Matthew J. Hoffman

Discrete phase space based on finite fields

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space.

Use of breeding to detect and explain instabilities in the global ocean

[1] The breeding method of Toth and Kalnay finds the perturbations that grow naturally in a dynamical system like the atmosphere or the ocean. Here breeding is applied to a global ocean model forced by reanalysis winds in order to identify instabilities of weekly and monthly timescales. This study extends the method to show how the energy equations for the bred vectors can be derived with only very minimal approximations and used to assess the physical mechanisms that give rise to the instabilities. Tropical Instability Waves in the tropical Pacific are diagnosed, confirming the existence of bands of both baroclinic and barotropic energy conversions indicated earlier by Masina et al. and others. In the South Atlantic Convergence Zone, the bred vector energy analysis shows that there is kinetic to potential ocean eddy energy conversion, suggesting that the growing instabilities found in this area are forced by the wind.

Feature Matching and Adaptive Prediction Models in an Object Tracking DDDAS

We consider the optical remote sensing tracking problem for vehicles in a complex environment using an adaptive sensor that can take spectral data at a small number of locations. The Dynamic Data-Driven Applications Systems (DDDAS) paradigm is well-suited for dynamically controlling such an adaptive sensor by using the prediction of object movement and its interaction with the environment to guide the location of spectral measurements. The spectral measurements are used for target identification through feature matching. We consider several adaptive sampling strategies for how to assign locations for spectral measurements in order to distinguish between multiple targets. In addition to guiding the measurement process, the tracking system pulls in additional data from OpenStreetMap to identify road networks and intersections. When a vehicle enters a detected intersection, it triggers the use of a multiple model prediction system to sample all possible turning options. The result of this added information is more accurate predictions and analysis from data assimilation using a Gaussian Sum filter (GSF).

An Advanced Data Assimilation System for the Chesapeake Bay: Performance Evaluation

AbstractAn advanced data assimilation system, the local ensemble transform Kalman filter (LETKF), has been interfaced with a Regional Ocean Modeling System (ROMS) implementation on the Chesapeake Bay (ChesROMS) as a first step toward a reanalysis and improved forecast system for the Chesapeake Bay. The LETKF is among the most advanced data assimilation methods and is very effective for large, nonlinear dynamical systems with sparse data coverage. Errors in the Chesapeake Bay system are due more to errors in forcing than errors in initial conditions. To account for forcing errors, a forcing ensemble is used to drive the ensemble states for the year 2003. In the observing system simulation experiments (OSSEs) using the ChesROMS-LETKF system presented here, the filter converges quickly and greatly reduces the analysis and subsequent forecast errors in the temperature, salinity, and current fields in the presence of errors in wind forcing. Most of the improvement in temperature and currents comes from satelli...

Reconstructing three-dimensional reentrant cardiac electrical wave dynamics using data assimilation.

For many years, reentrant scroll waves have been predicted and studied as an underlying mechanism for cardiac arrhythmias using numerical techniques, and high-resolution mapping studies using fluorescence recordings from the surfaces of cardiac tissue preparations have confirmed the presence of visible spiral waves. However, assessing the three-dimensional dynamics of these reentrant waves using experimental techniques has been limited to verifying stable scroll-wave dynamics in relatively thin preparations. We propose a different approach to recovering the three-dimensional dynamics of reentrant waves in the heart. By applying techniques commonly used in weather forecasting, we combine dual-surface observations from a particular experiment with predictions from a numerical model to reconstruct the full three-dimensional time series of the experiment. Here, we use model-generated surrogate observations from a numerical experiment to evaluate the performance of the ensemble Kalman filter in reconstructing such time series for a discordant alternans state in one spatial dimension and for scroll waves in three dimensions. We show that our approach is able to recover time series of both observed and unobserved variables matching the truth. Where nearby observations are available, the error is reduced below the synthetic observation error, with a smaller reduction with increased distance from observations. Our findings demonstrate that state reconstruction for spatiotemporally complex cardiac electrical dynamics is possible and will lead naturally to applications using real experimental data.

Feature Matching With an Adaptive Optical Sensor in a Ground Target Tracking System

We consider methods to address the optical feature-aided remote sensing tracking problem for vehicles in a challenging environment. Our approach is to apply the dynamic data driven application systems computing paradigm to implement control of an adaptive sensor. This adaptive sensor acquires a panchromatic image while simultaneously allowing the collection of visible-near infrared spectral data at specified pixels. This sensor holds the promise of delivering the increased accuracy of targeted spectral sensing without the enormous data volume of full spectral images. The target of interest is optimally imaged by the sensor based on the targets forecasted location and motion relative to the extracted content of the background. Background context is both extracted from the image and created from the OpenStreetMap road network. We describe the implementation of the tracking framework and testing of some of the components using simulated imagery created with the digital imaging and remote sensing image generation model. The Gaussian sum filter is employed to solve the data assimilation problem by forming a multimodel forecasting set that is used to increase the robustness and flexibility of tracking. For feature matching, we create an efficient sampling strategy that is informed by the viewing conditions to adaptively determine which pixels to measure spectrally in order to distinguish between different targets using a spectral distance measure.

