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Unscented Filtering and Nonlinear Estimation
 PROCEEDINGS OF THE IEEE
, 2004
"... The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the ..."
Abstract

Cited by 555 (3 self)
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on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement
Quantitative universality for a class of nonlinear Transformations
 J. Statistical Physics
, 1978
"... A large class of recursion relations xn+l = Af(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum 2. With f(2) f(x) ~ Ix 21 " (for Ix 21 su ..."
Abstract

Cited by 251 (0 self)
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). The numbers = and have been computationally determined for a range of z through their definitions, for a variety off's for each z. We present a recursive mechanism that explains these results by determining g * as the fixedpoint (function) of a transformation on the class off's. At present our
ON NONLINEAR TRANSFORMATIONS OF GAUSSIAN DISTRIBUTIONS
"... The unscented Kalman filter (UKF) relies on the unscented transformation (UT) that fits a Gaussian distribution to nonlinearly transformed so called sigma points. This contribution firstly gives the exact first and second order moments of the nonlinear transformation as a function of the rest ter ..."
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The unscented Kalman filter (UKF) relies on the unscented transformation (UT) that fits a Gaussian distribution to nonlinearly transformed so called sigma points. This contribution firstly gives the exact first and second order moments of the nonlinear transformation as a function of the rest
Properties of Nonlinear Transformations
, 2001
"... This paper shows that the properties of nonlinear transformations of a fractionally integrated process strongly depend on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a longmemory process with the same or a smaller longmemo ..."
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This paper shows that the properties of nonlinear transformations of a fractionally integrated process strongly depend on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a longmemory process with the same or a smaller long
The Universal Metric Properties of Nonlinear Transformations
, 1979
"... The role of functional equations to describe the exact local structure of highly bifurcated attractors of x~+l = Af(xn) independent of a specific f is formally developed. A hierarchy of universal functions g~(x) exists, each descriptive of the same local structure but at levels of a cluster of 2 ~ p ..."
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Cited by 124 (0 self)
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The role of functional equations to describe the exact local structure of highly bifurcated attractors of x~+l = Af(xn) independent of a specific f is formally developed. A hierarchy of universal functions g~(x) exists, each descriptive of the same local structure but at levels of a cluster of 2 ~ points. The hierarchy obeys g,l(x) =~gr(g~(x/~)), with g = limT ~ gT existing and obeying g(x) =~g(g(x/~)), an equation whose solution determines both g and ~. For r asymptotic g, ~ g ~~h (*) where 3> 1 and h are determined as the associated eigenvalue and eigenvector of the operator ~: ~4'[~] =~z[~b(g(x/a)) + g'(g(x/a))~( x/a)] We conjecture that A ' ~ possesses a unique eigenvalue in excess of 1, and show that this 3 is the Aconvergence rate. The form (*) is then continued to all A rather than just discrete A, and bifurcation values A, and dynamics at such A is determined. These results hold for the high bifurcations of any fundamental cycle. We proceed to analyze the approach to the asymptotic regime and show, granted ~'s spectral conjecture, the stability of the g, limit of highly iterated Af's, thus establishing our theory in a local sense. We show in the course of this that highly iterated Af's are conjugate to g,'s, thereby providing some elementary approximation schemes for obtaining h, for a chosen f.
Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 557 (36 self)
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Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal
Studies of transformation of Escherichia coli with plasmids
 J. Mol. Biol
, 1983
"... Factors that affect he probability of genetic transformation f Escherichia coli by plasmids have been evaluated. A set of conditions is described under which about one in every 400 plasmid molecules produces a transformed cell. These conditions include cell growth in medium containing elevated level ..."
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Cited by 1609 (1 self)
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Factors that affect he probability of genetic transformation f Escherichia coli by plasmids have been evaluated. A set of conditions is described under which about one in every 400 plasmid molecules produces a transformed cell. These conditions include cell growth in medium containing elevated
A New Extension of the Kalman Filter to Nonlinear Systems
, 1997
"... The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which ..."
Abstract

Cited by 747 (6 self)
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The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all
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