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Modeling synthetic aperture radar image dataMatthew Pianto, Donald 31 January 2008 (has links)
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Previous issue date: 2008 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nessa tese estudamos a estimação por máxima verossimilhança (MV) do parâmetro de aspereza
da distribuição G 0
A de imagens com speckle (Frery et al., 1997). Descobrimos que, satisfeita
uma certa condição dos momentos amostrais, a função de verossimilhança é monótona e as estimativas
MV são infinitas, implicando uma região plana. Implementamos quatro estimadores
de correção de viés em uma tentativa de obter estimativas MV finitas. Três dos estimadores
são obtidos da literatura sobre verossimilhança monótona (Firth, 1993; Jeffreys, 1946) e um,
baseado em reamostragem, é proposto pelo autor. Fazemos experimentos numéricos de Monte
Carlo para comparar os quatro estimadores e encontramos que não existe um favorito claro, a
menos quando um parâmetro (dado a priori da estimação) toma um valor específico. Também
aplicamos os estimadores a dados reais de radar de abertura sintética. O resultado desta análise
mostra que os estimadores precisam ser comparados com base em suas habilidades de classificar
regiões corretamente como ásperas, planas, ou intermediárias e não pelos seus vieses e
erros quadráticos médios
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Etude des séries temporelles en imagerie satellitaire SAR pour la détection automatique de changements / Study of satellite SAR time series for automatic change detectionQuin, Guillaume 27 January 2014 (has links)
Cette thèse présente la méthode de détection de changements MIMOSA (Method for generalIzed Means Ordered Series Analysis). Cette nouvelle méthode permet de détecter automatiquement des changements entre couples ou séries temporelles d’images SAR. En effet, grâce aux moyennes temporelles, le nombre d’images en jeu n’importe plus puisque seulement deux moyennes différentes sont comparées de sorte à détecter les changements (par exemple moyenne géométrique et moyenne quadratique). De ce fait, les grand volumes de données disponibles de nos jours sont exploitables plus facilement puisque l’information utile est «résumée» dans les moyennes. Le seul paramètre de la détection est le taux de fausses alarmes obtenu dans le résultat, ce qui rend son analyse plus intuitive. Les cartes de changements fournies par MIMOSA sont de très bonne qualité en comparaison à celles fournies par d’autres méthodes. De nombreux tests ont été mis en place pour constater la robustesse de la méthode MIMOSA face aux problèmes les plus souvent rencontrés, comme une mauvaise calibration radiométrique, ou encore un mauvais recalage. Une interface graphique a de plus été développée autour de MIMOSA, incorporant de nombreux outils de préparation et traitement des données, ainsi que des outils d’analyse des résultats. / This PhD thesis presents the MIMOSA (Method for generalIzed Means Ordered Series Analysis) change detection methood. This new technique can automatically detect changes between SAR image pairs or within time series. Indeed, thanks to the temporeal means, the number of involved images doesn’t matters because only two different means are compared to detect the changes (for example, the geometric and quadratic means). Thus, large data volumes can be processed easily, since the useful information is condensed within the temporal means. The only change detection parameter is the false alarm rate that will be MIMOSA method are very good compared to other methods. Several tests have been performed in order to quantify the robustness of the method facing the most common problems, like image misregistration or radiometric calibration errors. A graphical user interface has also been developed for MIMOSA, including many useful tools to prepare and process SAR data, but also several analyse tools.
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Windowed Factorized Backprojection for Pulsed and LFM-CW Stripmap SARMoon, Kyra Michelle 19 April 2012 (has links) (PDF)
Factorized backprojection is a processing algorithm for reconstructing images from data collected by synthetic aperture radar (SAR) systems. Factorized backprojection requires less computation than conventional time-domain backprojection with little loss in accuracy for straight-line motion. However, its implementation is not as straightforward as direct backprojection. Further, implementing an azimuth window has been difficult in previous versions of factorized backprojection. This thesis provides a new, easily parallelizable formulation of factorized backprojection designed for both pulsed and linearly frequency modulated continuous wave (LFM-CW) stripmap SAR data. A method of easily implementing an azimuth window as part of the factorized backprojection algorithm is introduced. The approximations made in factorized backprojection are investigated and a detailed analysis of the corresponding errors is provided. We compare the performance of windowed factorized backprojection to direct backprojection for simulated and actual SAR data.
