Suppression of the zero-order term in off-axis digital holography through nonlinear filtering

We present experimental validation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object autocorrelation,namely, the zero-order term,from holographic data,thereby improving the reconstruction bandwidth of complex wavefronts. The algorithm is based on nonlinear filtering and can be applied to standard DHM setups with realistic recording conditions.We study the robustness of the technique under different experimental configurations,and quantitatively demonstrate its enhancement capabilities on phase signals.

Application of nonlinear filtering to credit risk

Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the `Expectation-Maximization' method for estimating parameters. (C) 2010 Elsevier B.V. All rights reserved.

Artifact-free reconstruction from off-axis digital holograms through nonlinear filtering

We present experimental investigation of a new reconstruction method for off-axis digital holographic microscopy (DHM). This method effectively suppresses the object auto-correlation, commonly called the zero-order term, from holographic measurements, thereby suppressing the artifacts generated by the intensities of the two beams employed for interference from complex wavefield reconstruction. The algorithm is based on non-linear filtering, and can be applied to standard DHM setups, with realistic recording conditions. We study the applicability of the technique under different experimental configurations, such as topographic images of microscopic specimens or speckle holograms.

Aspects of optimum nonlinear filtering using nonlinear zero-memory elements.

"Cornell Aeronautical Laboratory internal research."

A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter. (C) 2013 Elsevier B.V. All rights reserved.

Extended Kalman filtering for robotic proximity sensing

The authors address the problems in using a fiber-optic proximity sensor to detect robot end-effector positioning errors in performing a contact task when uncertainties about target position exist. An extended Kalman filter approach is employed to solve the nonlinear filtering problem. Some experimental results are given.

Nonlinear communication channels with capacity above the linear Shannon limit

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel. © 2012 Optical Society of America.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

A stochastic model for natural feature representation

This paper presents a robust stochastic model for the incorporation of natural features within data fusion algorithms. The representation combines Isomap, a non-linear manifold learning algorithm, with Expectation Maximization, a statistical learning scheme. The representation is computed offline and results in a non-linear, non-Gaussian likelihood model relating visual observations such as color and texture to the underlying visual states. The likelihood model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The likelihoods are expressed as a Gaussian Mixture Model so as to permit convenient integration within existing nonlinear filtering algorithms. The resulting compactness of the representation is especially suitable to decentralized sensor networks. Real visual data consisting of natural imagery acquired from an Unmanned Aerial Vehicle is used to demonstrate the versatility of the feature representation.

Self excitation in equity indices

A "self-exciting" market is one in which the probability of observing a crash increases in response to the occurrence of a crash. It essentially describes cases where the initial crash serves to weaken the system to some extent, making subsequent crashes more likely. This thesis investigates if equity markets possess this property. A self-exciting extension of the well-known jump-based Bates (1996) model is used as the workhorse model for this thesis, and a particle-filtering algorithm is used to facilitate estimation by means of maximum likelihood. The estimation method is developed so that option prices are easily included in the dataset, leading to higher quality estimates. Equilibrium arguments are used to price the risks associated with the time-varying crash probability, and in turn to motivate a risk-neutral system for use in option pricing. The option pricing function for the model is obtained via the application of widely-used Fourier techniques. An application to S&P500 index returns and a panel of S&P500 index option prices reveals evidence of self excitation.

Filter and control performance bounds in the presence of model uncertainties with aerospace applications

This thesis establishes performance properties for approximate filters and controllers that are designed on the basis of approximate dynamic system representations. These performance properties provide a theoretical justification for the widespread application of approximate filters and controllers in the common situation where system models are not known with complete certainty. This research also provides useful tools for approximate filter designs, which are applied to hybrid filtering of uncertain nonlinear systems. As a contribution towards applications, this thesis also investigates air traffic separation control in the presence of measurement uncertainties.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.