Primal-dual interior-point algorithms for linear programs with many inequality constraints

Linear programs (LPs) are one of the most basic and important classes of constrained optimization problems, involving the optimization of linear objective functions over sets defined by linear equality and inequality constraints. LPs have applications to a broad range of problems in engineering and operations research, and often arise as subproblems for algorithms that solve more complex optimization problems. ``Unbalanced'' inequality-constrained LPs with many more inequality constraints than variables are an important subclass of LPs. Under a basic non-degeneracy assumption, only a small number of the constraints can be active at the solution--it is only this active set that is critical to the problem description. On the other hand, the additional constraints make the problem harder to solve. While modern ``interior-point'' algorithms have become recognized as some of the best methods for solving large-scale LPs, they may not be recommended for unbalanced problems, because their per-iteration work does not scale well with the number of constraints. In this dissertation, we investigate "constraint-reduced'' interior-point algorithms designed to efficiently solve unbalanced LPs. At each iteration, these methods construct search directions based only on a small working set of constraints, while ignoring the rest. In this way, they significantly reduce their per-iteration work and, hopefully, their overall running time. In particular, we focus on constraint-reduction methods for the highly efficient primal-dual interior-point (PDIP) algorithms. We propose and analyze a convergent constraint-reduced variant of Mehrotra's predictor-corrector PDIP algorithm, the algorithm implemented in virtually every interior-point software package for linear (and convex-conic) programming. We prove global and local quadratic convergence of this algorithm under a very general class of constraint selection rules and under minimal assumptions. We also propose and analyze two regularized constraint-reduced PDIP algorithms (with similar convergence properties) designed to deal directly with a type of degeneracy that constraint-reduced interior-point algorithms are often subject to. Prior schemes for dealing with this degeneracy could end up negating the benefit of constraint-reduction. Finally, we investigate the performance of our algorithms by applying them to several test and application problems, and show that our algorithms often outperform alternative approaches

Radiation-hardened fast acquisition/weak signal tracking system and method

A global positioning system (GPS) receiver and method of acquiring and tracking GPS signals comprises an antenna adapted to receive GPS signals; an analog radio frequency device operatively connected to the antenna and adapted to convert the GPS signals from an analog format to a digital format; a plurality of GPS signal tracking correlators operatively connected to the analog RF device; a GPS signal acquisition component operatively connected to the analog RF device and the plurality of GPS signal tracking correlators, wherein the GPS signal acquisition component is adapted to calculate a maximum vector on a databit correlation grid; and a microprocessor operatively connected to the plurality of GPS signal tracking correlators and the GPS signal acquisition component, wherein the microprocessor is adapted to compare the maximum vector with a predetermined correlation threshold to allow the GPS signal to be fully acquired and tracked

Autonomous Navigation Above the GNSS Constellations and Beyond: GPS Navigation for the Magnetospheric Multiscale Mission and SEXTANT Pulsar Navigation Demonstration

This talk will describe two first-of-their-kind technology demonstrations attached to ongoing NASA science missions, both of which aim to extend the range of autonomous spacecraft navigation far from the Earth. First, we will describe the onboard GPS navigation system for the Magnetospheric Multiscale (MMS) mission which is currently operating in elliptic orbits reaching nearly halfway to the Moon. The MMS navigation system is a key outgrowth of a larger effort at NASA Goddard Space Flight Center to advance high-altitude Global Navigation Satellite System (GNSS) navigation on multiple fronts, including developing Global Positioning System receivers and onboard navigation software, running simulation studies, and leading efforts to characterize and protect signals at high-altitude in the so-called GNSS Space-Service Volume (SSV). In the second part of the talk, we will describe the Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) mission that aims to make the first in-space demonstration of X-ray pulsar navigation (XNAV). SEXTANT is attached to the NASA astrophysics mission Neutron-star Interior Composition ExploreR (NICER) whose International Space Station mounted X-ray telescope is investigating the fundamental physics of extremes in gravity, material density, and electromagnetic fields found in neutron stars, and whose instrument provides a nearly ideal navigation sensor for XNAV

