Keith LeGrand

• Doctor of Philosophy
• Assistant Professor at Purdue University West Lafayette

Successful space domain awareness (SDA) requires maintaining track custody of cooperative and noncooperative cislunar space objects (CSOs) through both ballistic and maneuvering trajectories. The surveillance of CSOs is particularly challenging due to the underlying chaotic multi-body dynamics, which makes uncertainty propagation more difficult whe...

Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations offer distinct advantages over sampling based methods in their computational cost and continuous representation....

Angles-only orbit determination involves the estimation of a satellite's unknown orbit without access to range or velocity measurements. Angles measurements, which are typically passive, are the primary means for tracking distant orbits, where active sensing is energy-prohibitive. This paper presents a Bayesian approach for tracking objects in the...

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 (FoV) can be exploited to incorporate evidence of wher...

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...

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 o...

Minimizing the amount of communication required by a sensor network is crucial to minimizing both energy and time consumption, as well to operating covertly and robustly in communication-contested environments. This paper presents a novel intermittent communication control approach applicable to sensor networks deployed to sense and model spatio-te...

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...

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 a...

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 prese...

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 fu...

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 cla...

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...

As satellite proximity operations involving multiple neighbors, such as a nearby debris cloud or a cooperative swarm, become more common, satellite on-board relative navigation schemes must be augmented to be able to track more than one target. Multitarget intensity filter approaches have shown promise as tractable methods to track single or multip...

In classical orbital mechanics, the Lambert problem consists of computing the full state of an orbiting body given two positions and the time elapsed between them. Similarly, a relative Lambert problem may cast to determine the relative velocity given two relative positions and the time elapsed between them. When considering linear relative dynamic...

Finding zeros of algebraic sets is a fundamental problem in aerospace engineering computation. Geometrically, this problem can often be represented by the intersection of multiple conic or quadric surfaces. A common example is GPS trilateration, which is geometrically given by the intersection of three spheres. In this work, Macaulay resultant expr...

The potential benefits of using parallel computing in real-time visual-based satellite proximity operations missions are investigated. Improvements in performance and relative navigation solutions over single thread systems can be achieved through multi- and many-core computing. Stochastic relative orbit determination methods benefit from the highe...