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Target Motion Estimation Techniques for Single-Channel SARCrockett, Mark T. 13 June 2014 (has links) (PDF)
Synthetic aperture radar (SAR) systems are versatile, high-resolution radar imagers useful for providing detailed intelligence, surveillance, and reconnaissance, especially when atmospheric conditions are non-ideal for optical imagers. However, moving targets in SAR images are smeared. Along-track interferometry is a commonly-used method for extracting the motion parameters of moving targets but requires a dual-aperture SAR system, which may be power- size- or cost-prohibitive. This thesis presents a method of estimating target motion parameters in single-channel SAR data given geometric target motion constraints. I test this method on both simulated and actual SAR data. This estimation method includes an initial estimate, computation of the SAR ambiguity function, and application of the target motion constraints to form a focused image of the moving target. The constraints are imposed by assuming that target motion is restricted to a road. Finally, I measure its performance by investigating the error introduced in the motion estimates using both simulated and actual data.
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The Influence of Bubbles on the Seasonal SAR Backscatter Response of Perennially Ice-Covered Lakes, AntarcticaGaudreau, Adam 20 November 2023 (has links)
Antarctica is home to numerous perennially ice-covered (PIC) lakes that host rich benthic microbial ecosystems. These lakes are covered by a thick floating ice cover year-round and often have water columns supersaturated in dissolved gases, resulting in heavily bubbled ice covers, altering the optical properties of the ice and the amount of light that penetrates into the water column. Thus, understanding the optical properties of perennial lake ice can have important scientific implications to the study of life on Earth and the search for extraterrestrial life. Synthetic aperture radar (SAR) remote sensing has been used rigorously for over 50 years to study and monitor the seasonal response and long-term trends of backscatter over seasonally ice-covered (SIC) Arctic lakes. Limited studies have assessed the impacts of dissolved gases and ice/water interface bubbles on SAR backscatter variability over SIC lakes. The seasonal backscatter response of Antarctic PIC lakes remains unexplored; their physical nature asserts that their backscatter response should largely be decoupled from seasonal factors according to SIC lake backscatter theory. Additionally, gas supersaturated PIC lakes are ideal candidates to better understand the role of gas buildup and bubble formation on the backscatter response from floating ice covers.
This thesis leverages a dense stack of Sentinel-1 C-band SAR imagery over Lake Untersee, a well-sealed PIC lake in East Antarctica, to explore the relationships between SAR backscatter and ice/water interface bubbles. This analysis integrates field measurements and temporal observations at the ice/water interface. Lastly, a brief comparative analysis extends to other ice covers, including moat-forming PIC lakes, as well as first-year and multi-year Arctic sea and lake ice. It is shown that Lake Untersee has a seasonal backscatter regime that is linked to air temperature. A strong correlation is found between the timing of backscatter intensity increase in winter and ice thickness. This relationship is attributed to variations in ice thickness which affect the length of the freezing period under the ice, the rate of dissolved gas accumulation, and ultimately, the nucleation and abundance of bubbles at the ice/water interface. These findings can be applied to other PIC lakes that have seasonal gas regimes. This research provides valuable insights into the complex interplay between ice cover characteristics, gas dynamics, interface bubbles, and SAR backscatter, enhancing our understanding of polar aquatic ecosystems and their broader implications for global environments.
