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GNSS Satellite Geometry and Attitude Models

GNSS Satellite Geometry and Attitude Models

The next generation of satellites (including the original Block II spacecraft and the slightly improved and more massive IIA satellites) was again built by the same prime contractor. As of early 2015, 3–5 Block IIA spacecraft remain in operational use, but are about to be replaced by the new GPS IIF and III satellites within 1–2 years. It may be noted that two Block IIA satellites (SVN 35 and 36) were equipped with LRAs. However, the satellites were decommissioned in 2014 and are no longer tracked by the International Laser Ranging Service (ILRS; Pearlman et al., 2002 ). The body-fixed reference frame of the Block II/IIA satellites is described in design drawings reproduced in Degnan and Pavlis (1994) . As illustrated in Fig. 4 , the positive z-axis is parallel to the boresight direction of the navigation antenna, and the y-axis coincides with the rota- tion axis of the solar panels. The x-axis is parallel to the long side of the front panel and the positive direction can be identified from the location of the navigation antenna and the LRA, both of which are offset in þx-direction from the CoM. Also, the x/y-corner can be easily identified by the large “horn” that serves as Sun shade for the optical burst detector of the NUDET payload. Similar to the Block I spacecraft, the IGS-specific body frame R BF;IGS
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On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms

On the Recursive Joint Position and Attitude Determination in Multi-Antenna GNSS Platforms

As contemporary applications such as driverless cars or autonomous shipping are called to revolutionize intelligent transportation systems (ITS), there is a growing need for the provision of precise and reliable navigation information. Global Navigation Satellite Systems (GNSS) play a fundamental role, becoming the main information supplier of positioning, navigation, and timing (PNT) data. While standard GNSS techniques—based on code observations— provide a decent performance for many applications, they do not comply with the far more stringent precision requirements of modern safety-critical scenarios. That is the reason why the transition to carrier phase-based techniques is required to reach precise navigation. Indeed, carrier phase observations present noise levels two orders of magnitude lower than their code counterpart. However, carrier phase observations are ambiguous, since only their fractional part is measured by the receiver [ 1 ]. The unknown number of integer cycles between satellite and receiver, so-called ambiguities, must be estimated to enable high-precision navigation. The ambiguities’ estimation process is widely known as ambiguity resolution (AR) [ 2 – 5 ], which in turn results in a challenging estimation procedure.
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The role of attitude determination for inter-satellite ranging

The role of attitude determination for inter-satellite ranging

Since GRACE Follow-On is a very close rebuild of GRACE, the attitude determination and control system will be almost identical to GRACE, with only few upgrades. One of the upgrades will be mounting of three SCA heads onboard each spacecraft, which is very beneficial for reasons discussed in the previous section. At the moment, no further information about the sensor performance and mounting geometry has been published yet. Also, no information about the in-flight and on-ground SCA data processing have been provided yet. However, it is expected that the performance will be slightly better than the performance of the GRACE SCAs. Similarly to GRACE, using magnetic torquers and cold-gas thrusters for attitude control, the inter-satellite pointing will be maintained within a deadband of at most a few mrad. Such pointing precision will be sufficient for the microwave ranging, but surely the pointing requirements of the laser ranging interferometry will not be fulfilled. For this reason, the LRI features its own pointing control system. This is accomplished by using a quadrant photodetector, which allows for measuring tilt angles between the local oscillator wavefront and the received wavefront by using differential wavefront sensing (DWS) (Anderson, 1984). This tilt information is processed by a digital control loop and fed back to the steering mirror (SM) electronics (Schütze et al., 2014a).
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From Observational Geometry to Practical Satellite Design: AsteroidFinder/SSB

