Three Dimensional Bistatic Tomography Using HDTV

The thesis begins with a review of the principles of diffraction and reflection tomography; starting with the analytic solution to the inhomogeneous Helmholtz equation, after linearization by the Born approximation (the weak scatterer solution), and arriving at the Filtered Back Projection (Propagation) method of reconstruction. This is followed by a heuristic derivation more directly couched in the radar imaging context, without the rigor of the general inverse problem solution and more closely resembling an imaging turntable or inverse synthetic aperture radar. The heuristic derivation leads into the concept of the line integral and projections (the Radon Transform), followed by more general geometries where the plane wave approximation is invalid. We proceed next to study of the dependency of reconstruction on the space-frequency trajectory, combining the spatial aperture and waveform. Two and three dimensional apertures, monostatic and bistatic, fully and sparsely sampled and including partial apertures, with controlled waveforms (CW and pulsed, with and without modulation) define the filling of k-space and concomitant reconstruction performance. Theoretical developments in the first half of the thesis are applied to the specific example of bistatic tomographic imaging using High Definition Television (HDTV); the United States version of DVB-T. Modeling of the HDTV waveform using pseudonoise modulation to represent the hybrid 8VSB HDTV scheme and the move-stop-move approximation established the imaging potential, employing an idealized, isotropic 18 scatterer. As the move-stop-move approximation places a limitation on integration time (in cross correlation/pulse compression) due to transmitter/receiver motion, an exact solution for compensation of Doppler distortion is derived. The concept is tested with the assembly and flight test of a bistatic radar system employing software-defined radios (SDR). A three dimensional, bistatic collection aperture, exploiting an elevated commercial HDTV transmitter, is focused to demonstrate the principle. This work, to the best of our knowledge, represents a first in the formation of three dimensional images using bistatically-exploited television transmitters

Seafloor depth estimation by means of interferometric synthetic aperture sonar

The topic of this thesis is relative depth estimation using interferometric sidelooking sonar. We give a thorough description of the geometry of interferometric sonar and of time delay estimation techniques. We present a novel solution for the depth estimate using sidelooking sonar, and review the cross-correlation function, the cross-uncertainty function and the phase-differencing technique. We find an elegant solution to co-registration and unwrapping by interpolating the sonar data in ground-range. Two depth estimation techniques are developed: Cross-correlation based sidescan bathymetry and synthetic aperture sonar (SAS) interferometry. We define flank length as a measure of the horizontal resolution in bathymetric maps and find that both sidescan bathymetry and SAS interferometry achieve theoretical resolutions. The vertical precision of our two methods are close to the performance predicted from the measured coherence. We study absolute phase-difference estimation using bandwidth and find a very simple split-bandwidth approach which outperforms a standard 2D phase unwrapper on complicated objects. We also examine advanced filtering of depth maps. Finally, we present pipeline surveying as an example application of interferometric SAS

