A Study in GPS-Denied Navigation Using Synthetic Aperture Radar

In modern navigation systems, GPS is vital to accurately piloting a vehicle. This is especially true in autonomous vehicles, such as UAVs, which have no pilot. Unfortunately, GPS signals can be easily jammed or spoofed. For example, canyons and urban cities create an environment where the sky is obstructed and make GPS signals unreliable. Additionally, hostile individuals can transmit personal signals intended to block or spoof GPS signals. In these situations, it is important to find a means of navigation that doesn’t rely on GPS. Navigating without GPS means that other types of sensors or instruments must be used to replace the information lost from GPS. Some examples of additional sensors include cameras, altimeters, magnetometers, and radar. The work presented in this thesis shows how radar can be used to navigate without GPS. Specifically, synthetic aperture radar (SAR) is used, which is a method of processing radar data to form images of a landscape similar to images captured using a camera. SAR presents its own unique set of benefits and challenges. One major benefit of SAR is that it can produce images of an area even at night or through cloud cover. Additionally, SAR can image a wide swath of land at an angle that would be difficult for a camera to achieve. However, SAR is more computationally complex than other imaging sensors. Image quality is also highly dependent on the quality of navigation information available. In general, SAR requires that good navigation data be had in order to form SAR images. The research here explores the reverse problem where SAR images are formed without good navigation data and then good navigation data is inferred from the images. This thesis performs feasibility studies and real data implementations that show how SAR can be used in navigation without the presence of GPS. Derivations and background materials are provided. Validation methods and additional discussions are provided on the results of each portion of research

The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201

Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases

Compressive Inverse Scattering II. SISO Measurements with Born scatterers

Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident and the sampling directions are related in a precise way and are capable of recovering exactly scatterers of sufficiently low sparsity. For point targets, various sampling techniques are proposed to transform the scattering matrix into the random Fourier matrix. The results for point targets are then extended to the case of localized extended targets by interpolating from grid points. In particular, an explicit error bound is derived for the piece-wise constant interpolation which is shown to be a practical way of discretizing localized extended targets and enabling the compressed sensing techniques. For distributed extended targets, the Littlewood-Paley basis is used in analysis. A specially designed sampling scheme then transforms the scattering matrix into a block-diagonal matrix with each block being the random Fourier matrix corresponding to one of the multiple dyadic scales of the extended target. In other words by the Littlewood-Paley basis and the proposed sampling scheme the different dyadic scales of the target are decoupled and therefore can be reconstructed scale-by-scale by the proposed method. Moreover, with probes of any single frequency \om the coefficients in the Littlewood-Paley expansion for scales up to \om/(2\pi) can be exactly recovered.Comment: Add a new section (Section 3) on localized extended target

Emergency Response Equipment and Related Training: Airborne Radiological Computer System (Model II)

The materials included in the Airborne Radiological Computer System, Model-II (ARCS-II) were assembled with several considerations in mind. First, the system was designed to measure and record the airborne gamma radiation levels and the corresponding latitude and longitude coordinates, and to provide a first overview look of the extent and severity of an accident's impact. Second, the portable system had to be light enough and durable enough that it could be mounted in an aircraft, ground vehicle, or watercraft. Third, the system must control the collection and storage of the data, as well as provide a real-time display of the data collection results to the operator. The notebook computer and color graphics printer components of the system would only be used for analyzing and plotting the data. In essence, the provided equipment is composed of an acquisition system and an analysis system. The data can be transferred from the acquisition system to the analysis system at the end of the data collection or at some other agreeable time

Graphs Obtained From Collections of Blocks

Given a collection of $d$-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially. It is known that if $d \geq 3$, such block graphs can have arbitrarily large chromatic number. We prove that the chromatic number can be bounded with only a mild restriction on the sizes of the blocks. We also show that block graphs of block configurations arising from partitions of $d$-dimensional hypercubes into sub-hypercubes are at least $d$-connected. Bounds on the diameter and the hamiltonicity of such block graphs are also discussed