From Observational Geometry to Practical Satellite Design: AsteroidFinder/SSB

With respect to SSSBs, the innermost solar system still is largely uncharted territory. Information on the orbital parameters and approximate size of previously unknown IEOs and other objects passing through this region is critical for the evaluation of SSSB distribution models. These models are used primarily for two important purposes: In the planetary defence context, they serve to determine the overall risk and frequency of impacts on the Earth and other terrestrial planets, and the size-frequency and relative velocity distribution of the impactors. In the wider scientific context, many of these models are based on the orbital evolution of the solar system as a whole, and modelled SSSB populations serve as sets of test particles that as a whole record and statistically image the integrated influence of various gravitational and non-gravitational effects over time. To determine the relative strength of these effects and their variation over time, observed and modelled populations can be compared at varied parameter settings, and before and after correction for observational biases which may also be determined in the process. The energy-frequency distribution of impactors is also used to determine the age of solid surfaces in the solar system, expanding the relative dating of planetary surfaces from the size-frequency distribution of craters alone. For absolute dating, a reference is required which can only be provided by returned samples that are dated by isotope clocks, such as the Apollo and Luna Moon rocks. The orbital and size-frequency distribution of impactors varies across the solar system. For example, IEOs can presently not reach objects beyond the Earth-Moon-system, and Aten asteroids can not reach the surfaces of main belt asteroids, although both may well migrate over time due to long-term perturbations to hit or become part of either group of solar system bodies. These localized SSSB population differences have to be modelled to determine the absolute age of planetary surfaces outside the Earth-Moon system as long as local surface samples remain unavailable. The high number of observed and modelled bodies enables sound statistical results. Each body adds seven or more parameters to the database; its orbit parameters, estimated size, and occasionally its shape and other physical properties. For example, the model population by Bottke and Morbidelli used in the evaluation of the AsteroidFinder’s performance contains 57649 virtual objects, including 1190 virtual IEOs, down to a limiting absolute magnitude H = 23.0, corresponding to a diameter of about 100 m at an albedo of 0.15. [3]
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Development of algorithms for attitude determination and control of the AsteroidFinder satellite

Development of algorithms for attitude determination and control of the AsteroidFinder satellite

The whole task of algorithm development and testing is done with the help of a simulator en- vironment. This simulator is developed inside Matlab/Simulink . Matlab/Simulink is a well known and tested environment to analysis mathematical and engineering problems. An addi- tional favor of this environment is that it is able to interact with a lot of others programming languages e.g. C, C++, FORTRAN and ADA. Another advantage is the ability to communi- cate with a real time simulation system provided by the company dSpace. This system allows to execute simulated models in real time which is helpful for algorithm design. A so called dSpace System is available at the DLR and will be used for the future development process of AsteroidFinder’s attitude control system. During this diploma thesis a basic algorithm structure is developed which shall be able to be merged with the real time simulation system. Regarding to this Matlab/Simulink is the right environment for further algorithm development.
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Towards Airborne Multipath Models for Dual Constellation and Dual Frequency GNSS

Towards Airborne Multipath Models for Dual Constellation and Dual Frequency GNSS

Aeronautical navigation is increasingly based on the use of Global Navigation Satellite Systems (GNSS). It is a cornerstone of performance based navigation and enables airspace users to ensure that their navigation capabilities meet all requirements. For different phases of flight, different levels of integrity, accuracy and availability are required. The requirements for position errors reach from rather generous error budgets on the order of nautical miles horizontally with a 95% probability for the en-route phase down to 10 meters vertical with an integrity risk of just 10 -7 for precision approaches. Development of techniques and augmentation systems, such as (Advanced) Receiver Autonomous Integrity Monitoring (A)RAIM and Space and Ground Based Augmentation Systems (SBAS, GBAS) continues, in order to be able to satisfy all performance requirements for current and future airspace usage.
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GNSS Yaw Attitude estimation: Results for the Japanese Quasi‐Zenith Satellite System block‐II satellites using single‐ or triple‐frequency signals from two antennas

GNSS Yaw Attitude estimation: Results for the Japanese Quasi‐Zenith Satellite System block‐II satellites using single‐ or triple‐frequency signals from two antennas

Due to their eccentric and inclined orbits, the satellites reside over Japan at high elevation angles over long periods of time and thus improve the satellite visibility in urban canyons. In addition, the satellites also transmit augmentation information to enable improved navigation

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COORDINATED ORBIT AND ATTITUDE CONTROL OF A SATELLITE FORMATION IN A SATELLITE SIMULATOR TESTBED