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Contribution of New Types of Radar Data to Land Cover and Crop Classification in Remote SensingBusquier, Mario 20 July 2023 (has links)
For some time now, there has been a growing awareness in society about climate change, pollution, energy and the use of natural resources. This thinking has permeated society, mainly because the extreme natural phenomena that we are experiencing nowadays are no longer outliers in our time series of meteorological records. In this regard, it has been proven that the actual high temperatures are not only unparalleled, but also consistent around the globe which is something that had not happened until now (Neukom et al., 2019). The XX century was a turning point when it comes to the increase of the landuse for crops. In a context where the population doubled, the crop production for food from 1960 to 2010 tripled, helping to reduce the hungry population. When the world’s population is expected to continue to grow up to 9 billion people (Goodfray et al., 2010) by middle XXI century, it is essential to provide ourselves with the necessary tools to maximise crop production by taking advantage of all the resources available under a sustainable point of view. Under this context, all farmers in the European Union (EU) have the possibility to benefit from the Common Agricultural Policy (CAP), which came into force in 1960. The CAP is responsible for the financing of aid to farmers on a cross-compliance basis, based on the declaration of crop types. Traditionally, the authorities have checked the veracity of declarations in person through field inspections, which is clearly a highly inefficient, impractical and very expensive system. However, in 2018 the European Commission drafted an amendment to the CAP (European Commission, 2018), to be implemented in 2020, recommending the establishment of newprocedures for checking declarations, including the use of satellite data from the Copernicus programme or other new technologies. Among the various satellite technologies, Synthetic Aperture Radar (SAR) (Brown,1967; Curlander and McDonough, 1992) has proven the most reliable,as the images are acquired with a constant pass period and they are not subject to cloud problems (as is the case with sensors working in the optical domain) and information can be acquired both day and night. They are based in a SAR microwave sensor installed on a satellite platform with a forward trajectory which offers side-looking imaging geometries. Working in a range between 300 MHz and 30 GHz, the SAR sensor is in charge of emitting electromagnetic pulses and receiving the resulting echoes from the imaged target, which can help retrieve information about its dielectric properties, geometry, orientation, shape, and its behaviour along time. For a given target, the SAR backscattering response σ0 is function of many parameters (Lee and Pottier, 2017; Dobson et al., 1985): wave frequency, polarisation, imaging configuration, roughness, geometrical structure and dielectric properties. This makes the information extraction a major problem, as identical radar responses from two different targets may lead to the same result. To cope with this problem, the main techniques are based on extending the observation space by working with the full diversity of data. Thus, the main axes of SAR data are: • Time • Polarimetry • Interferometry • Frequency. Time series of radar data constitutes a major source of information for the classification of crops and land cover, since it makes it possible to distinguish between classes by their temporal behaviour: some land covers show a uniform response along time (e.g. urban areas), whereas there are others subject to seasonal changes (e.g. crops). It may happen that different crop species give the same radar response at a given time, however, when the time window becomes larger, and consecutive acquisitions are taken over a shorter time span, the more one can detect abrupt changes in the target over a longer time interval. Polarimetry is sensitive to the shape, orientation and the scattering mechanisms of the scatterers (Boerner et al.,1981; Zyl, Zebker, and Elachi, 1987). In that sense, when using different polarisations it is possible to discern better the true nature of the target, as some features may be visible in one polarisation but not in the others. Regarding multi-spectral data, it also constitutes a major source of information which can be exploited for classification purposes. Working with sensors operating at different frequencies, or wavelengths, provides diversity in the size of the elements of the scene to which the radar is sensitive as the radar backscattering will come from elements the size of the wavelength used it. For all of the above, multifrequency data provide complementary information, as each frequency operates and interacts with elements of the same wavelength or longer, and being transparent to all others. In addition, different bands are also associated with different spatial resolutions, so a high-frequency sensor can complement the classification performance of a low-frequency sensor when there are sufficiently small details in the scene that cannot be appreciated with the spatial resolution available at the lower frequency. From all the 4 axes exposed above, Interferometry (Graham, 1974) is without a doubt