The COVID-19 pandemic significantly shifted education from traditional to an online version, which was an emergent state for teachers and students. The substantive situation thus raises the importance of technology integration in education, and teachers are required to update their competencies, respectively. In this regard, the study assessed online teaching competencies of faculty members following, technological pedagogical content knowledge (TPACK) model. Closed-ended surveys were employed for quantitative analysis of randomly selected 256 faculty members from public universities in Karachi, Pakistan. Results indicated that teachers possessed adequate levels of knowledge across all the domains of TPACK. The highest competency was obtained by content knowledge (CK), while technological knowledge (TK) was reported at the lowest level. Furthermore, a significant difference was noted in terms of gender and teaching experience. Correspondingly, the study proposes that the TPACK model should be employed in the professional development programs to develop teachers’ TPACK for integrating information communication and technology in the pedagogical practices. The findings of the study present a constructive overview of teachers’ digital competencies and technology use in teaching and learning in the time of the COVID-19 and also play a significant role in the integration of technology in the post-pandemic time in higher education. The study also suggests relevant educational authorities and policymakers for assessing and enhancing the technological competencies of teachers for quality online education. As it can be seen worldwide, the COVID-19 pandemic has caused a significant interruption in all the domains of human lives. Likewise, the educational sector also encountered many challenges by the institutional closure from schools to universities, and traditional education shifted to the online paradigm . The sceMoreover, the effective integration of ICT is essential in systematizing an efficient online educational program. The successful application of ICT not only contributes to learners’ satisfaction but also helps individuals to acquire their desired outcomes . It is, via all the mentioned sub-components of TPACK during the pandemic phase, specifically in the context of higher education in Pakistan. In this regard, the present study examines the integration of ICT in faculty members’ pedagogical practices by unfolding their technological competencies level. Subsequently, lecturers and professors from public universities of Karachi city of Pakistan were considered for a case study under the guidance of the following research questions:In contrast, technological competency involves all the major components, such as knowledge , skills, and attitudes , whereasWhat are the levels of TPACK of faculty members across higher institutions of Karachi?Is there any significant difference between faculty members’ TPACK regarding their gender and teaching experience?via different digital platforms, (2) learning and learning materials can be accessed through technology, (3) the interaction between teacher and learner takes place via technology, and (4) teacher assists learner with the help of different digital channels of communication (The term online teaching can be exemplified with the help of these principles: (1) The learner and teacher interconnected with each other distantly nication . In a genication . On the nication . Withoutnication . Other rSeveral studies draw attention to the importance of technology integration in pedagogical practices and imply that it does not facilitate only students but also the teacher in the learning process . Islam eMoreover, the knowledge of technology and expertise in the utilization of technology are considered two different modes of competencies . For insIt is indicated by several empirical studies that teachers’ characteristics also play a significant role in integrating ICT, which may vary across the countries; for instance, some studies have identified a significant difference in gender with a more inclination of males toward digital instructional development than females . In termAnother element of central concern in the acquisition of digital competencies is the teaching experience of teachers. Regarding years of teaching experience, studies show mixed results. For instance, “There is a significant difference between faculty members’ TPACK with respect to their gender.”H1: “There is a significant difference between faculty members’ TPACK with respect to their teaching experience.”H2: via numerical representation  were females and 55.8% (n=143) were male faculty members. Their further details are presented in The population of the study comprises all the faculty members from public universities of Karachi, which consists of 11 universities with estimated 785 faculty members . For ensIn order to ensure the reliability of the findings, the study followed all the ethical concerns to conduct the study. These concerns include the granted approval from the supervisor on account of the ethical committee. The other ethical concerns include assurance of the privacy and honor of the participants of the study, and questionnaires were filled after taking their consent.The instrument utilized in this study was adopted from the validated scale formulated by χ2/df=4.1), which indicates the significant fitness of the model . Subsequently, the analysis was completed by applying the receiver operating characteristic (ROC) curve, which enabled the examination of the differences between subsamples with respect to their TPACK scores. The ROC curve is a two-dimensional graphical representation of the values of sensitivity vs. 1-specificity ranges from 0 to 1, which helps in determining the difference between different subgroups  and inferential test  at alpha level 0.05. Therefore, the hypothesis regarding faculty members’ TPACK with respect to their gender was accepted. Furthermore, male faculty members got a significantly higher mean score (4.12) than the female teaching faculty (3.67), which shows that the TPACK of male faculty members was greater than the female ones.All the components of TPACK were compared by applying the shown in . Resultsp=0.000 at alpha level 0.05.In addition, the gender difference with respect to TPACK scores was represented graphically through the ROC curve. The results shown in  showed hFurthermore, to investigate the most optimal predictors of teachers’ TPACK, the mean of all the sub-components was compared with respect to their gender shown in . ResultsFor examining the distinction between faculty members’ TPACK with regard to their teaching experience, the mean of TPACK was compared with the teaching experience of all the faculty members by applying the ANOVA test shown in . Resultspost-hoc test was conducted. Since Tukey’s HSD test helps to compare the means of all the possible pairs  in the acquisition of digital competencies during the COVID-19 period.In view of the obtained findings, the study reveals that faculty members possess adequate knowledge in all the sub-components of the TPACK model, which shows that teachers have sufficient knowledge and skills regarding technology use in their pedagogical practices. This finding shows consistency with the findings of The results further indicate that the highest competence of faculty members among all other domains was obtained by the content knowledge (CK), which shows that faculty members seem more confident in their content knowledge than other domains of expertise. A similar finding is also identified by Technological knowledge involves operating particular technologies, which plays a crucial role in integrating technology in the process of teaching and learning . BesidesThe knowledge regarding the interaction between all domains of TPACK plays a significant role in the development of an innovative learning environment . HoweverThis study further found that male teachers’ TPACK was significantly higher than female faculty members. This finding reflects the finding of In addition, the study suggests that the new technological instructional context in the COVID-19 phase appeared as an important moderator for teachers in upgrading their competencies in terms of TPACK. Regarding the contextual environment, Finally, remote work and online learning are teaching conditions that will continue to advance steadily. In turn, the post-COVID-19 reactivation and recovery processes do not seem to contemplate that the teaching and learning processes as before. Therefore, future research should be aimed not only at understanding human behavior while studying or teaching virtually but also at understanding the TPACK model and building better ways to integrate technology into educational practices. In this regard, the findings of the study are highly significant, not particularly in determining the technology integration during the COVID-19 pandemic phase, which is currently the most crucial issue, but also for the integration of technology in the post-pandemic time in higher education.Based on the obtained results, the study affirms that the COVID-19 pandemic phase significantly influenced the digital competencies of faculty members and reveals adequate knowledge in all the sub-components of the TPACK, with a significant difference in terms of gender and teaching experience. Regarding consistency, the TPACK model was verified by means of factorial analyses in terms of seven sub-components and in the context of higher education faculty members in Pakistan, which supports the value and appropriateness of the model. Accordingly, the study suggests that the TPACK model should be employed in the professional development programs to develop teachers’ TPACK for integrating technology efficiently by bridging the gap between ICT knowledge and ICT practice.The findings of this study contribute to society in several ways. Regarding theoretically, this study has enriched the literature on the technological competencies of teachers during the COVID-19 transitory period and verified the reliability of the TPACK model in the context of Karachi, Pakistan. It can be further used for verification in other cities and countries. In terms of methodological contribution, the study provides tentative insight in evaluating the impact of the COVID-19 transitory period on teachers’ digital competencies and their state of implementation in pedagogical practices. Regarding academics, this study provides a pragmatic direction to relevant educational authorities and policymakers for the improvement of online education by providing pertinent solutions and recommendations as per the situation. In addition, the future planning of professional development and training programs for the teachers can be based on the feedback provided by the faculty members. The study can further contribute to elevating e-learning outcomes and satisfaction during as well as post-pandemic phase.Furthermore, the study also noted some limitations. Firstly, faculty’s response biasness may have affected the results since digital competencies were assessed self-reported quantitatively. Therefore, the future studies may select other approaches to unfold the understanding of teachers and establish the criteria for evaluating the TPACK of teachers. Secondly, the current study only focused on the TPACK model to assess the digital competencies of faculty. The findings of this study can be further strengthened in the future by employing other indicators to examine the teachers’ competencies in teaching with technology.Finally, the analysis was cross-sectional and evaluated the teaching practices of university teachers during the period of the COVID-19 pandemic. Online technological, pedagogical, and content competencies of teachers may change over time, which should also be observed. Therefore, a longitudinal study should be conducted to strengthen the evidence by understanding the causal effects and interrelationships among various other variables, critical in elevating the online pedagogical practices at the higher level in Pakistan.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study.HA is the principal investigator of the study. From conceptualization to the data analysis, she conducted by herself. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