Introduction to GPS and Other Global Navigation Satellite Systems

No abstract availabl

New High-Altitude GPS Navigation Results from the Magnetospheric Multiscale Spacecraft and Simulations at Lunar Distances

As reported in a companion work, in its first phase, NASA's 2015 highly elliptic Magnetospheric Multiscale (MMS) mission set a record for the highest altitude operational use of on-board GPS-based navigation, returning state estimates at 12 Earth radii. In early 2017 MMS transitioned to its second phase which doubled the apogee distance to 25 Earth radii, approaching halfway to the Moon. This paper will present results for GPS observability and navigation performance achieved in MMS Phase 2. Additionally, it will provide simulation results predicting the performance of the MMS navigation system applied to a pair of concept missions at Lunar distances. These studies will demonstrate how high-sensitivity GPS (or GNSS) receivers paired with onboard navigation software, as in MMS-Navigation system, can extend the envelope of autonomous onboard GPS navigation far from the Earth

Performance Evaluation of Block Acquisition and Tracking Algorithms Using an Open Source GPS Receiver Platform

Location technologies have many applications in wireless communications, military and space missions, etc. US Global Positioning System (GPS) and other existing and emerging Global Navigation Satellite Systems (GNSS) are expected to provide accurate location information to enable such applications. While GNSS systems perform very well in strong signal conditions, their operation in many urban, indoor, and space applications is not robust or even impossible due to weak signals and strong distortions. The search for less costly, faster and more sensitive receivers is still in progress. As the research community addresses more and more complicated phenomena there exists a demand on flexible multimode reference receivers, associated SDKs, and development platforms which may accelerate and facilitate the research. One of such concepts is the software GPS/GNSS receiver (GPS SDR) which permits a facilitated access to algorithmic libraries and a possibility to integrate more advanced algorithms without hardware and essential software updates. The GNU-SDR and GPS-SDR open source receiver platforms are such popular examples. This paper evaluates the performance of recently proposed block-corelator techniques for acquisition and tracking of GPS signals using open source GPS-SDR platform

GPS Based Autonomous Navigation Study for the Lunar Gateway

This paper describes and predicts the performance of a conceptual autonomous GPS-based navigation system for NASA's planned lunar Gateway. This system is based on the flight-proven Magnetospheric Multiscale (MMS) GPS navigation system, augmented with an earth-pointed high-gain antenna and with an option for an atomic clock. High-fidelity simulations, calibrated against MMS flight data and making use of GPS transmitter patterns from the GPS Antenna Characterization Experiment (ACE) project are developed for operation of the system in the Gateway Near-Rectilinear Halo Orbit (NRHO). The results indicate that GPS can provide an autonomous, realtime navigation capability with comparable, or superior, performance to traditional Deep Space Network approach with eight hours of tracking per day

New High-Altitude GPS Navigation Results from the Magnetospheric Multiscale Spacecraft and Simulations at Lunar Distances

No abstract availabl

Adapting the SpaceCube v2.0 Data Processing System for Mission-Unique Application Requirements

The SpaceCube (sup TM) v2.0 system is a superior high performance, reconfigurable, hybrid data processing system that can be used in a multitude of applications including those that require a radiation hardened and reliable solution. This paper provides an overview of the design architecture, flexibility, and the advantages of the modular SpaceCube v2.0 high performance data processing system for space applications. The current state of the proven SpaceCube technology is based on nine years of engineering and operations. Five systems have been successfully operated in space starting in 2008 with four more to be delivered for launch vehicle integration in 2015. The SpaceCube v2.0 system is also baselined as the avionics solution for five additional flight projects and is always a top consideration as the core avionics for new instruments or spacecraft control. This paper will highlight how this multipurpose system is currently being used to solve design challenges of three independent applications. The SpaceCube hardware adapts to new system requirements by allowing for application-unique interface cards that are utilized by reconfiguring the underlying programmable elements on the core processor card. We will show how this system is being used to improve on a heritage NASA GPS technology, enable a cutting-edge LiDAR instrument, and serve as a typical command and data handling (C&DH) computer for a space robotics technology demonstration

Results from Navigator GPS Flight Testing for the Magnetospheric MultiScale Mission

No abstract availabl