the least exploited for classification purposes. While polarimetry is sensitive to the scattering mechanisms of the scene by means of the polarisation information, interferometry adds the third dimension by being sensitive to the spatial distribution of the scatterers (Treuhaft et al., 1996). Coherence and phase difference computed between two complex-valued SAR images are the main descriptors of interferometry (Bamler and Hartl, 1998), and together, can be used to derive topographic information, vegetation structure, and deformation (volcanoes, landslides, etc.). For this reason, interferometry is especially suited for classification of covers in which there is vertical distribution of elements, e.g. urban areas and vegetation (forests and crops). Polarimetric interferometric SAR (PolInSAR) (Cloude and Papathanassiou, 1998; Treuhaft and Cloude, 1999), constitutes the next step forward, and is based on the application of interferometry to all polarisation channels. Polarimetry can identify the different scattering mechanisms in the scene by using the polarisation information, whilst interferometry is able to locate the effective scattering phase centres, which are mainly dependent on frequency, the polarisation employed, the physical, geometrical structure and orientation of the scatterer. By using the combination of both we can retrieve the vertical structure of the scene, which shows a great potential for classification purposes, since classes characterised by similar backscattering or polarimetric responses can be separated if their heights are different (e.g. types of buildings, forests, crops, etc.), whereas classes with similar heights, and hence similar interferometric coherence values (e.g. grass, crops, bare soil, etc.) can be resolved using their polarimetric response. In summary, PolInSAR-based classification is attractive since polarimetric ambiguities are resolved by interferometric information and vice-versa. The lack of exploitation of the 4 data axes in the literature, plus the arrival of a new generation of SAR sensors in the near future such as ROSE-L, BIOMASS and NISAR among others, offers a new range of possibilities in terms of new types of features for classification whose results and impact must be analysed. In this context, there are many types of SAR data (i.e. features) that have not been used yet, acquired from different sensors (Sentinel-1, PAZ, TanDEMX, TerraSAR-X and ALOS-2), and whose diversity axes, either used individually or jointly, have not yet been explored for classification applications. Therefore, the exploration of these new types of SAR data, whose contribution to classification is unknown regarding crop-type mapping, is the main objective of this doctoral thesis, and consequently also its main novelty. Based on the current state of the art of the research topic the main objective of this PhD thesis is to explore the added value of new SAR features, and their potential, alone or used together, for crop type and land cover classification. In the end, several experiments will be carried out, in different test sites, in which the proposed new features will be evaluated and compared with the traditional observables used so far, with the aim of evaluating their internal potential in classification applications. / Work supported by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Projects TEC2017-85244-C2-1-P and PID2020-117303GB-C22. Mario Busquier received a grant from the University of Alicante UAFPU20-08.
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Study on isolation improvement between closely-packed patch antenna arrays based on fractal metamaterial electromagnetic bandgap structuresAlibakhshikenari, M., Virdee, B.S., See, C.H., Abd-Alhameed, Raed, Ali, Ammar H., Falcone, F., Limiti, E. 11 October 2018 (has links)
Yes / A decoupling metamaterial (MTM) configuration based on fractal electromagnetic-bandgap (EMBG) structure is shown to significantly enhance isolation between transmitting and receiving antenna elements in a closely-packed patch antenna array. The MTM-EMBG structure is cross-shaped assembly with fractal-shaped slots etched in each arm of the cross. The fractals are composed of four interconnected-`Y-shaped' slots that are separated with an inverted-`T-shaped' slot. The MTM-EMBG structure is placed between the individual patch antennas in a 2 × 2 antenna array. Measured results show the average inter-element isolation improvement in the frequency band of interest is 17, 37 and 17 dB between radiation elements #1 & #2, #1 & #3, and #1 & #4, respectively. With the proposed method there is no need for using metallic-via-holes. The proposed array covers the frequency range of 8-9.25 GHz for X-band applications, which corresponds to a fractional-bandwidth of 14.5%. With the proposed method the edge-to-edge gap between adjacent antenna elements can be reduced to 0.5λ 0 with no degradation in the antenna array's radiation gain pattern. Across the array's operating band, the measured gain varies between 4 and 7 dBi, and the radiation efficiency varies from 74.22 and 88.71%. The proposed method is applicable in the implementation of closely-packed patch antenna arrays used in SAR and MIMO systems. / Partially supported by innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET-722424 and the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1.
