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University of Notre Dame
1.
Nathaniel Rupprecht.
Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>.
Degree: Physics, 2020, University of Notre Dame
URL: https://curate.nd.edu/show/41687h1780w 
► Statistical mechanics attempts to describe the collective behavior of systems composed of many small interacting parts. Systems in equilibrium are particularly simple to analyze…
(more)
▼ Statistical mechanics attempts to describe
the collective behavior of systems composed of many small
interacting parts. Systems in equilibrium are particularly simple
to analyze since their behavior is stationary in time. For systems
out of equilibrium, the past and future states and behavior of the
system may be radically different then that of the
present. In this thesis, we analyze how
information about the past or future can be best used.
We start by establishing a theoretical framework
for quantifying how well the future and past of systems can be
inferred, which we call the prediction and
retrodiction entropies.
We use our measures to quantify
retrodiction and prediction for
systems of diffusing particles and for the Logistic map.
We then develop a formalism that allows us to
decide how to make small changes to a discrete Markov process such
that it becomes more susceptible to inference - either prediction
or
retrodiction. We test this procedure on several Markov systems:
an ensemble of random transition matrices, and a semi-classical
quantum system, showing that we are in fact able to get moderate
changes in predictability from small changes to the transition
matrix. Following this, we study two systems that
attempt to use information about the future to improve their
performance in the present. The first system is a collection of
agents that attempt to predict the future and use that information
to compete for a scarce resource. The second system is a Maxwell
demon that has constraints on how quickly it can open and close its
gate. Its uses knowledge of when particles collide with the gate it
controls to schedule a sequence of gate openings and closures, and
maximize its net rate of particle or energy
transfer.
Advisors/Committee Members: Zoltan Toroczkai, Committee Member, Dervis C. Vural, Research Director, Alan Lindsay, Committee Member, Boldizsar Janko, Committee Member.
Subjects/Keywords: Retrodiction; Thermodynamics; Inference; Non-equilibrium; Prediction; Statistical mechanics
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APA (6th Edition):
Rupprecht, N. (2020). Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/41687h1780w
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Rupprecht, Nathaniel. “Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>.” 2020. Thesis, University of Notre Dame. Accessed April 16, 2021.
https://curate.nd.edu/show/41687h1780w.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Rupprecht, Nathaniel. “Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>.” 2020. Web. 16 Apr 2021.
Vancouver:
Rupprecht N. Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>. [Internet] [Thesis]. University of Notre Dame; 2020. [cited 2021 Apr 16].
Available from: https://curate.nd.edu/show/41687h1780w.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Rupprecht N. Prediction and Retrodiction in Statistical Mechanical
Systems Out of Equilibrium</h1>. [Thesis]. University of Notre Dame; 2020. Available from: https://curate.nd.edu/show/41687h1780w
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
McMaster University
2.
KRISHNAN, KRISHANTH.
Prediction, Tracking and Retrodiction for Path-Constrained Targets.
Degree: MASc, 2012, McMaster University
URL: http://hdl.handle.net/11375/12450
► Prediction, tracking, and retrodiction for targets whose motion is constrained by external conditions (e.g., shipping lanes, roads) present many challenges to tracking systems. The…
(more)
▼ Prediction, tracking, and retrodiction for targets whose motion is constrained by external conditions (e.g., shipping lanes, roads) present many challenges to tracking systems. The targets are moving along a path, defined by way-points and segments. Measurements are obtained by sensors at low revisit rates (e.g., spaceborne). Existing tracking algorithms assume that the targets follow the same motion model between successive measurements, but in a low revisit rate scenario targets may change the motion model between successive measurements. A prediction algorithm is proposed here, which addresses this issue by considering possible motion model whenever targets move to a different segment. Further, when a target approaches a junction, it has the possibility to travel into one of the multiple segments connected to that junction. To predict the probable locations, multiple hypotheses for segments are introduced and a probability is calculated for each segment hypothesis. When measurements become available, segment hypothesis probability is updated based on a combined mode likelihood and a sequential probability ratio test is carried out to reject the hypotheses with low probability. Retrodiction for path constrained targets is also considered, because in some scenarios it is desirable to find out the target's exact location at some previous time (e.g., at the time of an oil leakage). A retrodiction algorithm is developed for path constrained targets so as to facilitate motion forensic analysis. Simulation results are presented to validate the proposed algorithms.
