zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new method for the nonlinear transformation of means and covariances in filters and estimators. (English) Zbl 0973.93053

Based on the intuition that it is easier to approximate a probability distribution than it is to approximate an arbitrary nonlinear function or transformation, the authors propose a new approach for applying the linear estimation theory to nonlinear systems. Instead of approximating the Taylor series to an arbitrary order, the paper considers the approximation of the first three moments of the prior distribution accurately, using a set of samples. The proposed algorithm predicts the mean and covariance accurately up to the third-order and, because the higher-order terms in the series are not truncated, it is possible to reduce the errors in the higher-order terms as well.

The new linear estimator is shown to yield a performance equivalent to the Kalman filters for linear systems, and generalizes elegantly to nonlinear systems without the linearization steps required by the extended Kalman filter (EKF). The authors prove analytically that the expected performance of the new approach is superior to that of the EKF method. Empirical evidence is provided to support the theoretical conclusions, demonstrating that the new filter is easier to implement; it does not involve any linearization steps, and eliminates the derivation and evaluation of the Jacobian matrices.

The proposed algorithm has been extended to capture the first four moments of a Gaussian distribution, and the first three moments of an arbitrary distribution. Various applications have been found to be suitable to represent the new algorithm; e.g. high-order nonlinear coupled systems, navigation systems for high-speed road vehicles, public transportation systems, underwater systems, etc.


MSC:
93E11Filtering in stochastic control
93C10Nonlinear control systems