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Structure and Persistence of Surface Ship WakesSomero, John Ryan 20 January 2021 (has links)
It has long been known that ship wakes are observable by synthetic aperture radar. However, incomplete physical understanding has prevented the development of simulation tools that can predict both the structure and persistence of wakes in the ocean environment. It is the focus of this work to develop an end-to-end multi-scale modeling-and-simulation methodology that captures the known physics between the source of disturbance and the sensor. This includes turbulent hydrodynamics, free-surface effects, environmental forcing through Langmuir-type circulations, generation of surface currents and redistribution of surface-active substances, surface-roughness modification, and simulation of the signature generated by reflection and scattering of electromagnetic waves from the ocean surface. The end-to-end methodology is based upon several customized computational fluid dynamics solvers and empirical models which are linked together. The unsteady Reynolds-averaged Navier-Stokes equations, including models for the Craik-Leibovich vortex force and near surface Reynolds-stress anisotropy, are solved at full-scale Reynolds and Froude numbers on domains that extend tens of kilometers behind the ship. A parametric study is undertaken to explore the effects of ship heading, ship propulsion, ocean-wave amplitude and wavelength, and the relative importance of Langmuir-type circulations vs. near-surface Reynolds-stress anisotropy on the generation of surface currents that are transverse to the wake centerline. Due to the vortex force, the structure of the persistent wake is shown to be a function of the relative angle between the ambient long-wavelength swell and the ship heading. Ships operating in head seas observe 1-3 streaks, while ships operating in following seas observe 2 symmetric streaks. Ships operating in calm seas generate similar wakes to those in following seas, but with reduced wake width and persistence. In addition to the structure of the persistent wake, the far wake is shown to be dominated by ship-induced turbulence and surface-current gradients generating a wide center wake. The redistribution of surface-active substances by surface currents is simulated using a scalar-transport model on the ocean surface. Simulation of surface-roughness modification is accomplished by solving a wave-action balance model which accounts for the relative change in the ambient wave-spectrum by the surface currents and the damping-effects of surface-active substances and turbulence. Simulated returns from synthetic aperture radar are generated with two methods implemented. The first method generates a perfect SAR image where the instrument and platform based errors are neglected, but the impact of a randomized ocean field on the radar cross section is considered. The second method simulates the full SAR process including signal detection and processing. Comparisons are made to full-scale field experiments with good agreement between the structure of the persistent wake and observed SAR imagery. / 1 / It has long been known that ship wakes are observable by synthetic aperture radar. However, incomplete physical understanding has prevented the development of simulation tools that can predict both the structure and persistence of wakes in the ocean environment, which is critical to understanding both the design and operation of maritime remote sensors as well as providing tactically relevant operational guidance and awareness of the maritime domain. It is the focus of this work to develop an end-to-end multi-scale modeling-and simulation methodology that captures the known physics between the source of disturbance and the sensor. This includes turbulent hydrodynamics, free-surface effects, environmental forcing, generation of surface currents and redistribution of surface-active substances, surface-roughness modification, and simulation of the signature from the ocean surface. The end-to-end methodology is based upon several customized computational fluid dynamics solvers and empirical models. The unsteady Reynolds-averaged Navier-Stokes equations, including models to account for environmental effects and near-surface turbulence, are solved at full-scale on domains that extend tens of kilometers behind the ship. A parametric study is undertaken to explore the effects of ship heading, ship propulsion, ocean-wave amplitude and wavelength, and the relative importance of environmental forcing vs. near-surface turbulence on the generation of surface currents that are transverse to the wake centerline. Due to the environmental forcing, the structure of the persistent wake is shown to be a function of the relative angle between the ambient long-wavelength swell and the ship heading. Ships operating in head seas observe 1-3 streaks, while ships operating in following seas observe 2 symmetric streaks. Ships operating in calm seas generate similar wakes to those in following seas, but with reduced wake width and persistence. In addition to the structure of the persistent wake, the far wake is shown to be dominated by ship-induced turbulence and surface-current gradients generating a wide center wake. The redistribution of surface films by surface currents is simulated using a scalar-transport model on the ocean surface. Simulation of surface-roughness modification is accomplished by solving a wave-action-balance model which accounts for the relative change in the ambient surface profile by the surface currents and the damping-effects of surface-active substances and turbulence. Simulated returns from synthetic aperture radar are generated with two methods implemented. The first method generates a perfect SAR image where the instrument and platform based errors are neglected, but the impact of a randomized ocean field on the radar cross section is considered. The second method simulates the full SAR process including signal detection and processing. Comparisons are made to full-scale field experiments with good agreement between the structure of the persistent wake and observed SAR imagery.