Master of Applied Science (MASc)
Advisors/Committee Members: Kirubarajan, T., Electrical and Computer Engineering.
Subjects/Keywords: prediction; target tracking; retrodiction; path-constrained targets; segment hypothesis; Electrical and Computer Engineering; Signal Processing; Electrical and Computer Engineering
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APA (6th Edition):
KRISHNAN, K. (2012). Prediction, Tracking and Retrodiction for Path-Constrained Targets. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/12450
Chicago Manual of Style (16th Edition):
KRISHNAN, KRISHANTH. “Prediction, Tracking and Retrodiction for Path-Constrained Targets.” 2012. Masters Thesis, McMaster University. Accessed April 16, 2021.
http://hdl.handle.net/11375/12450.
MLA Handbook (7th Edition):
KRISHNAN, KRISHANTH. “Prediction, Tracking and Retrodiction for Path-Constrained Targets.” 2012. Web. 16 Apr 2021.
Vancouver:
KRISHNAN K. Prediction, Tracking and Retrodiction for Path-Constrained Targets. [Internet] [Masters thesis]. McMaster University; 2012. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/11375/12450.
Council of Science Editors:
KRISHNAN K. Prediction, Tracking and Retrodiction for Path-Constrained Targets. [Masters Thesis]. McMaster University; 2012. Available from: http://hdl.handle.net/11375/12450
McMaster University
3.
Nadarajah, N.
Retrodiction for Multitarget Tracking.
Degree: PhD, 2009, McMaster University
URL: http://hdl.handle.net/11375/17364
► Multi-Target Tracking (MTT), where the number of targets as well as their states are time-varying, concerns with the estimation of both the number of…
(more)
▼ Multi-Target Tracking (MTT), where the number of targets as well as their states are time-varying, concerns with the estimation of both the number of targets and the individual states from noisy sensor measurements, whose origins are unknown. Filtering typically produces the best estimates of the target state based on all measurements up to current estimation time. Smoothing or
retrodiction, which uses measurements beyond the current estimation time, provides better estimation of target states. This thesis proposes smoothing methods for various estimation methods that produce delayer, but better, estimates of the target states. First, we propose a novel smoothing method for the Probability Hypothesis Density (PHD) estimator. The PHD filer, which propagates the first order statistical moment of the multitarget state density, a computationally efficient MTT algorithm. By evaluating the PHD, the number of targets as well as their individual states can be extracted. Recent Sequential Monte Carlo (SMC) implementations of the PHD filter have paved the way to its application to realistic nonlinear non-Gaussian problems. The proposed PHD smoothing method involves forward multitarget filtering using the standard PHD filter recursion followed by backward smoothing recursion using a novel recursive formula. Second, we propose a Multiple Model PH (MMPHD) smoothing method for tracking of maneuvering targets. Multiple model approaches have been shown to be effective for tracking maneuvering targets. MMPHD filter propagates mode-conditioned PHD recursively. The proposed backward MMPHD smoothing algorithm involves the estimation of a continuous state for target dynamic as well as a discrete state vector for the mode of target dynamics. Third, we present a smoothing method for the Gaussian Mixture PHD (GMPHD) state estimator using multiple sensors. Under linear Gaussian assumptions, the PHD filter can be implemented using a closed-form recursion, where the PHD is represented by a mixture of Gaussian functions. This can be extended to nonlinear systems by using the Extended Kalman Filter (EKF) or the Unscented Kalman Filter (UKF). In the case of multisenor systems, a sequential update of the PHD has been suggested in literature. However, this sequential update is susceptible to imperfections in the last sensor. In this thesis, a parallel update for GMPHD filter is proposed. The resulting filter outputs are further improved using a novel closed-form backward smoothing recursion. Finally, we propose a novel smoothing method for Kalman based Interacting Multiple Model (IMM) estimator for tracking agile targets. The new method involves forwarding filtering followed by backward smoothing while maintaining the fundamental spirit of the IMM. The forward filtering is performed using the standard IMM recursion, while the backward smoothing is performed using a novel interacting smoothing recursion. This backward recursion mimics the IMM estimator in the backward direction, where each mode conditioned smoother…
Advisors/Committee Members: Kirubarajan, T., Electrical and Computer Engineering.