Inventory and transport of plastic debris in the Laurentian Great Lakes

Plastic pollution in the worlds oceans has received much attention, but there has been increasing concern about the high concentrations of plastic debris in the Laurentian Great Lakes. Using census data and methodologies used to study ocean debris we derive a first estimate of 9887 metric tonnes per year of plastic debris entering the Great Lakes. These estimates are translated into population-dependent particle inputs which are advected using currents from a hydrodynamic model to map the spatial distribution of plastic debris in the Great Lakes. Model results compare favorably with previously published sampling data. The samples are used to calibrate the model to derive surface microplastic mass estimates of 0.0211 metric tonnes in Lake Superior, 1.44 metric tonnes in Huron, and 4.41 metric tonnes in Erie. These results have many applications, including informing cleanup efforts, helping target pollution prevention, and understanding the inter-state or international flows of plastic pollution.

Real-Time Vehicle Tracking in Aerial Video Using Hyperspectral Features

Vehicle tracking from a moving aerial platform poses a number of unique challenges including the small number of pixels representing a vehicle, large camera motion, and parallax error. This paper considers a multi-modal sensor to design a real-time persistent aerial tracking system. Wide field of view (FOV) panchromatic imagery is used to remove global camera motion whereas narrow FOV hyperspectral image is used to detect the target of interest (TOI). Hyperspectral features provide distinctive information to reject objects with different reflectance characteristics from the TOI. This way the density of detected vehicles is reduced, which increases tracking consistency. Finally, we use a spatial data based classifier to remove spurious detections. With such framework, parallax effect in non-planar scenes is avoided. The proposed tracking system is evaluated in a dense, synthetic scene and outperforms other state-of-theart traditional and aerial object trackers.

Spectral Validation of Measurements in a Vehicle Tracking DDDAS

Abstract Vehicle tracking in adverse environments is a challenging problem because of the high number of factors constraining their motion and possibility of frequent occlusion. In such conditions, identification rates drop dramatically. Hyperspectral imaging is known to improve the robustness of target identification by recording extended data in many wavelengths. However, it is impossible to transmit such a high rate data in real time with a conventional full hyperspectral sensor. Thus, we present a persistent ground-based target tracking system, taking advantage of a state-of-the-art, adaptive, multi-modal sensor controlled by Dynamic Data Driven Applications Systems (DDDAS) methodology. This overcomes the data challenge of hyperspectral tracking by only using spectral data as required. Spectral features are inserted in a feature matching algorithm to identify spectrally likely matches and simplify multidimensional assignment algorithm. The sensor is tasked for spectra acquisition by the prior estimates from the Gaussian Sum Filter and foreground mask generated by the background subtraction. Prior information matching the target features is used to tackle false negatives in the background subtraction output. The proposed feature-aided tracking system is evaluated in a challenging scene with a realistic vehicular simulation.

Integrating Hyperspectral Likelihoods in a Multidimensional Assignment Algorithm for Aerial Vehicle Tracking

Tracking vehicles through dense environments is an important and challenging task that is mostly tackled using visible and near IR wavelengths. Hyperspectral imaging is known to improve the robustness of target identification, but the massive increase in data created is usually prohibitive for tracking many targets. We present a persistent real-time aerial target tracking system, taking advantage of an adaptive, multimodal sensor concept and blending the hyperspectral likelihoods with kinematic likelihoods in a multidimensional assignment framework. The adaptive sensor is capable of providing wide field of view panchromatic images as well as the spectra of small number of pixels. The proposed system does not require large amount of hyperspectral data collection as we focus on tracking fewer number of targets with higher persistency. This overcomes the data challenge of hyperspectral tracking by following dynamic data-driven application systems (DDDAS) principles to control hyperspectral data collection where most beneficial. The DDDAS framework for controlling hyperspectral data collection is developed by incorporating prior information from the filter movement predictions and information from motion detection. The proposed multidimensional hyperspectral feature-aided tracker is compared to a 2-D hyperspectral feature-aided tracker and another cascaded hyperspectral data based tracker by generating a synthetic, realistic, aerial video on a dense scene.