Keith A LeGrand | Purdue University (original) (raw)

Papers by Keith A LeGrand

Cornell University - arXiv, Jul 22, 2022

In object tracking and state estimation problems, ambiguous evidence such as imprecise measuremen... more In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In particular, knowledge of a sensor's bounded field-of-view can be exploited to incorporate evidence of where an object was not observed. This paper presents a systematic approach for incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The resulting state estimation problem is nonlinear and solved using a new Gaussian mixture approximation based on recursive component splitting. Based on this approximation, a novel Gaussian mixture Bernoulli filter for imprecise measurements is derived and demonstrated in a tracking problem using only natural language statements as inputs. This paper also considers the relationship between bounded fields-of-view and cardinality distributions for a representative selection of multiobject distributions, which can be used for sensor planning, as is demonstrated through a problem involving a multi-Bernoulli process with up to one-hundred potential objects. Index Terms-Bounded field-of-view, Gaussian mixtures, imprecise measurements, negative information, Gaussian splitting, random finite set theory

Journal of Guidance, Control, and Dynamics, 2015

A method for performing bearings-only initial relative orbit determination of a nearby space obje... more A method for performing bearings-only initial relative orbit determination of a nearby space object in the absence of any information regarding the space object’s geometry and relative orbit is presented. To resolve the range ambiguity characteristic of a single optical sensor system, a second optical sensor is included at a known baseline distance on the observing spacecraft. To formulate an initial estimate of the space object’s relative orbit and its associated uncertainty, the angle measurements from both sensors are used to bound a region for all possible relative positions of the space object. A parameterized probability distribution in relative position that reflects uniform relative range uncertainty across the bounded region is constructed at two unique times. Linkage of the positional distributions is performed using a second-order relative Lambert solver to formulate a full-state probability density function in relative position and velocity, which can be further refined through processing subs...

Journal of Aerospace Information Systems

2021 IEEE 24th International Conference on Information Fusion (FUSION), 2021

Through automatic control, intelligent sensors can be manipulated to obtain the most informative ... more Through automatic control, intelligent sensors can be manipulated to obtain the most informative measurements about objects in their environment. In object tracking applications, sensor actions are chosen based on the predicted improvement in estimation accuracy, or information gain. Although random finite set theory provides a formalism for measuring information gain for multi-object tracking problems, predicting the information gain remains computationally challenging. This paper presents a new tractable approximation of the random finite set expected information gain applicable to multi-object search and tracking. The approximation presented in this paper accounts for noisy measurements, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the approach is demonstrated through a ground vehicle tracking problem using real video data from a remote optical sensor.

In search-detect-track problems, knowledge of where objects were not seen can be as valuable as k... more In search-detect-track problems, knowledge of where objects were not seen can be as valuable as knowledge of where objects were seen. Exploiting the sensor's known sensing extents, or field-of-view (FoV), this type of evidence can be incorporated in a Bayesian framework to improve tracking accuracy and form better sensor schedules. This paper presents new techniques for incorporating bounded FoV inclusion/exclusion evidence in object state densities and multi-object cardinality distributions. Some examples of how the proposed techniques may be applied to tracking and sensor planning problems are given.

2020 IEEE 23rd International Conference on Information Fusion (FUSION), 2020

The role of negative information is particularly important to search-detect-track problems in whi... more The role of negative information is particularly important to search-detect-track problems in which the number of objects is unknown a priori, and the size of the sensor field-ofview is far smaller than that of the region of interest. This paper presents an approach for systematically incorporating knowledge of the field-of-view geometry and position and object inclusion/exclusion evidence into object state densities and random finite set multi-object cardinality distributions. The approach is derived for a representative set of multi-object distributions and demonstrated through a sensor planning problem involving a multi-Bernoulli process with up to one-hundred potential targets.

2019 IEEE Aerospace Conference, 2019

In recent years, increasing interest in distributed sensing networks has led to a demand for robu... more In recent years, increasing interest in distributed sensing networks has led to a demand for robust multi-sensor multi-object tracking (MOT) methods that can take advantage of large quantities of gathered data. However, distributed sensing has unique challenges stemming from limited computational resources, limited bandwidth, and complex network topology that must be considered within a given tracking method. Several recently developed methods that are based upon the random finite set (RFS) have shown promise as statistically rigorous approaches to the distributed MOT problem. Among the most desirable qualities of RFS-based approaches is that they are derived from a common mathematical framework, finite set statistics, which provides a basis for principled fusion of full multi-object probability distributions. Yet, distributed labeled RFS tracking is a still-maturing field of research, and many practical considerations must be addressed before large-scale, real-time systems can be implemented. For example, methods that use label-based fusion require perfect label consistency of objects across sensors, which is impossible to guarantee in scalable distributed systems. This paper provides a survey of the challenges inherent in distributed tracking using labeled RFS methods. An overview of labeled RFS filtering is presented, the distributed MOT problem is characterized, and recent approaches to distributed labeled RFS filtering are examined. The problems that currently prevent implementation of distributed labeled RFS trackers in scalable real-time systems are identified and demonstrated within the scope of several exemplar scenarios.

