Abstract: This paper aimed to evaluate the use of Global Navigation Satellite System (GNSS) ellipsoidal heights in conjunction with height anomalies provided by Global Geopotential Model (GGM) XGM2019e, refined by Residual Terrain Modelling (RTM) technique, to obtain normal heights in Brazil, referred to the Imbituba Brazilian Vertical Datum (IBVD) and the International Height Reference System (IHRS). For this purpose, a local modelling approach has been analyzed in contrast to the national modeling one on the reference geopotential value. For this, a methodology based on geopotential space was adapted. In the local modeling, two study subregions were defined using the spatial clustering analysis of IBVD and GGM/RTM height anomalies differences outliers. The parameters have been estimated using three different configurations. In the parameters validation step, Root Mean Square Errors (RMSE) of the discrepancies between transformed and Brazilian official normal heights were calculated. In both subregions more accurate results have been obtained with the local modeling. In the SP1 subregion the accuracy increased tenfold (0.97m to 0.10m) and SP2 improved from 0.39m to 0.17m. For the linkage to the future realization of IHRS, the accuracy analysis was not possible. However, discrepancies between calculated normal heights and Brazilian official normal heights have been analyzed.

Abstract: In the Global Navigation Satellite System (GNSS), ambiguity resolution (AR) can shorten observation time and increase the positioning quality. The correct tropospheric modeling is intrinsically related to the ability to perform AR. Here, we assessed the influence of different tropospheric correction alternatives on AR for static Precise Point Positioning (PPP) in Brazilian territory. Our goal was to provide directions to users when choosing a suitable tropospheric model for application in PPP-AR under Brazilian atmospheric conditions. Thus, this study was carried out using well-known models such as the Saastamoinen model and the Zenith Tropospheric Delay (ZTD) Estimation and Numerical Weather Prediction (NWP) model from CPTEC/INPE. Six GNSS stations from the Brazilian Network for Continuous Monitoring (RBMC) (BRAZ, UFPR, RNNA, POVE, SMAR, and SAGA) were selected. Different GNSS processing setups were considered for GNSS data registered at selected stations during summer and winter. The assessment was based on a statistical analysis of positioning accuracy during one-hour sessions. The results indicated that such as the ZTD Estimation, the NWP model provides an accuracy of a few centimeters. On the other hand, the Saastamoinen model provided decimeter level accuracy, thus it is not the recommended choice for PPP-AR in the experimental conditions.

Abstract In this paper a novel model to orient a pushbroom linear optical satellite image is proposed. This one is based in the adaptation of the Orbit-Attitude model for use of the Modified UCL Kepler platform model. It has only the components of satellite position and velocity as unknowns. This implies not only the reduction of unknowns but also the elimination of initial adjustments of the orbit to estimate the polynomial parameters. In order to validate the model, four experiments were conducted using one HRC-CBERS 2B image. Two distributions of ground controls points (GCPs) were tested, 70 and 35 GCPs. A quantity of 43 check points (CPs) was used to analyze the planimetric accuracies of the orientations. For comparisons purpose the image was also oriented with platform model using 2nd order polynomial. The results showed that the planimetric accuracy difference in the use of the two models is 4 and 6 centimeters in the two mentioned configurations of GCPs, respectively. However, the main advantage of applying the proposed model is the direct use of ephemeris without the necessity of interpolations and pre-adjustments, which makes the orientation process simpler.

A extração de informações geoespaciais de uma imagem orbital requer a orientação interior e exterior da mesma. Os parâmetros de orientação exterior (POE) podem ser obtidos de forma direta, utilizando sensores GNSS/INS e estelares, ou indireta, utilizando feições de controle no espaço objeto. Os parâmetros de orientação interior (POI) são inicialmente obtidos por calibração em laboratório antes do lançamento do satélite, e podem também ser estimados periodicamente pela calibração geométrica em órbita. O objetivo deste trabalho foi realizar a calibração geométrica em órbita do sensor HRC-CBERS 2B. Para tanto, foram consideradas as correções dos efeitos sistemáticos causados pela geometria do plano focal do sensor e pelo sistema de lentes do mesmo. Uma densa quantidade de pontos de controle e verificação foi utilizada, sendo que a análise da exatidão planimétrica nos pontos de verificação foi aplicada para avaliar a calibração. Quatro experimentos foram realizados analisando três diferentes conjuntos de POI. Os resultados dos experimentos de calibração foram muito próximos, não apresentando diferenças significativas. Uma maior exatidão foi obtida quando se empregou o grupo de POI modelando a translação, rotação, fator de escala e flexão das matrizes de CCD (Charge-Coupled Device), juntamente com a distorção radial simétrica do sistema de lentes

