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University of Colorado
1.
Gehly, Steven.
Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods.
Degree: PhD, Aerospace Engineering Sciences, 2016, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/148 
► The use of near Earth space has increased dramatically in the past few decades, and operational satellites are an integral part of modern society. The…
(more)
▼ The use of near Earth space has increased dramatically in the past few decades, and operational satellites are an integral part of modern society. The increased presence in space has led to an increase in the amount of orbital debris, which poses a growing threat to current and future space missions. Characterization of the debris environment is crucial to our continued use of high value orbit regimes such as the geosynchronous (GEO) belt. Objects in GEO pose unique challenges, by virtue of being densely spaced and tracked by a limited number of sensors in short observation windows. This research examines the use of a new class of
multitarget filters to approach the problem of orbit determination for the large number of objects present. The filters make use of a recently developed mathematical toolbox derived from point process theory known as Finite Set Statistics (FISST). Details of implementing FISST-derived filters are discussed, and a qualitative and quantitative comparison between FISST and traditional
multitarget estimators demonstrates the suitability of the new methods for space object estimation. Specific challenges in the areas of sensor allocation and initial orbit determination are addressed in the framework. The sensor allocation scheme makes use of information gain functionals as formulated for FISST to efficiently collect measurements on the full
multitarget system. Results from a simulated network of three ground stations tracking a large catalog of geosynchronous objects demonstrate improved performance as compared to simpler, non-information theoretic tasking schemes. Further studies incorporate an initial orbit determination technique to initiate new tracks in the
multitarget filter. Together with a sensor allocation scheme designed to search for new targets and maintain knowledge of the existing catalog, the method comprises a solution to the search-detect-track problem. Simulation results for a single sensor case show that the problem can be solved for multiple objects with no a priori information, even in the presence of missed detections and false measurements. Collectively, this research seeks to advance the capabilities of FISST-derived filters for use in the estimation of geosynchronous space objects; additional directions for future research are presented in the conclusion.
Advisors/Committee Members: Penina Axelrad, Brandon Jones, Jay McMahon, Nisar Ahmed, Gregory Beylkin.
Subjects/Keywords: Geosynchronous Orbit; Information Gain; Initial Orbit Determination; Multitarget Filtering; Random Finite Sets; Sensor Allocation; Aerospace Engineering
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APA (6th Edition):
Gehly, S. (2016). Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/148
Chicago Manual of Style (16th Edition):
Gehly, Steven. “Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods.” 2016. Doctoral Dissertation, University of Colorado. Accessed April 16, 2021.
https://scholar.colorado.edu/asen_gradetds/148.
MLA Handbook (7th Edition):
Gehly, Steven. “Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods.” 2016. Web. 16 Apr 2021.
Vancouver:
Gehly S. Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Apr 16].
Available from: https://scholar.colorado.edu/asen_gradetds/148.
Council of Science Editors:
Gehly S. Estimation of Geosynchronous Space Objects Using Finite Set Statistics Filtering Methods. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/asen_gradetds/148
University of Michigan
2.
Kreucher, Christopher M.
An information-based approach to sensor resource allocation.
Degree: PhD, Electrical engineering, 2005, University of Michigan
URL: http://hdl.handle.net/2027.42/124852
► This work addresses the problem of scheduling the resources of agile sensors. We advocate an information-based approach, where sensor tasking decisions are made based on…
(more)
▼ This work addresses the problem of scheduling the resources of agile sensors. We advocate an information-based approach, where sensor tasking decisions are made based on the principle that actions should be chosen to maximize the information expected to be extracted from the scene. This approach provides a single metric able to automatically capture the complex tradeoffs involved when choosing between possible sensor allocations. We apply this principle to the problem of tracking multiple moving ground targets from an airborne sensor. The aim is to task the sensor to most efficiently estimate both the number of targets and the state of each target simultaneously. The state of a target includes kinematic quantities like position and velocity and also discrete variables such as target class and target mode (e.g., turning or stopped). In many experiments presented herein, target motion is taken from real recorded vehicle histories. The information-based approach to sensor management involves the development of three interrelated elements. First, we form the joint
multitarget probability density (JMPD), which is the fundamental entity capturing knowledge about the number of targets and the states of the individual targets. Unlike traditional methods, the JMPD does not assume any independence, but instead explicitly models coupling in uncertainty between target states, between targets, and between target state and the number of targets. Furthermore, the JMPD is not assumed to be of some parametric form (e.g., Gaussian). Because of this generality, the JMPD must be estimated using sophisticated numerical techniques. Our representation of the JMPD is via a novel
multitarget particle filter with an adaptive sampling scheme. Second, we use the estimate of the JMPD to perform (myopic) sensor resource allocation. The philosophy is to choose actions that are expected to maximize information extracted from the scene. This metric trades automatically between allocations that provide different types of information (e.g., actions that provide information about position versus actions that provide information about target class) without ad hoc assumptions as to the relative utility of each. Finally, we extend the information-based paradigm to non-myopic sensor scheduling. This extension is computationally challenging due to an exponential growth in action sequences with horizon time. We investigate two approximate methods to address this complexity. First, we directly approximate Bellman's equation by replacing the value-to-go function with an easily computed function of the ability to gain information in the future. Second, we apply reinforcement learning as a means of learning a non-myopic policy from a set of example episodes.
