# Browsing by Subject "Multi-target tracking"

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Item Applications of random finite set-based multi-target trackers in space situational awareness(2022-08-18) Ravago, Nicholas; Jones, Brandon A.; Zanetti, Renato; Jah, Moriba; Russell, Ryan P; Weisman, RyanShow more Space situational awareness, the ability to accurately characterize and predict the state of the space environment, has become a topic of interest as the population of operational satellites increases. This trend is being driven by the deployment of large constellations of satellites that could consist of tens of thousands of satellites when fully deployed. Tracking space objects accurately is important for predicting and preventing collisions between objects, which can result in catastrophic damage to operational satellites and create debris clouds that endanger other satellites. However, tracking space objects is complicated due in part to the uncertain origins of measurements, a problem known as data ambiguity. While multiple target tracking algorithms that can handle data ambiguity exist, tracking in the space environment presents other challenges. The number of available observations per object is generally low due to the large number of objects relative to available sensor resources, and many observations are left uncorrelated due to the aforementioned data ambiguity problem. The recent rise of large constellations presents another problem in that the involved satellites will utilize low thrust propulsion systems to maintain formation, requiring maneuvering target tracking capabilities for optimal performance. In this dissertation we will analyze two problems that are representative of the space object tracking challenges that operators will face in the near future. We will show how applicable algorithms can developed using finite set statistics, a mathematical framework that allows a top-down approach to be employed in developing rigorous Bayes-optimal multi-target filters with desired functionalities. The first problem we analyze is a large constellation tracking problem. We simulate a constellation of over 4,500 satellites in low Earth orbit and track them using a network of twelve ground-based myopic sensors. These sensors are tasked using a cost function that combines an information-theoretic reward. We also leverage tactical importance functions to enable the incorporation of mission-based objectives, like prioritization of objects at risk of collision, into the tasking logic. The collected data are processed using a labeled multi-Bernoulli filter. The state catalog estimate produced by the filter is used to motivate the next round of sensor tasking, resulting in an autonomous closed loop system for integrated tasking and tracking. After a five-day tracking period, the state catalog estimate is used to perform a conjunction analysis. We combine existing methods to produce a computationally efficient workflow for the filtering of close approaches between satellites and the quantification of risk. The second problem we analyze is tracking multiple targets when maneuvering targets are present. Maneuvering targets deviate from their natural trajectories in unpredictable ways and generally require specialized tracking algorithms for best performance. A common method for tracking such targets is the interacting multiple model filter which maintains a bank of models to represent the possible dynamics of a target. Unknown dynamics can be represented as white noise processes through the concept of equivalent noise. This allows maneuvering space objects to be tracked efficiently, but this algorithm lacks the ability to characterize maneuvers. Using finite set statistics, we are able to develop a formulation of the generalized labeled multi-Bernoulli filter that allows for the integration of arbitrary dynamical models. This allows us to utilize data-adaptive methods that model unknown dynamics more specifically, allowing the filter to perform maneuver characterization in addition to maneuvering target tracking. We also develop a consider-based least squares maneuver estimation algorithm that models unknown dynamics using a single impulsive velocity change. The timing of this maneuver is estimated through a multiple hypothesis method. This method is integrated with our formulation of the generalized labeled multi-Bernoulli filter and applied to a simulated constellation of geostationary Earth orbiting satellites that includes a satellite performing an unknown maneuver. Results in our large constellation tracking work showed that our integrated tasking and tracking algorithm was able to maintain custody of all simulated satellites. We were able to improve the accuracy of risk analysis by incorporating a measure of collision risk in the sensor tasking logic, but the improvement was marginal. We hypothesize that a more generalized optimization algorithm or different sensor architecture may allow mission objective-based tasking to exert greater influence. Our results for the maneuvering target tracking problem showed that we were able to characterize the maneuver dynamics with an acceptable level of accuracy. The absolute errors in our characterization were relatively high compared to the actual maneuvers, but we were able to maintain custody of all objects. Consistency metrics were stable through the occurrence of the maneuver, indicating accurate quantification of the estimated maneuver error uncertainty. Future work remains to scale this work up to a larger-scale scenario where maneuver detection will become a greater factor due to its impact on computational efficiency. Further work would also required to extend our algorithm to non-Gaussian state representations that are often utilized in low-Earth orbit tracking scenarios.Show more Item Multi-agent distributed coverage control and multi-target tracking in complex and dynamic environments(2022-05-06) Abdulghafoor, Alaa Zaki Abdulrahman; Bakolas, Efstathios; Chen, Dongmei "Maggie"; Sentis, Luis; Zanetti, Renato; Tanaka, TakashiShow more In this work, we study and investigate problems associated with decentralized/distributed area coverage control and deployment of multi-agent networks as well as density estimation, path planning and motion coordination of the latter networks for multi-target tracking in dynamic and complex environments. In particular, we consider deployment (which includes target tracking applications) and area coverage problems in which the members of the multi-agent network have to deploy and allocate themselves over a given domain in accordance with a time-varying Gaussian mixture reference density function (demand function for the network) in complex and non-complex environments (domains with or without obstacles (which can be either static or dynamic)). The latter density function can either represent the reference coverage density or the reference tracking density according to the application considered in each scenario. Hence, different scenarios of the latter problems are investigated in which the proposed problem is comprised of two sub-problems which are coupled and interconnected with each other. The first problem (high-level/macroscopic problem) corresponds to a density path planning and / or density estimation (implemented in a centralized manner) whereas the second problem (low-level/microscopic problem) to a decentralized and distributed control and motion coordination problem. Our proposed approach is based on a combination of the macroscopic and microscopic