A local sigma-point unscented Kalman filter for geophysical data assimilation

Herein, the purpose is to present a Kalman filter based on the sigma point unscented transformation development, aiming at real-time satellite orbit determination using GPS measurements. First, a brief review of the extended Kalman filter will be done. After, the sigma point Kalman filter will be introduced as well as the basic idea of the unscented transformation, in which this filter is based. Following, the unscented Kalman filter applied to orbit determination will be explained. Such explanation encloses formulations about the orbit determination through GPS; the dynamic model; the observation model; the unmodeled acceleration estimation; also an application of this new filter approaches on orbit determination using GPS measurements discussion.

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Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems

Journal of the Atmospheric Sciences ◽

10.1175/2008jas2681.1 ◽

2009 ◽

Vol 66 (2) ◽

pp. 261-285 ◽

Cited By ~ 37

Author(s):

Jaison Thomas Ambadan ◽

Youmin Tang

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Kalman Filters ◽

Joint Estimation ◽

Sigma Point ◽

Strongly Nonlinear ◽

Data Assimilation Scheme ◽

Higher Dimensional ◽

Highly Nonlinear ◽

Assimilation Scheme

Abstract Performance of an advanced, derivativeless, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The results of SPKF data assimilation schemes are compared with those of standard EKF and EnKF, in which a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments showed that in all cases the SPKF can give consistent results with better assimilation skills than EnKF and EKF and can overcome the drawbacks associated with the use of EKF and EnKF.

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Comment on “Highly Efficient Sigma Point Filter for Spacecraft Attitude and Rate Estimation”

Mathematical Problems in Engineering ◽

10.1155/2012/170391 ◽

2012 ◽

Vol 2012 ◽

pp. 1-5 ◽

Cited By ~ 4

Author(s):

Baiqing Hu ◽

Lubin Chang ◽

An Li ◽

Fangjun Qin

Keyword(s):

Kalman Filter ◽

Unscented Kalman Filter ◽

Orthogonal Transformation ◽

Spacecraft Attitude ◽

Integration Formula ◽

Dynamic Problems ◽

Numerical Accuracy ◽

Symmetrical Structure ◽

Sigma Point ◽

Construction Strategy

In light of the intuition that a better symmetrical structure can further increase the numerical accuracy, the paper by Fan and Zeng (2009) developed a new sigma point construction strategy for the unscented Kalman filter (UKF), namely, geometric simplex sigma points (GSSP). This comment presents a different perspective from the standpoint of the numerical integration. In this respect, the GSSP constitutes an integration formula of degree 2 with equal weights. Then, we demonstrate that the GSSP can be derived through the orthogonal transformation from the basic points set of degree 2. Moreover, the method presented in this comment can be used to construct more accurate sigma points set for certain dynamic problems.

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Comments on “Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems”

Journal of the Atmospheric Sciences ◽

10.1175/2009jas3245.1 ◽

2009 ◽

Vol 66 (11) ◽

pp. 3498-3500 ◽

Cited By ~ 17

Author(s):

Thomas M. Hamill ◽

Jeffrey S. Whitaker ◽

Jeffrey L. Anderson ◽

Chris Snyder

Keyword(s):

Kalman Filter ◽

Nonlinear Systems ◽

Data Assimilation ◽

Sigma Point ◽

Strongly Nonlinear

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Hybrid consensus sigma point approximation nonlinear filter using statistical linearization

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217691758 ◽

2018 ◽

Vol 40 (8) ◽

pp. 2517-2525 ◽

Cited By ~ 12

Author(s):

Guoqing Wang ◽

Ning Li ◽

Yonggang Zhang

Keyword(s):

Kalman Filter ◽

Unscented Kalman Filter ◽

Nonlinear Filter ◽

Statistical Linearization ◽

Nonlinear Functions ◽

Central Difference ◽

Sigma Point ◽

Point Approximation ◽

Cubature Kalman Filter ◽

Central Difference Kalman Filter

In this paper, a hybrid consensus sigma point approximation nonlinear filter is proposed for state estimation in collaborative sensor network, where hybrid consensus of both measurement and information is utilised. Statistical linearization of nonlinear functions is used in sigma point filters, that is, unscented Kalman filter (UKF), cubature Kalman filter (CKF), and central difference Kalman filter (CDKF). Stability of the proposed algorithm is also analysed with the help of linearization operation and some conservative assumptions. Two typical target tracking examples are used to demonstrate the effectiveness of the proposed algorithms. Simulation results show that the proposed algorithms are more stable than existing algorithms, and among our proposed algorithms, CKF- and CDKF-based algorithms are more accurate and stable than the UKF-based one.

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