It is said that image segmentation is a very difficult or complex task. First of all, we emphasize the subtle difference between the notions of difficulty and complexity. Then, in this article, we focus on the question of how two widely used color image complexity measures correlate with the number of segments resulting in over-segmentation. We study the evolution of both the image complexity measures and number of segments as the image complexity is gradually decreased by means of low-pass filtering. In this way, we tackle the possibility of predicting the difficulty of color image segmentation based on image complexity measures. We analyze the complexity of images from the point of view of color entropy and color fractal dimension and for color fractal images and the Berkeley data set we correlate these two metrics with the segmentation results, more specifically the number of quasi-flat zones and the number of JSEG regions in the resulting segmentation map. We report on our experimental results and draw conclusions. Segmentation is considered to be at the border between image processing and image analysis, as the segmentation map is often used for consequent object detection or recognition tasks. It is said that segmentation is one of the most difficult or complex operations performed on images [By definition, image segmentation is the process of dividing an input image into regions called n images . What man images  and Turbn images  approachn images .First of all, we should recall the definitions of the two main concepts mentioned so far: difficulty and complexity, as very often we are tempted to consider that the two concepts are overlapping, or as exactly the same concept. However, they do not represent the same concept ,6: diffiorder of complexity   is a datN quantization levels, where In information theory, Shannon  used theEquation ), HartleThe same definition of Shannon entropy was embraced in  as one owiggliness of a fractal object [E is the topological dimension of that object. In practice, the fractal dimension has been used for the discrimination between various signals or patterns exhibiting fractal properties, such as textures [Multi-scale approaches or measures are used for the analysis of color texture images. The most representative is the fractal dimension from fractal geometry . Fractall object . The fratextures . Often, ect [E,E+, where EThe theoretical fractal dimension is the Hausdorff dimension , also ca sausage , the gli sausage  etc.https://multibandtexture.recherche.usherbrooke.ca/colored_brodatz.html).Several attempts were made to extend the fractal dimension estimation techniques to the color image domain. The initial approaches which link the fractal measures to colour images were marginal colour analysis . The proQuasi-flat zones (QFZ) are morphological segmentation operators derived from the concept of flat zones . Flat zop from the gray-scale image f is [For instance, in the case of gray-scale images, the age f is :(3)Cα(p)R computes the difference between the maximal and minimal values of the set given as its argument.eshold ω :(4)Cα,ω. We chose this specific type of images as they do not exhibit any particular content, but instead a noise with properties of statistical self-similarity. For color image complexity we embraced the color entropy (CE) and the color fractal dimension (CFD). The chosen segmentation approaches were quasi-flat zones (QFZs) and JSEG, which were all detailed in the previous section.We performed a set of initial experiments with a set of nine images representing synthetic color fractal textures of varying complexity as a function of the Hurst parameter In Further on, we investigate the possible existing correlation between the two previously described complexity measures—color entropy and color fractal dimension—and the number of quasi-flat zones (QFZs) and number of JSEG segments, for the Berkeley image data set. We calculated the histograms of CE, CFD, number of QFZs and JSEG segments, computed on the BSDS500 data set, in order to see how all these measures are distributed over the data set. The resulting histograms are depicted in ing step  in orderred from , in ordeFor color entropy versus the number of QFZs, the Pearson correlation coefficient uni and consequently the image complexity should be null  content of the natural images in the Berkeley data base and that for such images more appropriate complexity measures must be defined and used. The Pearson correlation coefficient values we obtained in our experiments are similar to the ones reported in , meaning


The homogeneity of asphalt mixtures blended with reclaimed asphalt pavement (RAP) is affected by many factors. Due to the complicated compositions of recycled asphalt mixtures, the inhomogeneity issue might cause insufficient mechanical properties of asphalt mixtures, even though a design method was appropriately adopted. Therefore, it is of great significance to study the influence of mixing conditions on the homogeneity of asphalt mixtures blended with RAP materials. This study focused on the macro-scale homogeneity of produced asphalt mixtures. Specifically, asphalt mixtures incorporated with 40% RAP content were produced in a laboratory using different mixing times and mixing temperatures. A multi-direction indirect tensile stiffness modulus (ITSM) test was proposed to quantify the homogeneity of produced samples. In addition, the digital image processing (DIP) method was used to identify the distribution of aggregates and RAP binder. The results indicated that the influence of mixing time on the macro-homogeneity of asphalt mixtures indicated that a longer mixing time was favorable for the material dispersion. The influence of mixing temperature mainly rested on two perspectives. One was that the temperature variation induced the change of binder viscosity. The other was that the temperature influences the diffusion process between RAP binder and new bitumen, which further affected the mechanical performance of produced asphalt mixtures. Asphalt mixtures have been extensively used in the construction of pavements. However, when pavement suffers severe distress and, as a result, no longer functions with satisfactory quality, pavement has to be reconstructed . On the In the conventional production of asphalt mixtures, bitumen is evenly coated on the aggregate surface, and the aggregates are uniformly distributed, forming a relatively homogenous structure. A previous study demonstrated that the homogeneity issue played a critical role in the mechanical properties of produced asphalt mixtures . CommonlDue to clusters in RAP and the property variation between RAP materials and new mixtures, the segregation issue in production could possibly be more significant. Li et al.  adopted According to the studies introduced above, it can be concluded that many factors influence the homogeneity of asphalt mixtures incorporated with RAP materials. Comparing with conventional asphalt mixtures, the homogeneity issue concerning the recycled asphalt mixtures should be extended to a multi-scale solution. On the other hand, it is known that the production of recycled asphalt mixtures continue to use conventional mixing devices, which could be unfavorable for the homogeneity of the produced asphalt mixtures. Therefore, it is necessary to study the effect of mixing, including mixing time, mixing temperature, and mixing procedure, on the homogeneity of recycled asphalt mixtures. Additionally, the homogeneity of the mix from a multi-scale perspective should be considered in the investigations. This study aims to investigate the macro-homogeneity of asphalt mixtures incorporated with reclaimed asphalt pavement, considering different mixing conditions. Specifically, the influence of mixing temperature and mixing time on the mechanical performance of produced asphalt mixtures will be discussed. To this end, asphalt mixtures incorporated with 40% RAP content were produced in a laboratory at different mixing times and mixing temperatures. The thermal equilibrium state was intended to eliminate the influence of thermal conductivity on the final performance of asphalt mixtures, although it deviated from actual mixing condition. In this case, the variation of macro-scale homogeneity caused by mixing could be qualified. RAP production was completed in a laboratory to avoid material variation. After producing asphalt mixtures, a multi-direction indirect tensile stiffness modulus (ITSM) test was carried out, followed by variation analyses of the obtained data. In addition, a morphological analysis of sliced asphalt mixtures was conducted, aiming to present an intuitive visualization of the morphological structures of the produced asphalt mixtures.PG 70-22 bitumen was used to produce the RAP materials, and new bitumen was added to the mixing. In order to distinguish between the new bitumen and the aged bitumen in RAP materials, dyeing technology was applied for the bitumen in RAP. The dyeing technology was invented to change the color of bitumen by adding chemical additives. The use of iron oxide powder was introduced in the literature . SpecifiAlthough the variation between the new bitumen and the dyed bitumen could alter the flowability of binders, which further affected the mixing, this study used significantly different