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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 574 (5 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 ..."
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Cited by 260 (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 127 (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.
EntropyBased Algorithms For Best Basis Selection
 IEEE Transactions on Information Theory
, 1992
"... pretations (position, frequency, and scale), and we have experimented with featureextraction methods that use bestbasis compression for frontend complexity reduction. The method relies heavily on the remarkable orthogonality properties of the new libraries. It is obviously a nonlinear transformat ..."
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Cited by 676 (20 self)
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pretations (position, frequency, and scale), and we have experimented with featureextraction methods that use bestbasis compression for frontend complexity reduction. The method relies heavily on the remarkable orthogonality properties of the new libraries. It is obviously a nonlinear
Research Article On Poisson Nonlinear Transformations
, 2014
"... Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory ..."
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Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate
Unsupervised texture segmentation using Gabor filters
 Pattern Recognition
"... We presenf a texture segmentation algorithm inspired by the multichannel filtering theory for visual information processing in the early stages of human visual system. The channels are characterized by a bank of Gabor filters that nearly uniformly covers the spatialfrequency domain. We propose a s ..."
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Cited by 617 (20 self)
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systematic filter selection scheme which is based on reconstruction of the input image from the filtered images. Texture features are obtained by subjecting each (selected) filtered image to a nonlinear transformation and computing a measure of “energy ” in a window around each pixel. An unsupervised square
Systematic Nonlinear Planning
 In Proceedings of the Ninth National Conference on Artificial Intelligence
, 1991
"... This paper presents a simple, sound, complete, and systematic algorithm for domain independent STRIPS planning. Simplicity is achieved by starting with a ground procedure and then applying a general, and independently verifiable, lifting transformation. Previous planners have been designed directly ..."
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Cited by 449 (3 self)
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This paper presents a simple, sound, complete, and systematic algorithm for domain independent STRIPS planning. Simplicity is achieved by starting with a ground procedure and then applying a general, and independently verifiable, lifting transformation. Previous planners have been designed directly
Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging
 MAGNETIC RESONANCE IN MEDICINE 58:1182–1195
, 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample kspace. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
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Cited by 538 (11 self)
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due to random undersampling add as noiselike interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent
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