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Reliable On Board Data Processing System for the ICEYE- 1 satelliteKorczyk, Jakub January 2016 (has links)
Recent development in electronics for mobile devices has led to the decrease in sizes and cost of autonomous complex embedded systems such as satellites. It is now possible to build a satellite quicker and only for a fraction of previous costs by using Commercial Off The Shelf (COTS) components. Yet, there are some obstacles that need to be overcome before a successful small satellite can be designed. Among these are the radiation environment, thermal issues, the overall system complexity and tight schedules. This thesis addresses these issues and proposes an overall approach for designing small satellites’ electronics. This approach can be summarised in 6 recommendations: Keep it simple Use fast hardware iterations Do not use space grade components Use a single string design on the system level (no redundancy) Design with limited trust in the software Use simple, accessible and easy updatable documentation With respect to those recommendations an on board data processing system, the Processing Board, has been designed for the ICEYE-1 satellite. The ICEYE-1 satellite is a fully commercial Synthetic Aperture Radar (SAR) satellite that will be launched in December 2017. The designed board has been manufactured and verified during airborne test campaigns. / Nya elektronikutvecklingar för mobiltelefoner har lett till en minskning av storlek och kostnader för andra autonoma komplexa inbyggda system som t.ex. satelliter. Så kallade småsatelliter kan numera byggas snabbare och för endast en bråkdel av tidigare kostnader med hjälp av Commercial Off The Shelf (COTS) komponenter. Det finns dock vissa hinder som måste övervinnas om man vill designa en pålitligt fungerande småsatellit. Till dessa kan räknas strålningsmiljön, väl fungerande värmeledning, det totala systemets komplexitet samt snäva tidtabeller. Detta examensarbete behandlar dessa frågor och föreslår en övergripande strategi för att designa elektronik för småsatelliter. Detta tillvägagångssätt kan sammanfattas i 6 rekommendationer: Håll det enkelt Implementera snabba hårdvaruiterationer Använd inte rymdklassade komponenter Använd ingen redundans på systemnivå Designa med en begränsad tilltro på mjukvaran Dokumentera på ett enkelt, tillgängligt och lätt uppdateringsbart sätt Dessa rekommendationer har använts till att utveckla ett databehandlingssystem, kallat "Processing Board", till småsatelliten ICEYE-1. ICEYE-1 är en kommersiell Synthetic Aperture Radar (SAR) satellit som kommer att skjutas i omloppsbana i december 2017. Databehandlingssystemet i fråga har utvecklats och verifierats i samband med flygplansburna testkampanjer.
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Above-ground biomass estimation in boreal productive forests using Sentinel-1 dataRoc Roc, David January 2019 (has links)
Estimation of biomass has high importance for economic, ecologic and climatic reasons due to the multiple ecosystem services offered by forested landscapes. Measurements that are taken in the field incur personal and economic costs. Nevertheless, biomass surveying based on remote sensing techniques offer efficiency thanks to covering large areas. The European Space Agency (ESA) Sentinel-1 satellite offers promising capabilities for above-ground biomass (AGB) estimation through synthetic aperture radar (SAR) based microwave remote sensing. In this study, experimental AGB estimations based on Sentinel-1 C-band data were produced over the Remingstorp estate (Västergötland County, Sweden) to analyze its performance over boreal productive forests. The obtained measurements were compared against reference values obtained by combining photogrammetric, aerial laser scanning (ALS) and field measurements. Thus, a reference high-resolution canopy height model (CHM) was produced from the difference between photogrammetric digital surface model (DSM) values and ALS digital terrain model (DTM) values. The comparison of CHM observations against diameter at breast height (DBH) field measurements revealed the existence of a vegetation height - vegetation volume relationship for the study species (Pinus Sylvestris and Picea Abbies), which allowed bole volume estimation based on vegetation height values. SAR-based AGB estimates were produced by defining statistical relationships between backscatter intensity and interferometric coherence measurements against reference CHM values. Additionally, evaluation of biomass estimation through interferometric (InSAR) height was possible by comparing against reference photogrammetric DSM. Backscatter signal saturation of C-band at low biomass volumes prevented quantification of biomass but permitted differentiation between forested and non-forested surfaces. Estimation of AGB through interferometric coherence was possible through modeling volumetric decorrelation, which on the contrary prevented biomass retrieval from InSAR height. Due to the given frequency properties at C-band, HV cross-polarized channel was used in all cases for better detection of the canopy layer. Image acquisition under stable conditions was a priority to avoid noise derived from variable dielectric properties, acquisition geometry effects and temporal decorrelation. Hence, image acquisitions under stable hydrometeorological conditions (i. e. stable frozen or dry) and for the lowest repeat-pass interval (i. e. 6-days) were prioritized.
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