mixing temperatures to alter the influence of mixing temperature on the macro-homogeneity of the produced asphalt mixtures. It is worth noting that the incorporation of iron oxide increased the stiffness of the produced mixtures. Therefore, the incorporated amount of iron oxide was fixed for different mixing conditions. In this case, the difference in the measured modulus was mainly ascribed to the variation of the mixing conditions. For the evaluation of the homogeneity of asphalt mixtures based on the measured modulus, the coefficient of variation (CoV) was accordingly calculated for the parallel samples. This study used basalt as the aggregate and limestone as the filler. The objective gradation curve shown in Following the gradation used in this study, sufficient asphalt mixtures were mixed with 4% binder content. In what follows, part of the asphalt mixtures was subjected to SHRP short-term aging (at 135 °C for four hours) in a loose state . The comThe new aggregate was heated to 150 °C for eight hours to eliminate moisture to avoid thermal conductivity. The virgin bitumen was firstly heated to 135 °C to obtain sufficient flowability. The crushed RAP materials and new aggregates were preheated to targeted temperatures  for two hours. In order to produce the asphalt mixtures containing the RAP, the crushed RAP materials and new aggregate were firstly blended using a mechanical mixer. After that, flowable bitumen was added to the blend for a specific amount of time . The proportion of RAP was maintained at 40%. In this case, 12 kinds of mixing conditions were considered in the production of recycled asphalt mixtures. Four cylindrical specimens (with 150 mm diameter and 115 ± 5 mm height) were compacted using a gyratory compactor for each case. The specimens were conditioned at room temperature for one day and then cored into cylindrical specimens with a diameter of 100 mm. After that, two specimens were cut into two cylindrical specimens with a height of 40 mm, and another two specimens were sliced into 10-disc specimens with a thickness of 20 mm.As shown in High-quality pictures were taken for both sides of each disc specimen using a digital camera with carefully controlled lighting and exposure conditions. It was found that the binder was easier to identify when the specimen was wetted. Therefore, water was sprayed before pictures were taken. In total, 240 pictures of the specimens were collected.The obtained 240 images were subjected to the image analysis using MATLAB, which conformed to the following steps.Step 1: Preliminarily enhance the image quality: Image contrast is enhanced using the histogram equalization function. The histogram equalization method processes the image to adjust the contrast of the image by modifying the intensity distribution histogram. The purpose of this technique is to give an image of the cumulative probability function related to a linear trend.Step 2: Calculate sample colors in L*a*b color space for each region: for the image segmentation, the RGB image was firstly convert to the CIE L*ab space. CIE L*ab was defined by the lightness and the color-opponent dimensions a and b. The CIE L*ab space of an image is usually calculated for specific purpose, such as the image segmentation. Step 3: Classify each pixel using the nearest neighbor classification: By calculating the Euclidean distance between that pixel and each color marker. The smallest distance could determine that the pixel most closely matched that color marker.Step 4: Display results of nearest neighbor classification: The label matrix contains a color label for each pixel in the image. Based on this, the label matrix was calculated to separate objects in the original image by color.Step 5: Convert each classification region into binary images.Following the above steps, the aggregate component and RAP binder component can be successfully identified and segmented, as shown in According to ITSM measurements, the mean value, standard deviation (SD), and coefficient of variation (CoV) of ITSMs were calculated for each mixing condition. Similarly, the high stiffness obtained at a low temperature might be attributed to the low blending degree between the aged bitumen and the new bitumen. In contrast, mixing the asphalt mixture at high temperatures accelerated the diffusion between the aged bitumen and the new bitumen. Hence, a high stiffness modulus was observed at low temperatures. The minimum mean value of ITSM occurred at a temperature of 110 °C and a mixing time of 30 s. This observation indicated that the influence of temperature on the stiffness modulus of the asphalt mixtures was not monotonic. Therefore, a critical temperature was most unfavorable for forming asphalt mixture stiffness, for instance, 110 °C in this study. The mixing time benefited the formation of asphalt stiffness. There are two plausible reasons for this. With the increase in mixing temperature, the bitumen binders suffered secondary aging. Additionally, a longer mixing time made it easier to achieve a better morphological distribution, although morphological distribution on the stiffness formation requires further investigation.This section discusses the influence of mixing time on the stiffness of asphalt mixtures. Apart from the average ITSMs, the error bar and value boundary of ITSMs measured at specific mixing conditions are shown in (1)Momentary homogeneity with insufficient temperatureAs stated above, when the mixing time was very short, the produced asphalt mixture might achieve a momentary homogeneous state due to the clusters in RAP not being wholly crushed under external forces. In such a state, the aged bitumen in RAP and new bitumen were separated with limited interactions. Therefore, the diffusion process between them was limited. In this case, the temperature dominantly contributed to the flowability of aggregates both in RAP and in the newly added ones. Within an insufficient temperature range, the increase in temperature increased the flowability of particles. However, this improvement negatively influenced the breaking of clusters in RAP. As a result, the stiffness decreased, although the temperature increased. (2)Momentary homogeneity with sufficient temperatureIf the temperature continued to increase to a sufficient range, the clusters would be softened and would lose the adhesive force inside. In this case, the temperature played a positive role in the breaking of clusters in RAP. The momentary homogeneous state would shift into an unbalanced state when the blending degree of RAP and new aggregates started to grow. Therefore, the stiffness modulus increased when the temperature was at 130 °C, as seen in (3)Near-real homogeneity with insufficient temperatureExtending the mixing time is helpful for the formation of real homogeneity in asphalt mixtures. The mixing time and temperature mutually determined the homogeneity state of asphalt mixtures. As seen in (4)Real homogeneity with sufficient temperatureWhen the mixing time was 240 s, the asphalt mixtures almost achieved real homogeneity since the error bars were small. In this condition, the temperature mainly contributed to the diffusion between aged bitumen and new bitumen. With the increase in temperature, the diffusion rate would be accelerated, during which the aged bitumen would be softened, inducing a decrease in the stiffness modulus.The inhomogeneous state occurred in the rest area. It can be seen that the combination of temperature (110 °C) and mixing time (120 s) was the most unfavorable mixing condition in terms of the homogeneity. Additionally, the inhomogeneous state area was shown in a ‘Z’ shape. The most inhomogeneous state can be achieved quickly at a low temperature or a longer time at a high temperature. It is believed that In total, 240 images were subjected to image processing to identify aggregates and RAP binder morphologies, respectively. It can be seen that it is not possible to tell the difference caused by the mixing condition. The primary reason for this was that the aggregates in RAP or newly added aggregates could not be further distinguished. From another perspective, aggregates in RAP had identical properties to the newly added ones. Given that the binders were well coated on the aggregate surface, the mechanical performance of asphalt mixtures was mainly determined by the skeleton structure of aggregates, which was not a critical problem with a well-designed mixing procedure. Another limitation of examining the aggregate distribution shown in this study was that the dimension reduction from 3D to 2D might lose considerable structural information. Therefore, it is not recommended to evaluate the homogeneity of asphalt mixture by visualizing aggregate morphology. When the temperature was 90 °C, a relatively homogenous distribution of RAP binder was observed at 120 s. According to the last section’s analysis, the RAP binder’s viscosity was high, and the migration of RAP binders was mainly attributed to external force. Thus, extending the mixing time was beneficial to the migration of RAP binders. It is worth noting that the RAP binder was not detected in some parts of the image at 240 s, indicating that the cluster of new aggregate and new bitumen also occurred in the mixing process. Similar phenomena were observed at other mixing temperatures.Based on the results and discussion in this study, the following conclusions can be drawn:(1) The macro-homogeneity of asphalt mixtures is associated with mixing temperature and mixing time. The asphalt mixtures produced with different mixing conditions show distinct mechanical performance. (2) A long mixing time benefited the distribution of aggregates in both RAP materials and new mixtures. The increase of mixing temperature induced binder flowability, which improved the migration and diffusion of binders. According to the results, the influence of mixing time and temperature should not be determined separately. An optimal combination of mixing time and temperature exists to achieve a satisfying mechanical performance of asphalt mixtures containing RAP materials.(3) Although many efforts have been made to repeat the production of asphalt mixtures with RAP materials in the laboratory. The addition of iron oxide into bitumen significantly changed the binder properties. Therefore, it should be promising to use other technologies to identify the difference between RAP materials and newly added mixtures. The laboratory investigations provided a basic understanding of the macro-homogeneity of asphalt mixtures with different mixing temperatures and mixing times. However, in situ mixing procedures are different from laboratory ones. For a deep understanding of the homogeneity of asphalt mixtures containing RAP materials, carrying out a full-scale investigation in the field is recommended.