Signal Processing, Sensor/Information Fusion, and Target Recognition XXVII, 2018

The δ-generalized labeled multi-Bernoulli (δ-GLMB) tracker is the first multiple hypothesis track... more The δ-generalized labeled multi-Bernoulli (δ-GLMB) tracker is the first multiple hypothesis tracking (MHT)-like tracker that is provably Bayes-optimal. However, in its basic form, the δ-GLMB provides no mechanism for adaptively initializing targets at their first appearance from unlabeled measurements. By introducing a new multitarget likelihood function that accounts for new target appearance, a data-driven δ-GLMB tracker is derived that automatically initializes new targets in the tracker measurement update. Monte Carlo results of simulated multitarget tracking problems demonstrate improved multitarget tracking accuracy over comparable adaptive birth methods.

IEEE Transactions on Control of Network Systems, 2021

Future applications of autonomous systems promise to involve increasingly large numbers of collab... more Future applications of autonomous systems promise to involve increasingly large numbers of collaborative robots individually equipped with onboard sensors, actuators, and wireless communications. By sharing and coordinating information, plans, and decisions, these very-large-scale robotic (VLSR) networks can dramatically improve their performance and operate over long periods of time with little or no human intervention. Controlling many collaborative agents to this day presents significant technical challenges. Besides requiring satisfactory communications, the amount of computation associated with most coordinated control algorithms increases with the number of agents. It is well-known, for example, that the optimal control of N collaborative agents for path planning and obstacle avoidance is a PSPACE-hard problem. Also, while necessary for performing basic tasks such as localization and mapping, many sensing and estimation approaches suffer from the curse of dimensionality, and their performance may degrade as uncertainties from disparate sources propagate through the network.

2019 22th International Conference on Information Fusion (FUSION), 2019

In this paper, we present alternate integer programming formulations for the multi-dimensional as... more In this paper, we present alternate integer programming formulations for the multi-dimensional assignment problem, which is typically employed for multi-sensor fusion, multi-target tracking (MTT) or data association in general. The first formulation is the Axial Multidimensional Assignment Problem with Decomposable Costs (MDADC). The decomposable costs comes from the fact that there are only pairwise costs between stages or scans of a target tracking problem or corpuses of a data association context. The difficulty with this formulation is the large number of transitivity or triangularity constraints that ensure if entity AAA is associated to entity BBB and entity BBB is associated with entity CCC, then it must also be that entity AAA is associated to entity CCC. The second formulation uses both pairs and triplets of observations, which offer more accurate representation for kinematic tracking of targets. This formulation avoids the large number of transitivity constraints but signi...

The unobservability of space-based angles-only orbit determination can be mitigated by the inclus... more The unobservability of space-based angles-only orbit determination can be mitigated by the inclusion of angle measurements from a second optical sensor fixed at a known baseline on the observing spacecraft. Previous approaches to the problem have used these stereoscopic angles to triangulate the position of a second satellite at a given time step. However, due to the nonlinearity of stereo triangulation, zero-mean Gaussian noise of these measurements cannot be assumed. This work investigates a modified approach in which the uncertainty of both angle measurements is used to bound a region for all possible positions of the second satellite. A Gaussian mixture that represents uniform uncertainty across the bounded region for the position of the second object is constructed at two initial time steps. Linkage of the Gaussian mixtures is performed using a relative Lambert solver in order to formulate a full state probability density function that can be further refined through processing ...

The relative guidance, navigation, and control of a pair of spacecraft using real-time data from ... more The relative guidance, navigation, and control of a pair of spacecraft using real-time data from a stereoscopic imaging sensor are investigated. Because line-of-sight measurements from a single imager are typically insufficient for system observability, a second imager with a known baseline vector to the first imager is included to achieve system observability with the addition of relative range measurements. The stereoscopic imaging system as modeled provides measurements capable of achieving a complete navigation solution. An SDRE controller is used to provide closed-loop control to maintain a desired relative orbit. An Unscented Kalman Filter is used to estimate the chief spacecraft\u27s inertial states using GPS measurements and the deputy spacecraft\u27s inertial states with stereoscopic imaging relative position measurements. Relative Orbital Elements are implemented to model separation between the spacecraft. © 2013 2013 California Institute of Technology

NbO 2 has the potential for a variety of electronic applications due to its electrically induced ... more NbO 2 has the potential for a variety of electronic applications due to its electrically induced insulatorto-metal transition (IMT) characteristic. In this study, we find that the IMT behavior of NbO 2 follows the field-induced nucleation by investigating the delay time dependency at various voltages and temperatures. Based on the investigation, we reveal that the origin of leakage current in NbO x is partly due to insufficient Schottky barrier height originating from interface defects between the electrodes and NbO x layer. The leakage current problem can be addressed by inserting thin NiO y barrier layers. The NiO y inserted NbO x device is drift-free and exhibits high I on /I off ratio (>5400), fast switching speed (<2 ns), and high operating temperature (>453 K) characteristics which are highly suitable to selector application for x-point memory arrays. We show that NbO x device with NiO x interlayers in series with resistive random access memory (ReRAM) device demonstrates improved readout margin (>2 9 word lines) suitable for x-point memory array application.