Advisors/Committee Members: III, Alfred O. Hero, (advisor).
Subjects/Keywords: Approach; Based; Information Theory; Multitarget Tracking; Particle Filtering; Resource Allocation; Sensor
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APA (6th Edition):
Kreucher, C. M. (2005). An information-based approach to sensor resource allocation. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/124852
Chicago Manual of Style (16th Edition):
Kreucher, Christopher M. “An information-based approach to sensor resource allocation.” 2005. Doctoral Dissertation, University of Michigan. Accessed April 16, 2021.
http://hdl.handle.net/2027.42/124852.
MLA Handbook (7th Edition):
Kreucher, Christopher M. “An information-based approach to sensor resource allocation.” 2005. Web. 16 Apr 2021.
Vancouver:
Kreucher CM. An information-based approach to sensor resource allocation. [Internet] [Doctoral dissertation]. University of Michigan; 2005. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/2027.42/124852.
Council of Science Editors:
Kreucher CM. An information-based approach to sensor resource allocation. [Doctoral Dissertation]. University of Michigan; 2005. Available from: http://hdl.handle.net/2027.42/124852
Missouri University of Science and Technology
3.
McCabe, James Samuel.
Multitarget tracking and terrain-aided navigation using square-root consider filters.
Degree: PhD, Aerospace Engineering, Missouri University of Science and Technology
URL: https://scholarsmine.mst.edu/doctoral_dissertations/2726
► "Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of…
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▼ "Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of a vehicle, using current observations that are corrupted due to various sources, such as measurement noise, transmission dropouts, and spurious information. The study of filtering has been an active focus of research for decades, and the resulting filters have been the cornerstone of many of humankind's greatest technological achievements. However, these achievements are enabled principally by the use of specialized techniques that seek to, in some way, combat the negative impacts that processor roundoff and truncation error have on filtering. Two of these specialized techniques are known as square-root filters and consider filters. The former alleviates the fragility induced from estimating error covariance matrices by, instead, managing a factorized representation of that matrix, known as a square-root factor. The latter chooses to account for the statistical impacts a troublesome system parameter has on the overall state estimate without directly estimating it, and the result is a substantial reduction in numerical sensitivity to errors in that parameter. While both of these techniques have found widespread use in practical application, they have never been unified in a common square-root consider framework. Furthermore, consider filters are historically rooted to standard, vector-valued estimation techniques, and they have yet to be generalized to the emerging, set-valued estimation tools for multitarget tracking. In this dissertation, formulae for the square-root consider filter are derived, and the result is extended to finite set statistics-based multitarget tracking tools. These results are used to propose a terrain-aided navigation concept wherein data regarding a vehicle's environment is used to improve its state estimate, and square-root consider techniques provide the numerical stability necessary for an onboard navigation application. The newly developed square-root consider techniques are shown to be much more stable than standard formulations, and the terrain-aided navigation concept is applied to a lunar landing scenario to illustrate its applicability to navigating in challenging environments" – Abstract, page iii.
Subjects/Keywords: Consider filtering; Estimation; Multitarget tracking; Navigation; Square-root filtering; Terrain relative navigation; Aerospace Engineering
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APA (6th Edition):
McCabe, J. S. (n.d.). Multitarget tracking and terrain-aided navigation using square-root consider filters. (Doctoral Dissertation). Missouri University of Science and Technology. Retrieved from https://scholarsmine.mst.edu/doctoral_dissertations/2726
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Chicago Manual of Style (16th Edition):
McCabe, James Samuel. “Multitarget tracking and terrain-aided navigation using square-root consider filters.” Doctoral Dissertation, Missouri University of Science and Technology. Accessed April 16, 2021.
https://scholarsmine.mst.edu/doctoral_dissertations/2726.
Note: this citation may be lacking information needed for this citation format:
No year of publication.
MLA Handbook (7th Edition):
McCabe, James Samuel. “Multitarget tracking and terrain-aided navigation using square-root consider filters.” Web. 16 Apr 2021.