Information for Action! is a Joint Action (JA-InfAct) on Health Information promoted by the EU Member States and funded by the European Commission within the Third EU Health Programme (2014–2020) to create and develop solid sustainable infrastructure on EU health information. The main objective of this the JA-InfAct is to build an EU health information system infrastructure and strengthen its core elements by a) establishing a sustainable research infrastructure to support population health and health system performance assessment, b) enhancing the European health information and knowledge bases, as well as health information research capacities to reduce health information inequalities, and c) supporting health information interoperability and innovative health information tools and data sources.Following a federated analysis approach, JA-InfAct developed an ad hoc federated infrastructure based on distributing a well-defined process-mining analysis methodology to be deployed at each participating partners’ systems to reproduce the analysis and pool the aggregated results from the analyses. To overcome the legal interoperability issues on international data sharing, data linkage and management, partners (EU regions) participating in the case studies worked coordinately to query their real-world healthcare data sources complying with a common data model, executed the process-mining analysis pipeline on their premises, and shared the results enabling international comparison and the identification of best practices on stroke care.The ad hoc federated infrastructure was designed and built upon open source technologies, providing partners with the capacity to exploit their data and generate dashboards exploring the stroke care pathways. These dashboards can be shared among the participating partners or to a coordination hub without legal issues, enabling the comparative evaluation of the caregiving activities for acute stroke across regions.Nonetheless, the approach is not free of a number of challenges that have been solved, and new challenges that should be addressed in the eventual case of scaling up. For that eventual case, 12 recommendations considering the different layers of interoperability have been provided.The proposed approach, when successfully deployed as a federated analysis infrastructure, such as the one developed within the JA-InfAct, can concisely tackle all levels of the interoperability requirements from organisational to technical interoperability, supported by the close collaboration of the partners participating in the study. Any proposal for extension, should require further thinking on how to deal with new challenges on interoperability. The main aim of the JA-InfAct is to build an EU health information system infrastructure and strengthen its core elements by a) establishing a sustainable research infrastructure to support population health and health system performance assessment, b) enhancing the European health information and knowledge bases, as well as health information research capacities to reduce health information inequalities, and c) supporting health information interoperability and innovative health information tools and data sources. One of the underlying tasks has been setting up the pillars for the design, preparation and implementation of a federated research infrastructure (FRI) that leverages the use of health data to carry out policy-oriented research.“the ability of organisations to interact towards mutually beneficial goals, involving the sharing of information and knowledge between these organisations, through the business processes they support, by means of the exchange of data between their ICT systems”. In the specific case of JA-InfAct, interoperability refers to the capacity to capture coherent data in the different partners, being able to reproduce the same analyses and being capable of sharing the results of these analyses. The design, development and implementation of the JA-InfAct federated research infrastructure have built upon the interoperability layers introduced by the EIF and depicted in Fig. Paramount in the development of a federated research infrastructure, where data is leveraged from multiple and heterogeneous data sources hosted in multiple sites with different governance models, is interoperability. JA-InfAct interoperability elements are framed in the recommendations report by the European Interoperability Framework (EIF) . AccordiThis paper seeks to describe the process and challenges followed in the context of JA-InfAct to cope with the different layers of interoperability when trying to answer population health research queries in the context of a federated infrastructure. Likewise, the report provides recommendations for the eventual real-life implementation of such a federated infrastructure.n.b. a more extensive description of the three use cases is at https://www.inf-act.eu/wp10).JA-InfAct has addressed the different interoperability challenges to build an FRI, following an approach based on case studies . In Table The last approach is the one that has defined the actual FRI solution, providing full insight on how to make interoperability a reality. In short, the JA-InfAct federated analysis infrastructure is an ad hoc infrastructure solution proposed to perform a cross-border analysis, where different infrastructures, information models, and even legal frameworks may apply. The core element of the analysis infrastructure is the process-mining methodology. Process mining is a series of data analysis techniques able to discover, analyze, and improve business processes based on event data. In this context, process mining is applied to real-world datasets that are combined and processed to generate the care pathways process models within the premises of each participant partner.security- and privacy-by-design approaches and to fulfil the interoperability challenges.The analysis methodology is encapsulated in a software distribution solution that acts as the central element of the federated analysis infrastructure, that leverages the data capture and execution of the analyses across different partners and the exchange of the results. All the methodologies and solutions are designed and implemented following This section is organised to describe these three elements, using as a case study the empirical discovery of care pathways of acute ischemic stroke. Code Stroke, defined in , a practical roll out of DIPOH, distributed infrastructure on population health research, current candidate to get into the ESFRI roadmap. In addition, all this insight is playing a fundamental part of the European Health Research and Innovation Cloud, a cloud for health data exchange between European health research infrastructures and health services, to be designed under the HealthyCloud project [https://healthycloud.eu]. Finally, this knowledge is currently helping to give shape to the future European Health Data Space, the project to regulate the secondary use of health data across Europe, under the framework of the TEHDaS Joint Action [https://tehdas.eu].To conclude, it is important to note that all the know-how gathered during the development of the JA-InfAct federated analysis infrastructure and some of the recommendations provided are currently being implemented in PHIRI, population health information research infrastructure


The increase in the dimension of grandiosity is associated with the passage to potentially highly lethal suicidal gestures. Conclusions: Suicidal ideation and conduct seem to serve the function of restoring a sense of control and self-esteem in narcissistic individuals experiencing a state of affective dysregulation. Narcissistic pathological functioning seems to play an important role in the adolescent suicidal process, quite like adulthood. Assessing an adolescent’s narcissistic functioning may provide useful clinical information in understanding and managing the suicidal risk in this phase of life.Background: Clinical and empirical research evidenced a complex link between pathological narcissism and the suicidal process in adulthood. Given the relevance of suicidality and the peculiar narcissistic vicissitudes of adolescence, the proposed research investigated the relationship between pathological narcissism analyzed from the multi-dimensional perspective of the Diagnostic Interview for Narcissism (DIN) and suicidal ideation conducted in a sample of Italian Adolescents. Methods: One hundred and three Italian male and female adolescents between 12 and 18 were administered the DIN, SCIDII, CSSRS, and Kiddie-SADS with six months follow-up. Results: The correlation,  According to the latest available report from the World Health Organization (WHO) , suicideEmpirical studies show that any risk factor considered on its own seems to account only for a small percentage of suicides. Current orientations prefer to identify configurations of different risk factors interacting with each other in a sequential process that begins before the actual suicidal behavior takes place and even before the suicidal ideation becomes conscious . This prBoth clinical and research evidence indicates a role for narcissistic personality for both the recurrence of suicidal ideation and lethality of suicidal attempts in adulthood ,26,27,28In this paper, the potential role of narcissistic pathological functioning for suicidality has been investigated in a sample of Italian adolescents in order to enhance the understanding and management of this severe clinical challenge in this phase of life.In general, empirical studies have individuated some specific characteristics of the connection between narcissistic pathological functioning and suicidality, with some issues that still remain controversial and others that need further investigation. The relatively modest extant research seems to suggest that NPD is associated with repeated attempts and greater risk of death and of highly lethal suicide attempts, but is either not associated or moderately protective against lower lethality attempts . At an eSome of these more controversial issues have been dealt with from a more theoretical and clinical perspective. From this perspective, the emphasis is posed upon the function that the diverse steps of the suicidal process may acquire for the regulation of emotions and self-esteem in narcissistic individuals .In particular, suicidal ideation is interpreted as “a first line strategy”, that comes into play to help narcissistic individuals recover their self-esteem by establishing emotional control, a sense of agency, and personal mastery . When thThe general aim of this work is to therefore investigate the relationship between narcissistic pathological functioning, observed from a multi-dimensional perspective, and suicidality in adolescence. Three main research objectives have been established: (1) to verify which aspect of pathological narcissism as assessed through the diagnostic interview for narcissism (DIN) are associated (correlate with) suicidal ideation (severity and intensity) as assessed through the Columbia Suicide Severity Rating Scale (CSSRS); (2) to verify which aspect of pathological narcissism as assessed through the