GNSS-R as a source of opportunity for remote sensing of the cryosphere

This work evaluates the potential use of signals from the Global Navigation Satellite Systems (GNSS) that scatter off the Earth surface for the retrieval of geophysical information from the cryosphere. For this purpose, the present study is based on data collected with a dedicated reflectometry GNSS receiver during two field campaigns, which were focused on two types of characteristic surfaces of the cryosphere: thin sea ice covers and thick dry snow accumulations. During the first experiment, the complete process of formation, evolution and melting of sea ice was monitorized for more than seven months in a bay located in Greenland. This type of ice is typically characterized by its thickness, concentration and roughness. Different observables from GNSS reflections are analyzed to try to infer these properties. The ice thickness is linked to the free-board level, defined as the height of the sea ice surface. Accurate phase altimetry is achieved, showing good agreement with an Arctic tide model. In addition, the long term results of ellipsoidal height retrievals are consistent with the evolution of the ice surface temperature product given by MODIS, which is a key parameter in the rate of growth of sea ice. On the other hand, the presence of salinity in the sea ice modifies its dielectric properties, resulting in different amplitude and phase for the co- and cross-polar components of the complex Fresnel coefficients. The polarimetric measurements obtained show good agreement with visual inspections of ice concentration from an Arctic weather station. Finally, the shape of the reflected signals and its phase dispersion are tested as potential signatures of surface roughness. For comparison, ice charts of the experimental area are employed. In particular, maximums in roughness given by the GNSS observables coincide with fast ice events. Fast ice is defined as ice anchored to the coast, where the tidal movements contribute to the development of strange patterns, cracks, and fissures on its surface, thus consistent with the GNSS-R roughness retrievals. The second experiment took place on Antarctica, monitoring a pristine snow area which is well-known for the calibration of remote sensing instruments. Due to the relative stability of the snow layers, the data acquisition was limited to ten continuous days. Interferometric beats were found after a first analysis of the amplitude from the collected signals, which were consistent with a multipath model where the reflector lies below the surface level. Motivated by these results, a forward model is developed that reconstructs the complex received signal as a sum of a finite number of reflections, coming from different snow layers (a snow density profile obtained from in-situ measurements). The interferometric information is then retrieved from the spectral analysis applied to time series from both real and modeled signals (lag-holograms). We find that the frequency bands predicted by the model are in general consistent with the data and the lag-holograms show repeatability for different days. Then, we attempt a proper inversion of the collected data to determine the dominant layers of the dry snow profile that contribute to L-band reflections, which are related to significant gradients of snow density/permittivity.Aquest treball avalua el possible ús dels senyals dels sistemes mundials de navegació per satèl lit (GNSS) que es reflecteixen a la superfície terrestre, per a l’extracció de la informació geofísica de la criosfera. Amb aquest propòsit, el present estudi es basa en dades recollides amb un reflectòmetre GNSS durant dues campanyes experimentals, centrades en dos tipus de superfícies característiques de la criosfera: cobertes de gel marí i gruixudes acumulacions de neu seca. En el primer experiment, el procés complet de formació, evolució i fusió del gel marí va ser monitoritzat durant més de set mesos a una badia situada a Groenlàndia. Aquest tipus de gel es caracteritza típicament amb el seu gruix, concentració i rugositat. Diferents observables de les reflexions GNSS són analitzats per tractar de fer una estimació d’aquestes propietats. El gruix de gel està relacionat amb el nivell de francbord, que a la seva vegada està relacionat amb l’alçada de la superfície de gel marí. S’ha aconseguit altimetria de fase precisa, que mostra correlació amb un model de marea de l’Àrtic. A més, els resultats a llarg termini de l’alçada elipsoidal segueixen l’evolució de les mesures de temperatura de superfície de gel donades per MODIS. La temperatura és un paràmetre clau en el ritme de creixement del gel marí. Per altra banda, la presència de sal a aquest tipus de gel modifica les seves propietats dielèctriques, el que implica variacions d’amplitud i fase per als coeficients de Fresnel complexos amb polaritzacions oposades. Les mesures polarimètriques obtingudes mostren concordança amb els valors de concentració de gel obtinguts des d’una estació meteorològica propera. Finalment, la forma de la senyal reflectida i la dispersió de la seva fase s’evaluen com a potencials indicadors de la rugositat de superfície. Per a la seva comparació, es fan servir mapes del