlinearity by using the firstorder Taylor expansion. Unscented Kalman filter (UKF) [33] approximates the nonlinearity with unscented transform, which can approximate the nonlinearity with the second order.…”

Section: Related Workmentioning

confidence: 99%

Joint Localization Based on Split Covariance Intersection on the Lie Group

Yang

2021

IEEE Trans. Robot.

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This paper presents a pose fusion method that accounts for the possible correlations among measurements. The proposed method can handle data fusion problems whose uncertainty has both independent part and dependent part. Different from the existing methods, the uncertainties of the various states or measurements are modeled on the Lie algebra and projected to the manifold through the exponential map, which is more precise than that modeled in the vector space. The dealing of the correlation is based on the theory of covariance intersection, where the independent and dependent parts are split to yield a more consistent result. In this paper, we provide a novel method for correlated pose fusion algorithm on the manifold. Theoretical derivation and analysis are detailed first, and then the experimental results are presented to support the proposed theory. The main contributions are threefold: (1) We provide a theoretical foundation for the split covariance intersection filter performed on the manifold, where the uncertainty is associated on the Lie algebra. (2) The proposed method gives an explicit fusion formalism on SE(3) and SE(2), which covers the most use cases in the field of robotics. (3) We present a localization framework that can work both for single robot and multi-robots systems, where not only the fusion with possible correlation is derived on the manifold, the state evolution and relative pose computation are also performed on the manifold. Experimental results validate its advantage over state-of-the-art methods.

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“…This creates numerical instabilities and imprecision within the Kalman (optimal) filtering process. Several studies have been committed to solving these problems, and decomposition of the covariance matrix (the process of breaking down a matrix or its expression into an equivalent product of factors) has been proposed as direction to solving the above mentioned problem (Roncero 2014;Sastry 1971).…”

Section: B Kalman Filtermentioning

confidence: 99%

A Time-Varying Causality Formalism Based on the Liang–Kleeman Information Flow for Analyzing Directed Interactions in Nonstationary Climate Systems

et al. 2019

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The interaction between the land surface and the atmosphere is of significant importance in the climate system because it is a key driver of the exchanges of energy and water. Several important relations to heat waves, floods, and droughts exist that are based on the interaction of soil moisture and, for instance, air temperature and humidity. Our ability to separate the elements of this coupling, identify the exact locations where they are strongest, and quantify their strengths is, therefore, of paramount importance to their predictability. A recent rigorous causality formalism based on the Liang–Kleeman (LK) information flow theory has been shown, both theoretically and in real-world applications, to have the necessary asymmetry to infer the directionality and magnitude within geophysical interactions. However, the formalism assumes stationarity in time, whereas the interactions within the land surface and atmosphere are generally nonstationary; furthermore, it requires a sufficiently long time series to ensure statistical sufficiency. In this study, we remedy this difficulty by using the square root Kalman filter to estimate the causality based on the LK formalism to derive a time-varying form. Results show that the new formalism has similar properties compared to its time-invariant form. It is shown that it is also able to capture the time-varying causality structure within soil moisture–air temperature coupling. An advantage is that it does not require very long time series to make an accurate estimation. Applying a wavelet transform to the results also reveals the full range of temporal scales of the interactions.

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Decomposition of the extended Kalman filter

Cited by 21 publications

References 3 publications

A Loosely Coupled Extended Kalman Filter Algorithm for Agricultural Scene-Based Multi-Sensor Fusion

A Loosely Coupled Extended Kalman Filter Algorithm for Agricultural Scene-Based Multi-Sensor Fusion

Joint Localization Based on Split Covariance Intersection on the Lie Group

A Time-Varying Causality Formalism Based on the Liang–Kleeman Information Flow for Analyzing Directed Interactions in Nonstationary Climate Systems

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