DIN distinguish pure ideators from attempters at a longitudinal level; (3) to verify whether and which aspects of pathological narcissism contribute more to the potential lethality of the suicidal conducts.Mapping pathological narcissism as a multi-dimensional construct: the Diagnostic Interview for Narcissism.The Diagnostic Interview for Narcissism  is a semOther instruments:The Columbia Suicide Severity Rating Scale (CSSRS)  is a scaThe structured clinical interview for DSM-IV axis II personality disorders (SCID II)  is desigThe Kiddies Schedule for Affective Disorders and Schizophrenia for School-Age Children–Present and Lifetime Version (KIDDIE–SADS–PL)  is a diaA sample of 103 adolescents aged between 12 and 18 was recruited with the method of subsequent admission between 2018 and 2020 at in-patient and Day Hospital Units of Italian Adolescent Mental Health Services. All patients included in the sample had been referred to one of the two services either for a suicide attempt or for suicidal risk .Only patient scoring over a cut-off of 2 at the CSSRS  were included in the sample.All patients that met diagnostic criteria for any psychotic disorders group as assessed by DSM-V .The suicidal risk assessment obtained through the CSSRS retrospectively investigates the appearance of suicidal ideation or conducts and has to be held valid for three months preceding the session of administration.As far as the suicidal conducts are concerned, a six-month follow-up was carried out evaluating the appearance of a first suicide or further suicide attempt. Among the patients included in the sample, the suicidal conducts variables included in the database refer to the subject’s overall course of suicidal gestures at T2 (from three months before the intake to six months after T1 assessment): the suicidal conduct variables are then the ones finally evaluated at T2.Hence, the overall clinical sample of 103 adolescents was divided into two clinical subgroups: (a) Stay-ideators: subjects reporting suicidal ideation (above 2 on CSSRS) at T1 and having not attempted suicide from three months before to six months after the first assessment ; (b) attempters: subjects having committed at least one suicide attempt from T1 to T2.t-test analysis for independent samples was run to understand which narcissistic dimension differentiates the ideators sub-group from the attempters sub-group. A second t-test analysis for independent samples was run to understand which narcissistic dimension differentiates the attempters who made a high lethality attempt from those who had made a low lethality attempt. A linear regression model was run to verify which narcissistic dimension contributes to explain the variance of the suicidal behavior indexes. Only the variables found to be significant in the previous analyzes were included in the model. The presence of a mood unipolar or bipolar disorder was included in the model since they are typically indicated in the literature as prominent risk factors. The presence of narcissistic personality disorder was also included, in order to consider its effect combined with the DIN variables.SPSS  was used for the statistical analysis. First, a preliminary bivariate correlational analysis was run to understand the association between the suicidality dimension (CSSRS) and narcissistic dimension (DIN). Then, a Descriptive analyses are shown in p = 0.030. The DIN subscale affects and mood is significantly associated with potential lethality r = 0.211; p = 0.032 and with both severity and intensity of the suicidal ideation .A preliminary bivariate correlational analysis was run. The results are shown in t-test analysis for independent samples was run to understand which narcissistic dimensions differentiate the ideators group from the attempters group. Grandiosity significantly differentiates the ideators group from the attempters group t(101) = −2.361, p = 0.020, where attempters  seem to have higher grandiosity scores than ideators . Moreover, affects and mood significantly differentiates the ideators group from the attempters group t(101) = −2.046, p = 0.043, where attempters  seem to have higher affects and mood scores than the ideators .A t-test analysis for independent samples was run to understand which narcissistic dimensions differentiate the attempters who made a high lethality attempt from those who had made a low lethality attempt. Only Grandiosity significantly differentiates the low lethality attempters group  from the high lethality attempters group  t(48) = −2.342, p = 0.023, where the higher the attempt’s lethality score, the higher the grandiosity scores.A 2 = 0.054; p = 0.02; β = 0.233, p = 0.02.A linear stepwise regression model was run to verify which narcissistic dimension contributes to explain the variance of the suicidal behavior indexes. The results are shown in As indicated in the introduction, the literature in adult suicidal individuals has evidenced a link between pathological narcissism and suicidality, but some questions still need clarification. This study aimed at investigating the contribution of pathological narcissism and its dimensions to the subsequent stages of the suicidal process in a sample of adolescents through three specific research objectives. With reference to these three objectives, the results seem to confirm what was already shown in the studies on adults and to add some useful empirical information to some of the research questions raised in the literature.Firstly, the association between the diverse clinical areas of pathological narcissism and the severity and intensity of suicidal ideation has been evaluated. The results show that the increase in the narcissistic affects and mood  is significantly associated with an increase in the intensity and severity of suicidal ideation. This result is in tally with the clinical view positing a specific function of suicidal ideation for the narcissistic individuals’ emotional regulation . AccordiHowever, other results from this study seem to indicate a more complex relationship between narcissistic pathological functioning and suicidal conduct. In verifying the second and third objectives of this research, results emerging from this sample of adolescents overlap with studies on narcissism and suicidality in the adult population. On a longitudinal level, attempters can be distinguished from stay-ideators subjects because of their significantly higher scores in the dimensions of narcissistic affects and moods and grandiosity. Furthermore, the regression model employing the grandiosity narcissistic dimension has a significant impact on the increase in the lethality of the suicide attempted by the boys and girls of the sample. Within this regression model, it is only the dimension of grandiosity that constitutes a significant predictor of the high lethality of suicidal conduct. The apparent contradiction between the scarce predictive value of NPD for emergence and recurrence of suicidal gestures in general, and the impact of pathological narcissism on the lethality of suicidal attempts has been already highlighted in the literature ,50. We cAs previously stated, the experience of inner vulnerability due to the increase in narcissistic affects and mood can be initially dealt with by suicidal ideation. The literature indicates that when the state of vulnerability is further increased due to external causes  or internal factors  suicidal ideation may no longer suffice the purpose of self-esteem regulation ,28,51,52The investigation of suicidal ideation and motivation in narcissistic individuals explicitly includes contents such as fantasies of escape from unbearable frustrations, the denial of real or imaginary conditions of physical or psychic inferiority, supremacy over bodily needs and emotions, the assertion of superiority and self-sufficiency over affective bonds, and vulnerability to losses and separations. Additional contents are the return to a state of perfection and self-ideal, the revenge and triumph over malignant others, to demonstrate the strength to overcome the fear of death, and to survive one’s physical disappearance ,49,57. ISome limits to this study should also be taken into consideration that may also represent relevant guidance for further research. In particular, the recruited sample did not include subjects who finally succeeded in committing suicide. Secondly, the window of longitudinal observation is definitely too short (nine months—considering the three months preceding the time of administration of the instruments and the following six months of the second observation) to leap to generalizable conclusions as to the predictive value of our observations. Thirdly, analysis by gender, performing the correlations between women and men separately, could yield interesting and different results. Finally, a comparison with other personality pathological conditions could have been included, also considering the level of comorbidity between personality disorders. By the same token, we believe that the dimensional assessment of pathological narcissism deserves a secluded study. Since external frustrations and life events have a role in triggering the narcissistic affective dysregulation and possible ensuing recourse to suicidality , the nexFurthermore, the considerations concerning the role of pathological narcissism in shaping the suicidal ideational process could be analyzed in more detail. In particular, the link between the dimensions of the DIN and the motivational profiles for suicide identified by our research group can be empirically investigated in a future study .The understanding and management of suicidal risk in adolescence is a relevant challenge for any mental health professional. Consistent literature has pointed to the role of personality pathology to increase suicidal risk in both adulthood and adolescence ,59. In tIn particular, the level of narcissistic vulnerability emerging through specific affects and mood should be taken into account in the first place. The perception of an affective dysregulation engendered by internal events or external conditions seems to be the starting point of the volitional stage of the suicidal process in adolescents with pathological narcissism. The progressive intensification of affective dysregulation along with a concurrent increase in grandiose compensation represents an aspect to be carefully assessed when gauging the likelihood of a passage to actual suicidal attempts. Clinicians should also pay attention to the level of splitting between the intensification of the perception of narcissistic affects and grandiosity and the ensuing level of dissociation. This perspective of evaluation can provide a useful integration for the assessment, which can be more naturally embedded in the daily practice of clinicians involved in the challenging task of managing the clinical risk of a highly unpredictable population such as that one of adolescents.Finally, we believe that this approach may prove particularly effective in detecting the impact that the current conditions, engendered by the restrictions and life events due to the pandemic, may have on the potentially altered narcissistic functioning inherent to adolescent development .