gel de la zona experimental. En concret, els valors màxims a la rugositat estimada a partir pels observables GNSS coincideixen amb el gel fixe, que es refereix a gel ancorat a la costa, on els moviments de les marees contribueixen al desenvolupament de patrons estranys, esquerdes i fissures en la seva superfície. El segon experiment es va dur a terme a l’Antàrtida, monitoritzant una àrea de neu pristina que és ben coneguda per al calibratge d’instruments de teledetecció. A causa de la relativa estabilitat de les capes de neu, l’adquisició de dades es va limitar a deu dies consecutius. Es van trobar pulsacions interferomètriques a partir d’un primer anàlisi de l’amplitud de les senyals recollides, les quals eren compatibles amb un model de propagació multicamí a on el reflector es troba per sota del nivell de superfície. Com a conseqüència d’aquests resultats, s’ha desenvolupat un model que reconstrueix el senyal complexe rebut com la suma d’un nombre finit de reflexions, procedents de diferents capes de neu (determinat per mesures locals). La informació interferomètrica es recupera després de l’anàlisi espectral aplicat a les sèries temporals tant de les senyals reals, com de les modelades (lag-hologrames). Trobem que les bandes de freqüències predites pel model són en general consistents amb les dades i que els lag-hologrames mostren repetibilitat per dies diferents. Posteriorment, es realitza un anàlisi de les dades recollides per determinar les capes dominants del perfil de neu seca que contribueixen a les reflexions en banda L, i que a la seva vegada, estan relacionades amb gradents significatius de densitat/permitivitat.Este trabajo evalúa el posible uso de las señales de los sistemas globales de navegación por satélite (GNSS) que se reflejan en la superficie terrestre para la extracción de información geofísica de la criosfera. Con este propósito, el presente estudio se basa en datos recogidos con un reflectómetro GNSS durante dos campañas experimentales, centradas en dos tipos de superficies características de la criosfera: capas de hielo marino y gruesas acumulaciones de nieve seca. Durante el primer experimento, el proceso completo de formación, evolución y fusión del hielo marino fue monitorizado durante más de siete meses en una bahía ubicada en Groenlandia. Este tipo de hielo se caracteriza típicamente por su grosor, concentración y rugosidad. Diferentes observables de las reflexiones GNSS son analizados para tratar de estimar dichas propiedades. El espesor de hielo está relacionado con el nivel de francobordo o borda libre, que a su vez está relacionado con la altura de la superficie de hielo marino. Se ha logrado altimetría de fase precisa, mostrando correlación con un modelo de marea del Ártico. Además, los resultados a largo plazo de la altura elipsoidal siguen la evolución de las mediciones de temperatura de superficie de hielo proporcionadas por MODIS. La temperatura es un parámetro clave en el ritmo de crecimiento del hielo marino. Por otro lado, la presencia de sal en este tipo de hielo modifica sus propiedades dieléctricas, lo que implica variaciones en las amplitudes y fases de los coeficientes complejos de Fresnel con polarizaciones opuestas. Los resultados polarimétricos concuerdan con los valores de concentración de hielo obtenidos mediante inspección visual desde una estación meteorológica cercana. Por último, la forma de la señal reflejada y la dispersión de su fase son evaluadas como potenciales indicadores de la rugosidad de superficie. Para su comparación, se emplean mapas del hielo de la zona experimental. En particular, valores máximos de rugosidad estimada por los observables GNSS coinciden con hielo fijo, que se refiere al hielo anclado a la costa, donde los movimientos de las mareas contribuyen al desarrollo de patrones extraños, grietas y fisuras en su superficie. El segundo experimento se llevó a cabo en la Antártida, monitorizando una área de nieve pristina que es bien conocida para la calibración de instrumentos de teledetección. Debido a la relativa estabilidad de las capas de nieve, la adquisición de datos se limitó a diez días consecutivos. Se encontraron pulsaciones interferométricas a partir de un primer análisis de la amplitud de las señales recibidas, las cuales eran compatibles con un modelo de propagación multicamino donde el reflector se encuentra por debajo del nivel de la superficie. Como consecuencia de estos resultados, se ha desarrollado un modelo que reconstruye la señal recibida como la suma de un número finito de reflexiones, procedentes de diferentes capas de nieve (caracterizados por mediciones locales). La información interferométrica se recupera después del análisis espectral aplicado a las series temporales tanto de las señales reales, como de las modeladas (lag-hologramas). Encontramos que las bandas de frecuencias predichas por el modelo son en general consistentes con los datos y que los lag-hologramas muestran repetibilidad para días diferentes. Posteriormente, se realiza un análisis de los datos recogidos para determinar las capas dominantes del perfil de nieve seca que contribuyen a las reflexiones en banda L, y que a su vez, están relacionadas con gradientes significativos de densidad/permitivida