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Vancouver:
McCabe JS. Multitarget tracking and terrain-aided navigation using square-root consider filters. [Internet] [Doctoral dissertation]. Missouri University of Science and Technology; [cited 2021 Apr 16].
Available from: https://scholarsmine.mst.edu/doctoral_dissertations/2726.
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Council of Science Editors:
McCabe JS. Multitarget tracking and terrain-aided navigation using square-root consider filters. [Doctoral Dissertation]. Missouri University of Science and Technology; Available from: https://scholarsmine.mst.edu/doctoral_dissertations/2726
Note: this citation may be lacking information needed for this citation format:
No year of publication.
McMaster University
4.
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 ·
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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
5.
Sithiravel, Rajiv.
B-Spline Based Multitarget Tracking.
Degree: PhD, 2014, McMaster University
URL: http://hdl.handle.net/11375/16068
► Multitarget tracking in the presence of false alarm is a difficult problem to consider. The objective of multitarget tracking is to estimate the number of…
(more)
▼ Multitarget tracking in the presence of false alarm is a difficult problem to consider. The objective of
multitarget tracking is to estimate the number of targets and their states recursively from available observations. At any given time, targets can be born, die and spawn from already existing targets. Sensors can detect these targets with a defined threshold, where normally the observation is influenced by false alarm. Also if the targets are with low signal to noise ratio (SNR) then the targets may not be detected.
The Random Finite Set (RFS) filters can be used to solve such
multitarget problem efficiently. Specially, one of the best and most widely used RFS based filter is the Probability Hypothesis Density (PHD) filter. The PHD filter approximates the posterior probability density function (PDF) by the first order moment only, where the targets SNR assumed to be much higher. The PHD filter supports targets die, born, spawn and missed-detection by using the well known implementations including Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and Gaussian Mixture Probability Hypothesis Density (GM-PHD) methods. The SMC-PHD filter suffers from the well known degeneracy problems while GM-PHD filter may not be suitable for nonlinear and non-Gaussian target tracking problems.
It is desirable to have a filter that can provide continuous estimates for any distribution. This is the motivation for the use of B-Splines in this thesis. One of the main focus of the thesis is the B-Spline based PHD (SPHD) filters. The Spline is a well developed theory and been used in academia and industry for more than five decades. The B-Spline can represent any numerical, geometrical and statistical functions and models including the PDF and PHD. The SPHD filter can be applied to linear, nonlinear, Gaussian and non-Gaussian
multitarget tracking applications. The SPHD continuity can be maintained by selecting splines with order of three or more, which avoids the degeneracy-related problem. Another important characteristic of the SPHD filter is that the SPHD can be locally controlled, which allow the manipulations of the SPHD and its natural tendency for handling the nonlinear problems. The SPHD filter can be further extended to support maneuvering
multitarget tracking, where it can be an alternative to any available PHD filter implementations.
The PHD filter does not work well for very low observable (VLO) target tracking problems, where the targets SNR is normally very low. For very low SNR scenarios the PDF must be approximated by higher order moments. Therefore the PHD implementations may not be suitable for the problem considered in this thesis. One of the best estimator to use in VLO target tracking problem is the Maximum-Likelihood Probability Data Association (ML-PDA) algorithm. The standard ML-PDA algorithm is widely used in single target initialization or geolocation problems with high false alarm. The B-Spline is also used in the ML-PDA (SML-PDA) implementations. The SML-PDA algorithm has the capability…
Advisors/Committee Members: Thiagalingam, Kirubarajan, Electrical and Computer Engineering.
Subjects/Keywords: Multitarget tracking, Nonlinear filtering, Probability Hypothesis Density filter, Splines; Maneuvering target tracking, Maximum-Likelihood-Probabilistic Data Association Algorithm, Track initialization, Low observable target tracking, Joint Maximum-Likelihood-Probabilistic Data Association Algorithm
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APA ·
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Manager
APA (6th Edition):
Sithiravel, R. (2014). B-Spline Based Multitarget Tracking. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/16068
Chicago Manual of Style (16th Edition):
Sithiravel, Rajiv. “B-Spline Based Multitarget Tracking.” 2014. Doctoral Dissertation, McMaster University. Accessed April 16, 2021.
http://hdl.handle.net/11375/16068.
MLA Handbook (7th Edition):
Sithiravel, Rajiv. “B-Spline Based Multitarget Tracking.” 2014. Web. 16 Apr 2021.
Vancouver:
Sithiravel R. B-Spline Based Multitarget Tracking. [Internet] [Doctoral dissertation]. McMaster University; 2014. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/11375/16068.
Council of Science Editors:
Sithiravel R. B-Spline Based Multitarget Tracking. [Doctoral Dissertation]. McMaster University; 2014. Available from: http://hdl.handle.net/11375/16068
. 
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