descriptions of the multi-agent network. The macroscopic description of the network corresponds to the probability distribution of the agents' locations over a given region. In this description, the multi-agent network is treated as one unit (characterized by the networks PDF). The microscopic description of the network corresponds to the collection of all individual positions of the network's agents. The objective of our work is to find control algorithms that will allow a multi-agent network to attain a spatial distribution that matches the reference density function (macroscopic high-level problem) through the local interactions of the agents at the individual level (microscopic low-level distributed control problem). The high-level problem is associated with an interpolation problem in the class of Gaussian Mixtures (GMs) which seeks to find a density path that connects two boundary GMs. Moreover, the low-level control problem is addressed by utilizing the Lloyd's algorithm together with Voronoi tessellations and a time-varying GM reference density function which corresponds to the solution of the high-level problem. Because the high-level and the low-level problems of all the considered scenarios are inherently coupled to each other (interconnected in the sense that in order to solve the second problem we require the solution of the first problem), we propose an iterative scheme that combines the solutions of the first and the second problems in order to solve and address the path planning/density estimation, motion coordination, deployment and area coverage control problems of multi-agent networks in dynamic and complex environments in a successful, complete, safe and holistic way. In the first scenario (Scenario 1 presented in Chapter 2), the goal of the multi-agent network is to track the time-varying GM reference coverage density function that reshapes the agents' distribution from an initial single Gaussian probability distribution to a Gaussian mixture distribution in a domain with no obstacles (non-complex environment). In the second scenario (Scenario 2 presented in Chapter 3) the aim is to transfer the distribution of the agents from an initial GM to a final desired GM over a cluttered complex domain populated by static obstacles that the agents must not collide with while at all times as they are moving and trying to track the time-varying GM reference coverage density. In Scenarios 1 and 2, the high-level problem (first problem) was solved analytically by providing a closed form solution. The low-level control problem (second problem) corresponds to a decentralized and distributed control problem (collision avoidance requirement is now enforced at all times) which is solved by utilizing Lloyd's algorithm together with Voronoi tessellations and a time-varying GM reference coverage density function which corresponds to the centralized solution of the high-level coverage control problem (first problem). For Scenario 2, our approach utilizes a modified version of Voronoi tessellations which are comprised of what we refer to as Obstacle-Aware Voronoi Cells (OAVC) in order to enable coverage control while ensuring obstacle avoidance. In contrast with the first two scenarios (Scenarios 1 and 2), the next scenarios to be discussed (Scenarios 3 and 4) the time-varying GM reference densities are not known a priori and will correspond to the reference tracking density of a multi-target system which is characterized as a GM tracking density utilized to steer the agents to follow the targets; thus, in the first problems of the latter scenarios, state-of the-art estimation techniques will be employed to obtain their solutions. In the third scenario (Scenario 3 presented in Chapter 4) we address a multi-target tracking problem for a multi-agent network. Thus, we consider a density estimation, path planning and distributed/decentralized motion coordination problem for a multi-agent network whose members have to track multiple moving targets over a cluttered complex environment with static obstacles. In the first problem, which corresponds to a density estimation and path planning problem, the goal is to obtain a GM reference tracking density path of the multi-target network that the multi-agent system must track as a whole. In the proposed solution approach of the latter problem, the probability density of the multi-target system is characterized by a Gaussian mixture distribution density which is estimated by an adaptive Gaussian sum filter (AGSF) in order incorporate the complete evolution of the targets' PDFs between two measurements during the estimation. Therefore, the weights (mixing proportions) of the Gaussian components/ mixands (which correspond to the individual target's PDF) update continuously at every time step during the propagation of the state PDFs between two measurements by solving a convex optimization problem which requires the GM approximation to satisfy the so called Fokker-Planck-Kolmogorov equation (FPKE) for continuous time dynamical systems. In the second problem, which corresponds to a distributed and decentralized motion coordination problem, we seeks to find the individual control inputs that steer the agents to follow and track the mobile targets (by tracking the GM reference tacking density estimated solution of the first problem) while avoiding collisions at all times. Hence the same solution approach utilized for Scenario 2 will be employed to solve the second problem of Scenario 3. In the Fourth scenario (Scenario 4 presented in Chapter 5) we address an optimal path planning, density estimation and motion coordination problem for a very-large-scale multi-agent network whose members are aimed to track a very-large-scale system of mobile targets that maneuver while avoiding dynamic moving obstacles in an uncertain changing environment. The goal of the multi-agent network is to follow the targets by tracking their optimal reference estimated probability density which is represented as a GM distribution while avoiding collision with all the dynamic obstacles over the uncertain region. The estimated reference density is optimal in the sense that it represents the GM density of the targets as they seek the shortest path to reach their final destinations in the shortest time while avoiding the dynamic obstacles in the uncertain domain. The first problem corresponds to the optimal path planning and density estimation of the VLST system in the uncertain dynamic environment while the second problem is the motion coordination problem of the very-large-scale multi-agent network. Therefore, the solution approach to tackle the first problem depends on the utilization of an adaptive distributed optimal control (ADOC) framework which is in turn based on tools and concepts from optimal mass transport theory as well as reinforcement learning and approximate dynamic programming (and optimization) in the Wasserstein-GMM space where the value functional is defined in terms of the PDF (corresponds to a GM density) of the targets and the time-varying obstacle map function which describes the dynamic uncertain environment. The key challenge in the latter approach, is estimating and the continuously updating the PDF of the VLST system in accordance with the real time/"online" approximation of the time-varying obstacle map which describe the dynamic obstacles and the uncertain changing environmental information which affect the estimation of latter PDF. The second problem of Scenario 4 will be addressed similarly to that of Scenarios 2 and 3.Show more