The Sigma Point Class: The Unscented Kalman Filter

2012 ◽  
pp. 128-139
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Sigma Point ◽  
Point Class

scholarly journals A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Paula Cristiane Pinto Mesquita Pardal ◽  
Helio Koiti Kuga ◽  
Rodolpho Vilhena de Moraes
Keyword(s):  
Kalman Filter ◽  
Dynamic Model ◽  
Extended Kalman Filter ◽  
Orbit Determination ◽  
Unscented Kalman Filter ◽  
Satellite Orbit ◽  
Observation Model ◽  
Gps Measurements ◽  
Unscented Transformation ◽  
Sigma Point

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.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
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.

Hybrid consensus sigma point approximation nonlinear filter using statistical linearization

2018 ◽  
Vol 40 (8) ◽  
pp. 2517-2525 ◽  
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.

scholarly journals Reduced-Rank Sigma-Point Kalman Filter and Its Application in ENSO Model

2014 ◽  
Vol 31 (10) ◽  
pp. 2350-2366 ◽  
Author(s):  
K. K. Manoj ◽  
Youmin Tang ◽  
Ziwang Deng ◽  
Dake Chen ◽  
Yanjie Cheng
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Southern Oscillation ◽  
Estimation Accuracy ◽  
Dimensional System ◽  
Square Root ◽  
Reduced Rank ◽  
Sigma Point ◽  
Enso Events

Abstract The huge computational expense has been a main challenge while applying the sigma-point unscented Kalman filter (SPUKF) to a high-dimensional system. This study focuses on this issue and presents two methods to construct a reduced-rank sigma-point unscented Kalman filter (RRSPUKF). Both techniques employ the truncated singular value decomposition (TSVD) to factorize the covariance matrix and reduce its rank through truncation. The reduced-rank square root matrix is used to select the most important sigma points that can retain the main statistical features of the original sigma points. In the first technique, TSVD is applied on the covariance matrix constructed in the data space [RRSPUKF(D)], whereas in the second technique TSVD is applied on the covariance matrix constructed in the ensemble space [RRSPUKF(E)]. The two methods are applied to a realistic El Niño–Southern Oscillation (ENSO) prediction model [Lamont-Doherty Earth Observatory model, version 5 (LDEO5)] to assimilate the sea surface temperature (SST) anomalies. The results show that both the methods are more computationally efficient than the full-rank SPUKF, in spite of losing some estimation accuracy. When the truncation reaches a trade-off between cost expense and estimation accuracy, both methods are able to analyze the phase and intensity of all major ENSO events from 1971 to 2001 with comparable estimation accuracy. Furthermore, the RRSPUKF is compared against ensemble square root filter (EnSRF), showing that the overall analysis skill of RRSPUKF and EnSRF are comparable to each other, but the former is more robust than the latter.

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