This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are affected by zero-mean Gaussian errors. These tools consist of: (1) the analytical derivation of the gravity direction expectation and its covariance matrix, and (2) a continuous description of the geoid model correction as a linear combination of a set of orthogonal surfaces. The accuracy of the statistical quantities is validated by extensive Monte Carlo tests and the application in an Extended Kalman Filter (EKF) has been included. The continuous geoid description is needed as the geoid represents the true gravity direction. These tools can be implemented in any problem requiring high-precision estimates of the local gravity direction. The direct measurement of gravity using inclinometers has a variety of practical applications. Tilt sensors, such as accelerometers or inclinometers, are the hardware of choice for measuring a planet’s gravitational field. While the gravity is perturbed on a global scale by other massive bodies , local perturbations to the gravity vector’s pointing direction depend on nearby mass distributions and anomalies, or a lack thereof. A detailed review of various kinds of solid tilt sensors with comparisons between the most typical tilt sensing techniques can be found in .From a sensory perspective, inclinometers are commonly used to measure inclination angle magnitudes and structural deformations. Measured values are typically provided as a percentage or angular deflection with respect to a level reference surface, whose nominal orientation is perpendicular to the local gravity vector. Other classic inclinometer use cases include measuring the slope gradient during activities such as tunneling, de-watering and excavation, as well as those that require monitoring the integrity of the ground around a structure.In land surveying and mapping, an inclinometer can provide a rapid measurement of the slope of a geographic feature  or be usn 3D points, known as Perspective-n-Point (PnP) problems [Inclinometers are also used in more complex systems, such as in problems of estimating the position and orientation of a calibrated camera observing a set of problems , and in problems ,16,17, wToday, new types of inclinometers are emerging, such as the two-dimensional highly sensitive fiber-optic inclinometer proposed by , which cPrior to being deployed in the field, inclinometers are efficiently calibrated in a laboratory setting. Because of vibrations and subsequent thermal fluctuations, the orientation of the inclinometer assembly degrades over time, requiring re-calibration methods to properly account for new measurement errors. Reference  proposesThe monitoring of possible road subsidence is proposed using a combination of theodolite measurements and inclinometers  to detecThe analytical tools to best estimate the gravity direction. These tools consist of: (a) an exact estimate of the gravity direction when inclinometer measurements are affected by zero-mean Gaussian noise, and (b) the associated gravity covariance matrix. These tools can be used in static and filtered dynamic scenarios to accurately estimate the actual gravity direction and to model the local subtle gravity variations.N linearly independent orthogonal surfaces that are derived from Chebyshev orthogonal polynomials of the first kind.A continuous mathematical model to describe the true gravity direction deviation with respect to the latest (1984) revision of the approximated World Geodetic System (WGS-84) ellipsoidal model. Two deflection correction models are proposed for the north–south and east–west deflection variations. These models are expressed using combinations of a set of This study considers the classic system of two non-orthogonal inclinometers affected by zero-mean Gaussian error (hypothesis) to measure the gravity direction, and it provides the non-approximated mathematical tools to best estimate the gravity direction for any static and/or dynamic scenario (objective). In particular, we provide:These tools and models find relevance in a variety of gravity measurement tasks and associated use, especially in filtered systems, such as the one developed for geo-technical monitoring in .The system under consideration in this study is shown in The gravity direction in the d ϑy see , allow tThis section contains the covariance analysis of the gravity direction estimated by two identical inclinometers, as shown in Let the two measured angles, The angles, To estimate the gravity direction, Equation  requiresThe term Equation  simplifiTo compute n series :(3)E{cosReference  providesSubstituting Equation  into EquTherefore, we obtainThis result allows us to find the expected values of the first two components of the gravity direction: a zero-mean inclinometer provides biased angles. This phenomenon is generated by our three-dimensional spherical world, and only vanishes under two situations: (a) when the measurement angle is perfectly This bias effect is actually very small, even for poorly accurate commercial inclinometers. However, since the inclinometer axis direction is normally placed perpendicular to the gravity direction, this effect is even smaller, because the inclinometer works around the nominal orthogonality displacement of The gravity direction covariance matrix isTo compute the The term The Therefore,Equations  and 10)10) allowUsing Equations  and 11)11), the This expression can be simplified into the following more compact form:To derive the analytical expression of the term, quations  and (13)After some simple manipulations and simplifications, the previous equation can be written in the more compact formNote that, as a sanity check, if the two inclinometers were perfectly orthogonal, meaning if Equation  becomes Equation .As for the term the covariance term,  This result, which has been numerically verified by extensive Monte Carlo tests, remains with no explanation. Note also that, if the two inclinometers were perfectly orthogonal  parameterizations by the Jacobian, quations , 9) and andJ, ofquations , while tThe first four elements of the Jacobian can be computed from Equation . Their eFinally, the expression of the Jacobian of the transformation isEquation  and EquaEquation , respectThe covariance law can actually be used to estimate all the elements of the covariance matrix. However, this law has been used here only to estimate the three missing elements of the covariance matrix, quations –16), ar, arPThe irregular Earth shape (and mass distribution) has presented significant challenges to surveyers and cartographers throughout history. The early map makers considered the Earth to be a perfect sphere prior to Isaac Newton positing an oblate spheroid shape model. The axial–symmetric ellipsoid description of Earth, which has been formalized as the World Geodetic System (WGS-84) , is reliDescribing a point on the Earth’s surface can be done by Cartesian coordinates (The relationship between these two latitude definitions is :(31)tanθThe greatest angular difference between geocentric and geodetic latitudes is, for the WGS-84 model, approximately 700 arcseconds, a difference that would introduce over 21 km of position error on Earth. However, even if the WGS-84 ellipsoidal model describes the gravity direction better than the sphere model, the actual gravity direction is dictated by the geoid model .P is a point on the Earth’s surface that is located at altitude h normal to the ellipsoid and altitude H normal to the geoid. This point on the geoid surface is located at altitude N with respect to the WGS-84 ellipsoid. The angle between the true gravity direction  and the fictitious gravity direction  is the geoid correction.The geoid was first described by Gauss as the shape that the ocean’s surface would take if the only acceleration forces acting on it were Earth’s gravitational field and the rotational dynamics of the planet. In reality, this is still a simplification of the surface always orthogonal to the gravity direcion. The geoid is particularly useful for describing the effect that mass anomalies (such as mountain ranges or caverns) have on the local pointing direction of gravity, which can deviate from the reference ellipsoid by tens, hundreds or even thousands of arcseconds. n, order m and argument It is also worth pointing out that, unlike the WGS-84 axial–symmetric ellipsoid model, the geoid cannot be described by a simple equation because it is a function of the Earth’s mass distribution. However, the geometry of the geoid surface can be derived with respect to the WGS-84 model using the derivatives of the Earth’s gravitational potential. The Earth’s gravitational potential can be described in terms of spherical harmonics:Taking normalized partial derivatives of Equation  with reseference .The analytical complexities associated with the infinite series of Equations  and 33)33) make N orthogonal surfaces:The continuous geoid model is provided by expressing the These orthogonal surfaces are built using orthogonal polynomials, such as Chebyshev polynomials, Using Chebyshev orthogonal polynomials, the orthogonal surfaces can be defined asChebyshev orthogonal polynomials of the first kind can conveniently be computed in a recursive way. Starting with The problem of fitting the geoid data grids, This continuous description of the geoid is applied in the next subsection to a geographical region where the geoid gravity direction deviations are particularly significant.The results of a numerical example of this procedure are shown in The associated geoid database consists of a By selecting orthogonal polynomials , the condition number of the least-squares matrix to invert is reduced and, consequently, the numerical process becomes more robust and provides a more reliable numerical estimation of the unknown coefficient vectors, This study introduced the mathematical tools necessary for extracting a highly accurate estimation of the local gravity (plumb-line) direction from a pair of non-orthogonal inclinometers. The statistical analyses performed herein can be used to quantify the performance