Information Theoretic Limits on Non-cooperative Airborne Target Recognition by Means of Radar Sensors

The main objective of this research is to demonstrate that information theory, and specifically the concept of mutual information (MI) can be used to predict the maximum target recognition performance for a given radar concept in combination with a given set of targets of interest. This approach also allows for the direct comparison of disparate approaches to designing a radar concept which is capable of target recognition without resorting to choosing specific feature extraction and classification algorithms. The main application area of the study is the recognition of fighter type aircraft using surface based radar systems, although the results are also applicable to airborne radars. Information theoretic concepts are developed mathematically for the analysis of the radar target recognition problem. The various forms of MI required for this application are derived in detail and are tested rigorously against results from digital communication theory. The results are also compared to Shannon’s channel capacity bound, which is the fundamental limit on the amount of information which can be transmitted over a channel. Several sets of simulation based experiments were conducted to demonstrate the insights achievable by applying MI concepts to quantitatively predict the maximum achievable performance of disparate approaches to the radar target recognition problem. Asymptotic computational electromagnetic code was applied to calculate the target’s response to the radar signal for freely available geometrical models of fighter aircraft. The calculated target responses were then used to quantify the amount of information which is transmitted back to the radar about the target as a function of signal to noise ratio (SNR). The information content of the F-14, F-15 and F-16 were evaluated for a 480 MHz bandwidth waveform at 10 GHz as a baseline. Several ultra-wideband (UWB) waveforms, spanning 2-10 GHz, 10- 18 GHz and 2-18 GHz, but which were highly range ambiguous, were evaluated and showed SNR gains of 0.5-2 dB relative to the baseline. The effect of sensing the full polarimetric response of an F-18 and F-35 was evaluated and SNR gains of 5-7 dB over a single linear polarisation were measured. A Boeing 707 scale model (1:25) was measured in the University of Pretoria’s compact range spanning 2-18 GHz and gains of 2 dB were observed between single and dual linear polarisations. This required numerical integration in 8004 dimensions, demonstrating the stability of the MI estimation algorithm in high dimensional signal spaces. The information gained by including the difference channel signal of an X-band monopulse radar for the F-14 data set was approximately 3 dB at 50 km and increased to 4.5 dB at 2 km due to the increased target extent relative to the antenna pattern. This experiment necessitated the use of target profiles which were matched to the range of the target to achieve maximum information transfer. Experiments were conducted to evaluate the loss in information due to envelope processing. For the baseline data set, SNR losses in the region of 7 dB were measured. Linear pre-processing using the fast Fourier transform (FFT) and principal component analysis (PCA), before envelope processing, were compared and the PCA algorithm outperformed the FFT by approximately 1 dB at high MI values. Finally, the expression for multi-target MI was applied in conjunction with Fano’s inequality to predict the probability of incorrectly classifying a target. Probability of error is a critical parameter for a radar user. For the baseline data set, at P(error) = 0.001, maximum losses in the region of 0.6 to 0.9 dB were measured. This result shows that these targets are easily separable in the signal space. This study was only the proverbial “tip of the iceberg” and future research could extend the results and applications of the techniques developed. The types of targets and configurations of the individual targets could be increased and analysed. The analysis should also be extended to describe effects internal to the radar such as phase noise, spurious signals and analogue to digital converters and external effects such as clutter and multipath. The techniques could also be applied to quantify the gains in target recognition performance achievable for multistatic radar, multiple input multiple output (MIMO) radar and more exotic concepts, such as the fusion of data from multiple monostatic microwave radars with multi-receiver multi-band passive bistatic radar (PBR) data