Subjects/Keywords: electrical and computer engineering; retrodiction; multitarget tracking; smoothing; filtering
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APA (6th Edition):
Nadarajah, N. (2009). Retrodiction for Multitarget Tracking. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/17364
Chicago Manual of Style (16th Edition):
Nadarajah, N. “Retrodiction for Multitarget Tracking.” 2009. Doctoral Dissertation, McMaster University. Accessed April 16, 2021.
http://hdl.handle.net/11375/17364.
MLA Handbook (7th Edition):
Nadarajah, N. “Retrodiction for Multitarget Tracking.” 2009. Web. 16 Apr 2021.
Vancouver:
Nadarajah N. Retrodiction for Multitarget Tracking. [Internet] [Doctoral dissertation]. McMaster University; 2009. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/11375/17364.
Council of Science Editors:
Nadarajah N. Retrodiction for Multitarget Tracking. [Doctoral Dissertation]. McMaster University; 2009. Available from: http://hdl.handle.net/11375/17364
McMaster University
4.
Tager, Sean.
GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking.
Degree: MASc, 2013, McMaster University
URL: http://hdl.handle.net/11375/13389
► In the field of Tracking and Data Fusion most, if not all, computations executed by a computer are carried out serially. The sole part…
(more)
▼ In the field of Tracking and Data Fusion most, if not all, computations executed by a computer are carried out serially. The sole part of the process that is not entirely serial is the collection of data from multiple sensors, which can be executed in parallel. However, once the data is to be filtered the most likely candidate is a serial algorithm. This is due in large part to the algorithms themselves that have been developed over the last several decades for use on conventional computers that have been left void of parallel computing capabilities, until now. With the arrival of graphical processing units, or GPUs, the tracking community is in a favourable position to exploit the functionality of parallel processing in order to track a growing number of targets. The problem, however, begins with the sheer labour of having to convert all the pre-existing serial tracking algorithms into parallel ones. This is clearly a daunting task when one considers the extent to which the tracking community has gone to develop modern day filters such as Alpha Beta filters, Probabilistic Data Association filters, Interacting Multiple Model filters, and several dozen, if not hundred, variants of the aforementioned. It is most likely that these filters will find some kind of a parallelization in the near future as ever more sensors are dispersed throughout society and even more targets are monitored with these sensors. The volume of targets then becomes simply too unmanageable for a serial algorithm and more focus is placed iv on parallel ones. Yet, before the parallel algorithms can be utilized they have to be derived. It is the derivation of these parallel algorithms which is the focus of this thesis. However, it should be made clear that it would be impossible to formulate a parallelization for every filter found in the literature, and so the goal here is to direct the attention onto one filter in particular, the Kalman filter.
Master of Applied Science (MASc)
Advisors/Committee Members: Kirubarajan, T., Bruce, I., Field, T.R., Electrical and Computer Engineering.
Subjects/Keywords: Retrodiction; Parallel Algorithm; Large Scale Target; Prefix Sum; Signal Processing; Signal Processing
Record Details
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Record Details
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APA ·
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MLA ·
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CSE |
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Tager, S. (2013). GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/13389
Chicago Manual of Style (16th Edition):
Tager, Sean. “GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking.” 2013. Masters Thesis, McMaster University. Accessed April 16, 2021.
http://hdl.handle.net/11375/13389.
MLA Handbook (7th Edition):
Tager, Sean. “GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking.” 2013. Web. 16 Apr 2021.
Vancouver:
Tager S. GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking. [Internet] [Masters thesis]. McMaster University; 2013. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/11375/13389.
Council of Science Editors:
Tager S. GPU-Specfic Kalman Filtering and Retrodiction for Large-Scale Target Tracking. [Masters Thesis]. McMaster University; 2013. Available from: http://hdl.handle.net/11375/13389
. 
Open Access Theses and Dissertations