of static tilt sensors, since the measured direction of gravity is known to be normal to the reference geoid surface. The next section provides an example use case of these tools for high-precision continuous gravity direction estimates under static operating conditions.The static Stellar Positioning System ,16,17 inMore accurate models will require the computation of the Hessian or even higher-order terms. The subsequent derivatives needed in these cases can be computed recursively:Including the mounting angle deviation from orthogonality, Integrating the proposed system with an Inertial Measurement Unit (IMU) to extend the use of the static “Stellar Positioning System” to dynamical scenarios. Similar to the previous point, this will extend the EKF state vector to account for the variations in the transformation matrix between the inclinometer and IMU reference frames.Including in the EKF state estimator, for the static use “Stellar Positioning System,” the transformation matrix between the inclinometer and the night camera reference frames.The authors are planning to validate the proposed gravity direction estimation method using two non-orthogonal inclinometers by:Investigating the convergence radius as a function of the geographical coordinates.Investigating the accuracy of the convergence as a function of the geoid database grid resolution.Including, in the current nonlinear position estimation algorithm, a divergence identification algorithm that re-initializes the estimation process using a new random guess selected within an admissible distance bound.As for the continuous geoid model, the authors are planning to complete the analysis on the geoid north–south and east–west deflection estimates by:This study introduces a new approach to accurately estimate the gravity direction using a pair of non-orthogonal inclinometers affected by zero-mean Gaussian errors. The proposed approach estimates the gravity direction and its Since the gravity direction is normal to the geoid surface, a continuous geoid model for the north–south and east–west corrections is provided as a linear combination of a set of orthogonal surfaces that are derived using Chebyshev polynomials of the first kind. An example application is provided for a specific region  to show the continuous description of the gravity direction deviations with respect to the WGS-84 ellipsoid model.This covariance analysis, along with the continuous description of the geoid, can be applied to any static or dynamic scenarios involving the measurement of gravity using a two-axis inclinometer.


Global Positioning System (GPS) satellites offer promising opportunity for Passive Radar systems due to their global coverage and the availability of multiple satellites throughout the world. However, their low power at ground level limits system coverage. In this paper, a GPS based Passive Radar which exploits a single illumination source, and uses digital array processing for ground targets localization is presented. To face signal power problems, a processing scheme combining reconstructed reference signals, adaptive filtering techniques and spatial filtering is implemented. Conventional beamforming techniques are used to increase the level of the target echo before the detection stage, and high resolution DoA estimation techniques are applied to estimate targets azimuth. Ground target localization in local Cartesian space is performed taking into account the system geometry, range and azimuth information. Both synthetic and real radar data are used to analyse system operation. During the measurement campaign, a cooperative vehicle was used for validation purposes. Results confirm that ground targets detection and localization are feasible using a single GPS transmitter. A Passive Radar (PR) is defined as a set of techniques that use non-cooperative signal sources, denominated Illuminators of Opportunity (IoO), to detect and extract characteristics  from the targets inside an Area of Interest (AoI) . Due to There is a growing interest in exploiting satellite platforms as IoOs due to the great diversity of constellations, signal waveforms and frequencies, which provide high availability, global coverage, and almost total invulnerability to natural disasters. Nevertheless, the large distance from the transmitter reduces signal power at ground level and compromises the PR performance. An important reduction of the ground coverage, although IoO availability is guaranteed along all the Earth surface, is expected in comparison with PRs which use ground-based illumination sources .The satellite’s orbit determines the influence of the platform dynamic on the PR scenario. Geostationary orbits produce a negligible relative movement whereas medium and low Earth orbits produce variations in PR geometry which affect the acquired signal characteristics. Coherent processing of the reference and surveillance signals can be applied when the platform movement is negligible and the transmission and reception characteristics allow the direct isolation of the desired illumination signal such as in DVB-S based PRs ,8. More GNSS satellites are promising illumination sources for PRs because of the global coverage they provide, and the simultaneous availability of multiple transmitters anywhere in the world. GNSS constellations have been exploited for maritime target detection and imaging ,10,11,12In this paper, a digital processing scheme is proposed for ground target passive localization by means of a single GPS transmitter. This work is a continuation of , where aThe rest of the paper is organised as follows: in The basic geometry of a PR based on a space-borne IoO is depicted in A traditional PR bases its operation in the coherent processing of both acquired channels. After a preprocessing stage, that reduces DPI and Clutter interferences, a Cross Ambiguity Function (CAF) between the reference and surveillance signals is computed according to Expression .(1)SCAFm,p) related to its location and movement with respect to the PR geometry.The presence of a target echo in the surveillance signal gives rise to a local maximum at a bistatic range-Doppler shift pair , in three different frequency bands . In this work, civil signals in the L1 band are considered as illumination sources. All GPS L1 signals share the same carrier frequency in a Code Division Multiple Access (CDMA) method requiring a signal reconstruction stage to isolate the selected reference signal. In addition, the platform location in an MEO generates a time variant geometry that should be considered in reference signal reconstruction and PR measurement interpretation. Both issues are considered in the following subsections.The PR configuration considered in this work is depicted in m is determined by the difference of the path lengths travelled by the wave received directly from the illuminator and the wave scattered by the target, as expressed in m=RTp, which is the frequency difference between the reference signal and target echo. In a moving transmitter environment, a Doppler frequency appears in both acquired signals: in the reference one due to satellite movement; and in the radar echo due to both transmitter and target movements. To calculate the Doppler shift, the projections of the current velocity vector on all signal paths are considered:The second PR measurement is the Doppler shift, Finally, the presence of a surveillance array allows us to estimate the target’s azimuth In each GPS transmitter, the navigation message of the signal civil part, The civilian signal transmitted in the L1 band is described by , where ii represents the PRN associated with the GPS satellites in line of sight from PR location. Each individual GPS signal will be delayed in time, The acquired direct path signal, elled as , where tThe GPS receiver software available in the literature allows the GPS signal search and tracking process necessary for signal reconstruction . In thisBefore CAF generation, direct path interference components from all available satellites are filtered in the surveillance signals acquired by the different single radiating elements of the surveillance antenna array, using ECA filters .The search stage ideally finds all GPS signals that are acquired on the reference channel. However, very low power echoes are expected from targets, and signals with low correlation levels compromise the performance of the PR. In this work, the target location will be obtained using a single satellite signal. Therefore, the coherent radar processing stage to generate the Range Doppler Maps (RDMs) is performed with the CAF taking as input the reconstructed reference signal associated with the most powerful received satellite, and the filtered surveillance signal.In PRs, echoes received from targets are characterized by low power. For GPS-based PRs, the power budget is even more restrictive, because even the direct reference signal is at or below the noise level, which jeopardizes the detection and localization of small targets, such as terrestrial ones. To increase the power of target echoes and enable target localization, a two-stage spatial filtering approach is designed by taking advantage of a surveillance array system.The proposed approach is based on  in whichThe functional block of the proposed processing scheme is depicted in This stage focuses on increasing the target echo power to enable detection of small targets in the range-Doppler domain, taking advantage of the beamforming gain in a ubiquitous radar configuration with a set of two simultaneous beams. The selected digital beamforming algorithm operates in the frequency domain after applying the CAF to the individual surveillance channels. This approach takes advantage of the inherent clutter and target mapping in the range-Doppler domain of the coherent processing stage to isolate the energy of each contributor .N orthogonal beam steering angles, To form the first set of simultaneous beams, digital beamforming techniques were selected under the requirement of sidelobe level control to generate orthogonal beams along with the azimuth sector of the single radiating element. An iterative process was followed to define the N − 1 steering angles, The orthogonal beams design procedure reduces the contribution to signal power in the current beam of targets whose DoAs are the steering directions of adjacent beams. However, the decrease in gain with respect to the maximum at the intersection points of the beams can be greater than 3 dB, negatively affecting the echoes of the targets in those directions . As the p) to compute the weight vector The optimization problem was solved for each steering direction and Doppler shift pair  based detector is selected. To manage the 3-dimensional matrix, The estimated location of targets in detection space is the centroid of positively detected points or the position of the maximum level. However, a more accurate estimation of the targets range can be obtained when the reference and surveillance signals are oversampled by taking advantage of the signal correlation characteristics . An imprA is a scalar coefficient, typically in the interval At this stage, the azimuth of the detected targets is estimated using a high-accuracy DoA estimation technique. The accuracy of azimuth estimation was increased by generating a new set of steering angles nsidered . The estpression .