2015 18th International Conference on Information Fusion (Fusion), 2015

Multitarget intensity filters, such as the probability hypothesis density (PHD) filter and cardin... more Multitarget intensity filters, such as the probability hypothesis density (PHD) filter and cardinalized probability hypothesis density (CPHD) filter have been recently proposed as a means to track multiple space objects from both ground-based and space-based platforms. In many applications, the CPHD is chosen over the PHD filter, as it has been claimed to offer significant improvements in the accuracy of both its cardinality estimates and state estimates. To that end, in this study, Gaussian mixture implementations of both the PHD and CPHD filters are developed to track the relative states of nearby space objects with respect to an inspector spacecraft using angles-only measurements. The performance of each solution is evaluated over several metrics, including cardinality error, optimal sub-pattern assignment distance, and execution speed.

Unobservability of space-based angles-only orbit determination can be mitigated by including angl... more Unobservability of space-based angles-only orbit determination can be mitigated by including angle measurements from a second optical sensor. Previous approaches have used stereoscopic angles to triangulate a second satellite’s position. Due to triangulation nonlinearities, zero-mean Gaussian noise cannot be assumed. In this work, the uncertainty of both angle measurements is used to bound the possible positions of the second satellite. Uniform uncertainty is approximated over these bounded regions at two times using Gaussian mixtures. Linkage of the mixtures is performed using a Lambert solver to formulate a full state uncertainty for use in a Bayesian filter

2018 IEEE Aerospace Conference, 2018

A method for solving the multi-target tracking (MTT) problem in urban environments is presented. ... more A method for solving the multi-target tracking (MTT) problem in urban environments is presented. The difficulties specific to urban environments include changing target cardinality, high target density, and targets that present different types of motion. The solution presented involves the use of the Multi-Object Particle Multi-Bernoulli (MOP-MB) filter, a computationally efficient approximation of the Bayes' Multi-Object Filter. This filter is then extended to employ the use of multiple motion models that combine to provide a better estimate of target state and cardinality. The new filter, called the Interacting Multiple Model Multi-Object Particle Multi-Bernoulli (IMM-MOP-MB), uses the multi-object particles (MOPs) to additionally estimate the target's motion mode. We then compare the performance of these MB filters with an IMMJPDAF with track management software in terms of cardinality tracking and position estimates. This is done through the use of the Generalized Optima...

Information driven control can be used to develop intelligent sensors that can optimize their mea... more Information driven control can be used to develop intelligent sensors that can optimize their measurement value based on environmental feedback. In object tracking applications, sensor actions are chosen based on the expected reduction in uncertainty also known as information gain. Random finite set (RFS) theory provides a formalism for quantifying and estimating information gain in multi-object tracking problems. However, estimating information gain in these applications remains computationally challenging. This paper presents a new tractable approximation of the RFS expected information gain applicable to sensor control for multi-object search and tracking. Unlike existing RFS approaches, the approximation presented in this paper accounts for noisy measurements, missed detections, false alarms, and object appearance/disappearance. The effectiveness of the information driven sensor control is demonstrated through a multi-vehicle search-whiletracking experiment using real video data...

Concerns about population ageing apply to both developed and many developing countries and it has... more Concerns about population ageing apply to both developed and many developing countries and it has turned into a global issue. In the forthcoming decades the population ageing is likely to become one of the most important processes determining the future society characteristics and the direction of technological development. The present paper analyzes some aspects of the population ageing and its important consequences for particular societies and the whole world. Basing on this analysis, we can draw a conclusion that the future technological breakthrough is likely to take place in the 2030s (which we define as the final phase of the Cybernetic Revolution). In the 2020s-2030s we will expect the upswing of the forthcoming sixth Kondratieff wave, which will introduce the sixth technological paradigm (system). All those revolutionary technological changes will be connected, first of all, with breakthroughs in medicine and related technologies. We also present our ideas about the financial instruments that can help to solve the problem of pension provision for an increasing elderly population in the developed countries. We think that a more purposeful use of pension funds' assets together with an allocation (with necessary guarantees) of the latter into education and upgrading skills of young people in developing countries, perhaps, can partially solve the indicated problem in the developed states.