Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 < H < 1. A reproducing kernel Hilbert space for the FBM is...
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Our objective is to study a nonlinear filtering problem for the observation process perturbed by a Fractional Brownian Motion (FBM) with Hurst index 1/2 < H < 1. A reproducing kernel Hilbert space for the FBM is considered and a "fractional" Zakai equation for the unnormalized optimal filter is derived.
In weak scattering diffraction tomography, there is a well-known Fourier relationship between the field scattered by an unknown object and the scattering potential that characterizes the object. For these weakly scatt...
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In weak scattering diffraction tomography, there is a well-known Fourier relationship between the field scattered by an unknown object and the scattering potential that characterizes the object. For these weakly scattering objects, those that satisfy the Born or Rytov approximation, the scattered field generated from a sequence of different illumination directions complements Fourier data on the unknown scattering potential, A low-pass reconstruction is found by Fourier inversion. A simulation is presented in which the scattered far field from several strongly scattering penetrable two-dimensional cylinders is backpropagated into the object domain. For these more strongly scattering objects, a single wavelength and a single illumination direction are used to provide Limited Fourier data on the product of the scattering potential and the total field. A nonlinear filtering technique, known as differential cepstral filtering, is used to isolate the scattering potential and to suppress artifacts introduced by the perturbing field component. Reconstructed images calculated by this technique from exact scattered-field data hom cylindrically symmetric objects are shown. (C) 1996 Optical Society of America.
Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. nonlinear filters that rel...
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Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. nonlinear filters that relax the Gaussian assumption, on the other hand, typically approximate the distribution of the state with a finite sum of point masses or Gaussian distributions. In this work, the distribution of the state is approximated by a polynomial transformation of a Gaussian distribution, allowing for all moments, central and raw, to be rapidly computed in a closed form. Knowledge of the higher order moments is then employed to perform a polynomial measurement update, i.e., the value of the measurement enters the update function as a polynomial of arbitrary order. A filter employing a Gaussian approximation with linear update is, therefore, a special case of the proposed algorithm when both the order of the series and the order of the update are set to one: it reduces to the extended Kalman filter. At the cost of more computations, the new methodology guarantees performance better than the linear/Gaussian approach for nonlinear systems. This work employs monomial basis functions and Taylor series, developed in the differential algebra framework, but it is readily extendable to an orthogonal polynomial basis.
A nonlinear filtering setup visualizes wavefront aberrations. In a single-beam scheme, however, the negative and positive phase shifts cannot be distinguished. As an improvement, a two-beam nonlinear scheme is propose...
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A nonlinear filtering setup visualizes wavefront aberrations. In a single-beam scheme, however, the negative and positive phase shifts cannot be distinguished. As an improvement, a two-beam nonlinear scheme is proposed. It has self-aligning properties and mechanical stability, and can be used for remote testing of large optical objects such as photolithography masks, liquid crystal substrates, jet streams and turbulence.
In support of Canada's proposed Polar Communication and Weather mission, this study examined the accuracy to which GPS-based autonomous navigation might be realized for spacecraft in a Molniya orbit. A navigation ...
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In support of Canada's proposed Polar Communication and Weather mission, this study examined the accuracy to which GPS-based autonomous navigation might be realized for spacecraft in a Molniya orbit. A navigation algorithm based on the Extended Kalman Filter was demonstrated to achieve a three-dimensional root-mean-square accuracy of 58.9 m over a Molniya orbit with 500 km and 40,000 km perigee and apogee altitudes, respectively. Despite the inclusion of biased and non-white error models in the generated GPS pseudorange measurements - a first for navigation studies in this orbital regime - algorithms based on the Unscented Kalman Filter and the Cubature Kalman Filter were not found to improve this result;their benefits were eclipsed due to the accurate pseudorange measurements which were available during periods of highly nonlinear dynamics. This study revealed receiver clock bias error to be a significant source of navigation solution error. For reasons of geometry, the navigation algorithm is not able to differentiate between this error and a radial position error. A novel dual-mode dynamic clock model was proposed and implemented as a means to minimize receiver clock bias error over the entire orbital regime. (C) 2016 IAA. Published by Elsevier Ltd. All rights reserved.
The paper treats the nonlinear filtering problem for jump-diffusion processes. The optimal filter is derived for a stochastic system where the dynamics of the signal variable is described by a jump-diffusion equation....
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The paper treats the nonlinear filtering problem for jump-diffusion processes. The optimal filter is derived for a stochastic system where the dynamics of the signal variable is described by a jump-diffusion equation. The optimal filter is described by stochastic integral equations. (c) 2005 Elsevier B.V. All rights reserved.
nonlinearfiltering operations can be performed in coherent optical systems with the help of the halftone screen process. Theoretical and practical considerations regarding this type of system are presented. The use o...
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nonlinearfiltering operations can be performed in coherent optical systems with the help of the halftone screen process. Theoretical and practical considerations regarding this type of system are presented. The use of these methods to achieve logarithmic filtering is emphasized. Applications to separation of multiplicative signals and noise, speckle noise reduction, and processing of radiographic images are considered. Experimental results are presented.
The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonline...
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The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonlinear equation can be reduced to a linear one. Extended Kalman filter, iterated filter and second order filter formulas are derived for the nonlinear state equation with linear measurement equation. Simulations results show that the accuracy of azimuth error estimation using extended Kalman filter is better than that of using standard Kalman filter while the iterated filter and second order filter can give even better estimation accuracy.
A certain method of nonlinear filtering of high-frequency disturbances in control systems is presented;it is based on involving the data on determined reference signal to limit the rate of feedback signal variation.
A certain method of nonlinear filtering of high-frequency disturbances in control systems is presented;it is based on involving the data on determined reference signal to limit the rate of feedback signal variation.
Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dir...
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Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dirichlet form setting. Then, we study the uniqueness of solutions of the filtering equations via the Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. Furthermore, we investigate the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes. (C) 2009 Elsevier B.V. All rights reserved.
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