The geospatial information extraction from orbital images requires the internal and external orientation. The external orientation parameters (EOPs) can be obtained directly from GNSS/INS and star sensors, or indirectly by control features in the object space. The interior orientation parameters (IOPs) are first determined from laboratory calibration process prior the satellite launch, and can be estimated by the periodically on-orbit geometric calibration. This paper aimed to perform the on-orbit geometric calibration of the HRC-CBERS 2B sensor. The corrections of systematic effects caused by the focal plane of the sensor and by lens system were considered in the calibration process. A dense number of ground control and check points are used, and the accuracy analysis of the planimetric checkpoints was then applied to evaluate the calibration. Four experiments are performed analyzing three different groups of IOPs. The results obtained from calibration experiments were similar and did not shown significant differences. A slightly highest accuracy was obtained when the group of IOPs was used considering the translation, rotation, scale factor and bending of the CCD chips, with symmetric radial distortion of the lens system

Imagens obtidas por sensores de varredura linear orbitais assumem característica dinâmica, uma vez que cada linha obtida pelo CCD apresenta um conjunto de parâmetros de orientação exterior (POE) diferentes. A modelagem matemática da estimativa dos POE para cada instante durante o tempo de formação da imagem tem sido alvo de pesquisas durante as duas últimas décadas. Este trabalho investigou a modelagem a partir da utilização da teoria do Movimento Uniformemente Variado (MUV), associando as acelerações desta às equações de Dinâmica Orbital. Primeiramente foi considerada uma órbita sem perturbações (Movimento Kepleriano) e posteriormente uma órbita com a perturbação proveniente da atração gravitacional terrestre levando em conta a sua elipticidade, representado pelo harmônico zonal de grau 2 (J2), a qual é indicada como uma das mais significativas perturbações. Também foram testados e comparados modelos de plataforma polinomiais. A partir do uso dos diferentes modelos de plataforma foram realizados diversos experimentos com duas imagens PRISM-ALOS. Com base em uma distribuição de pontos de verificação sobre as imagens, as exatidões planimétricas foram calculadas. De forma quase geral, os valores estimados de erro quadrático médio para os pontos de verificação foram muito próximos em termos de GSD (Ground Sample Distance).

Images obtained by orbital pushbroom sensor assume linear dynamic characteristic, since each line obtained by the CCD presents a different set of exterior orientation parameters (EOP). The mathematical modeling of the estimate of EOP for each point during the image formation time has been the subject of research over the last two decades. This work investigated the modeling from the use of the theory of Uniformly Accelerated Motion, involving the acceleration of this theory to the equations of Orbital Dynamics, considering an undisturbed orbit (Keplerian motion) and an orbit with the disturbance from Earth's gravitational attraction due to its ellipticity, represented by the zonal harmonic of degree 2 (J2), which is indicated as one of the most significant disturbance. We also tested and compared polynomial models. From the use of different platform models were performed several experiments with two PRISM-ALOS images. Based on a distribution of check points on the images, planimetric accuracies were calculated. Almost general, the estimated values of mean square error for the check points were very close in terms of GSD (Ground Sample Distance).

Nos últimos 20 anos, pesquisas voltadas ao desenvolvimento de modelos rigorosos para a orientação de sensores orbitais puhbroom lineares vêm sendo desenvolvidas e apresentadas. Na maioria destas pesquisas, a trajetória e a orientação do satélite durante a formação das cenas são obtidas a partir de polinômios de 1º, 2º e até 3º grau. Porém, a atribuição de significado físico aos coeficientes polinomiais indica que o primeiro e o segundo termo se referem à velocidade e a aceleração da plataforma no instante referente à aquisição da primeira linha da cena. Estas quantidades podem ser associadas ao Problema dos Dois Corpos, sendo desenvolvido de acordo com a equação do Movimento Uniformemente Variado. O modelo resultante deste desenvolvimento foi denominado por Michalis e Dowman como Modelo de Kepler. Nesta pesquisa, o Modelo de Kepler é aplicado na orientação de imagens HRC/CBERS 2B e comparado com os modelos que utilizam polinômios para a propagação dos Parâmetros de orientação exterior (POE), amplamente utilizados atualmente. Os resultados obtidos ao comparar o Modelo de Kepler e os modelos polinomiais indicaram que o uso do primeiro modelo permitiu a obtenção de melhores resultados em relação ao segundo.

Over the past 20 years, research aimed at developing of rigorous models for the orientation of linear pushbroom sensors aboard orbiting platforms have been developed and presented. In most studies, the trajectory and orientation of the satellite during the formation of different lines of a scene has been obtained from polynomials of 1st, 2nd and even 3rd degree. However, the assignment of physical significance to the polynomial coefficients indicates that the first and the second terms refer to the velocity and acceleration of the platform at acquisition time of the first line of the scene respectively. In this case, these quantities can be associated whit the Two Bodies Problem which is developed according to the equation of Uniformly Varied Motion. The resulting model was named by Michalis and Dowman as Kepler Model. In this research, the Kepler Model is applied to the orientation of HRC/CBERS 2B images and compared to models using polynomials for the spread of exterior orientation parameters (POE), widely used today. The results obtained by comparing the Kepler model and polynomial models indicated that use of the first model allowed to obtain better results when compared to the second.