(8)Sm,pm), and DoA (The measurement vector provides information of the target’s bistatic range (m), defines a three-dimensional ellipsoid of revolution with the GPS satellite and the PR located at the foci. The equation of this ellipsoid is (13) in an auxiliary coordinate system, z-axis with an angle y-axis according to the satellite’s inclination, The measured bistatic range x=xSince targets of interest are ground vehicles and their movements are assumed to be confined to roads in the area of interest, an initial velocity estimate can be made by including external geographic information system data. The velocity vector can be estimated from the bistatic velocity of the targets (essed in .(15)vb=y-axis direction vx=PR measurements are applied directly to a Cartesian tracking stage based on the Kalman filter , to obtaThe performance of the Kalman filter is described with Expressions  and 19)19), whicpression  correspoThese estimates are updated using a weighted average of the next measurements, once observed.T is the transpose operation). A quasi-constant acceleration model in both x and y dimensions is selected to describe the expected dynamics of the targets, the acceleration derivative being modelled as a white noise process with power spectral density q [In order to use a Kalman filter for tracking moving targets, a dynamic model of the target motion must be designed. Since the intended targets are ground vehicles, motion in a plane with X and Y coordinates is considered, and a state vector is defined whose elements are the position, velocity, and acceleration of the target in both dimensions (ensity q . Therefoented in .(20)F1=h by a local linearisation [h with respect to the state vector and the measurement noise, respectively.Due to the linearity of the selected state function, the filter estimation stage is implemented with the standard Kalman filter equations . On the essed in , tacklinrisation .(21)Kk=For tracker initialisation, target’s location and velocity are calculated following the procedure described in The localization and tracking scheme was first validated with synthetic data. A simulated radar scenario was generated considering the variant geometry and signal characteristics of the GPS constellation. The PR receiver is considered at the center of the local Cartesian space where the simulation is performed. The PR receiver antennas were considered at 2 m from the ground level where the movement of the targets was performed following the trajectories represented in Six different targets with random initial positions around the PR location were simulated. A model with a quasi-constant modulus acceleration vector with independent components in X and Y coordinates was selected as the dynamic model of the targets. Initial velocities and accelerations were randomly selected from typical ground vehicle values.The position and dynamics of the IoO and targets were recalculated every 250 ms, simulating the PR refresh rate. Bistatic range, Doppler shift, and azimuth measurements were calculated from each instantaneous radar geometry. Additive white Gaussian noise with standard deviations of The localization and tracking results in the measurement and the tracking spaces for the simulated scenario are depicted in The localization error was also calculated as the Euclidean distance between the estimated track and the actual target location. A real radar data acquisition campaign was carried out to evaluate the ground target detection and localization performance of the proposed GPS-based PR. An area of the external campus of the University of Alcalá, near the Faculty of Physiotherapy and Nursing, was selected as the radar scenario. An updated version of the IDEPAR technological demonstrator, developed at the University of Alcalá  was emplFor the tests, the GPS satellite constellation was selected as IoOs, and the civil GPS signal in the L1 band was selected as the illumination signal. The PR demonstrator was configured to acquire 40 s of continuous signal at GPS L1 band (1575.42 MHz). The illumination signal was oversampled up to an acquisition rate of 25 MHz to increase the bistatic range accuracy and to allow ground target localization at low ranges. The acquired data were divided into 160 non-overlapping Coherent Processing Intervals (CPI), each of 250 ms duration, that were processed following the scheme described in A search of available GPS satellites was performed, identifying seven satellites, with PRNs 2, 6, 12, 25, 29, 31, and 32. The GPS signals associated with these PRN codes were reconstructed and considered in the adaptive filtering process to reduce their interference contributions in the RDMs. The satellite transmitting PRN 32 was selected as IoO due to its higher power at ground level.Some tests have been performed on the radar scenario with moving cooperative targets to evaluate the performance of the system. The cooperative targets started from the rear of the passive radar. A straight road trajectory of 390 m was defined, with the targets moving at a nearly constant speed of 30 km/h along the trajectory on the AoI. Nevertheless, the variation of the bistatic geometry produced an accelerated motion in the bistatic range-Doppler domain.In this subsection, some results of ground target detection with the PR using GPS satellites as IoO are presented to demonstrate the actual system performance in the radar scenario.The first result to be described correspond to the detection of a cooperative target in the radar scenario. y-axis. As it was expected from targets’ detections in the RDMs, the cooperative target reaches the higher detection distances from PR location (98 m) due to its movement was performed during the beginning of the acquisition and overpassed the detection coverage. The detection range for non-cooperative targets remains lower (68 m and 55 m) due to their movements along the AoI were carried out at the end of the measurement, and could not overpass the detection coverage before the end of the acquisition.The targets’ location estimations in the local Cartesian spaces were transformed to the geodetic coordinates for easy integration into the Google Earth application. System localization capability has also been analysed, taking into account the Euclidean distance between the estimated and the actual location provided by the GPS data of the target. Results obtained for both non-cooperative targets are shown in A summary of the location statistics (mean The assumption of a known target altitude limits the use of the proposed processing scheme to maritime and terrestrial targets. The reflectivity of maritime targets is usually higher, which allows the detection at higher distances. Since the localization error depends directly on the target’s range when only the DoA information is exploited, the absolute error in target localization is expected to be larger. To address both the increase of localization errors with target distance and the position of airborne targets, future works will study solutions based on multi-static configurations exploiting several line-of-sight GPS transmitters.This paper presents a GPS-based PR exploiting digital array processing techniques for ground target detection and localization. To cope with problems related to the temporal variation and low power of the received signal at ground level, a processing scheme combining reference signal reconstruction, adaptive filtering techniques, and a two-stage spatial filtering algorithm is implemented. Conventional beamforming techniques are used to increase the echo level of the target prior to the detection stage. A high-resolution DoA estimation technique is applied to estimate the target azimuth and allow the target to be located on the ground, first in local Cartesian space and then in geodetic coordinates.Real radar data were recorded using an updated version of IDEPAR demonstrator at the external campus of the University of Alcalá, in order to analyse the system detection and localization performance. During the measurement campaign, a cooperative vehicle was used for validation purposes and two additional non-cooperative targets were available in the AoI. The use of a linear array in the surveillance channel increased the target’s echo level improving the system detection capabilities and the maximum detection range. The target localization capability was validated along the trajectory of the cooperative targets with an average estimation error of 2.38 m. Non-cooperative targets were also correctly located along their trajectories. The results confirm the possibility of detecting ground targets with GPS-based PR, but at low ranges currently. Further research is necessary to increase the detection range, maintaining the positive characteristics of these radars.