Proceedings ArticleDOI
The square-root unscented Kalman filter for state and parameter-estimation
R. van der Merwe,Eric A. Wan +1 more
- Vol. 6, pp 3461-3464
TLDR
The square-root unscented Kalman filter (SR-UKF) is introduced which is also O(L/sup 3/) for general state estimation and O( L/sup 2/) for parameter estimation and has the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.Abstract:
Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.read more
Citations
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Journal ArticleDOI
Unscented filtering and nonlinear estimation
Simon Julier,Jeffrey Uhlmann +1 more
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Journal ArticleDOI
Cubature Kalman Filters
TL;DR: A third-degree spherical-radial cubature rule is derived that provides a set of cubature points scaling linearly with the state-vector dimension that may provide a systematic solution for high-dimensional nonlinear filtering problems.
Book
Kalman Filtering and Neural Networks
TL;DR: This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear.
Sigma-point kalman filters for probabilistic inference in dynamic state-space models
TL;DR: This work has consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.
Journal ArticleDOI
Unscented Filtering for Spacecraft Attitude Estimation
TL;DR: In this paper, an unscented filter is used to estimate the attitude of a spacecraft in the presence of a gyro-based model for attitude propagation, and a multiplicative quaternion-error is derived from the local attitude error, which guarantees that quaternions normalization is maintained in the filter.
References
More filters
Journal ArticleDOI
Numerical Recipes in C: The Art of Scientific Computing
Mary C. Seiler,Fritz A. Seiler +1 more
Proceedings ArticleDOI
New extension of the Kalman filter to nonlinear systems
Simon Julier,Jeffrey Uhlmann +1 more
TL;DR: It is argued that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.
Proceedings ArticleDOI
The unscented Kalman filter for nonlinear estimation
Eric A. Wan,R. van der Merwe +1 more
TL;DR: The unscented Kalman filter (UKF) as discussed by the authors was proposed by Julier and Uhlman (1997) for nonlinear control problems, including nonlinear system identification, training of neural networks, and dual estimation.
Journal ArticleDOI
A state-space approach to adaptive RLS filtering
Ali H. Sayed,Thomas Kailath +1 more
TL;DR: This article is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control.