COORDINATED ORBIT AND ATTITUDE CONTROL OF A SATELLITE FORMATION IN A SATELLITE SIMULATOR TESTBED

supplies air as propellant gas for 16 cold gas thrusters. There are also three reaction wheels for torque actuation and a balancing system, where small weights are moved by step motors to place the center of mass directly in the center of rotation of the spherical air bearing. An on-board-computer, an IMU, a battery and a power supply system are mounted on top of the attitude platform, too. The on-board computer executes the control algorithms in real time. The different models for the controllers can be developed in the Matlab/Simulink environment. The Matlab/Simulink coder generates C code from the models, which can be compiled and uploaded to the on-board-computer. During the tests the external mode of Matlab/Simulink is used to receive data from the model running on the on-board computer. Infrared targets mounted on the attitude platform are tracked by the laboratory’s position and attitude tracking system.
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A Decentralized Processing Schema for Efficient and Robust Real-time Multi-GNSS Satellite Clock Estimation

A Decentralized Processing Schema for Efficient and Robust Real-time Multi-GNSS Satellite Clock Estimation

As one of the most popular positioning technologies, precise point positioning (PPP) [ 1 , 2 ] has been widely used thanks to its high accuracy, proficiency, stability, and flexibility [ 3 – 5 ]. Recently, with the great progress of global navigation satellite systems (GNSS), the Russian GLONASS, European Galileo, and Chinese BeiDou have increased the number of satellites to more than 80, which will grow to about 120 in 2020. Compared with GPS-only solutions, better performance of PPP with multi-GNSS would be achieved in terms of not only convergence but also accuracy because of the improved satellite geometry due to the increasing number of satellites [ 6 – 10 ]. With the progress in high-speed internet communication and the achievements in the GNSS data stream protocol and format design, i.e., Radio Technical Commission for Maritime (RTCM) and Networked Transport of RTCM via Internet Protocol (NTRIP) [ 11 ], great efforts are underway towards the global real-time GNSS precise positioning service, where the real-time high precision satellite orbit and clock product is fundamental [ 12 ]. Though the quality of the International GPS Service (IGS) precise clock products have been improved continually
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Multiple View Geometry in Remote Sensing: An Empirical Study Based on Pléiades Satellite Images

Multiple View Geometry in Remote Sensing: An Empirical Study Based on Pléiades Satellite Images

This work deals with the aspect of multiple view geometry in remote sensing. The presented study was based on six multi view Pléiades images that depicts a scene from multiple orbits and multiple incidence angles forming along and across track stereo pairs. The analysis of the sensor models pointing precision showed very high accuracy. This could be traced back to the highly accurately measured GCPs, ICPs, and to the quality of image coordinates. Generation of DSMs was possible for all stereo pairs. It could be observed that a smaller intersection angle yields more complete reconstructions (less nodata regions), while the accuracy is lower than for pairs with larger intersection angle. Therefore, a selection of stereo pairs with medium range intersection angles represents a useful tradeoff. The fusion of all pairs resulted in the highest completeness. In future the currently employed local fusion process will be replaced by a global one.
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Attitude Determination via GNSS Carrier Phase and Inertial Aiding

Attitude Determination via GNSS Carrier Phase and Inertial Aiding

Attitude Determination (AD) constitutes an important navigation component for vehicles that require orienta- tion information, such as spacecraft or ships. Global Navigation Satellite Systems (GNSS) enable resolving the orientation of a vehicle in a precise and absolute manner, by employing a setup of multiple GNSS antennas rigidly mounted onboard the tracked vehicle. To achieve high-precision attitude estimation based on GNSS, the use of carrier phase observations becomes indispensable, with the consequent added complexity of resolving the integer ambiguities. The use of inertial aiding has been extensively exploited for AD, since it enables tracking fast rotation variations and bridging short periods of GNSS outage. In this work, the fusion of inertial and GNSS information is exploited within the recursive Bayesian estimation framework, applying an Error State Kalman Filter (ESKF). Unlike common Kalman Filters, ESKF tracks the error or variations in the state estimate, posing meaningful advantages for AD. On the one hand, ESKF represents attitude using a minimal state representation, in form of rotation vector, avoiding attitude constraints and singularity risks on the covariance matrix estimates. On the other hand, second-order products on the derivation of the Jacobian matrices can be neglected, since the error- state operates always close to zero. This work details the procedure of recursively estimating the attitude based on the fusion of GNSS and inertial sensing. The GNSS attitude model is parametrized in terms of quaternion rotation, and the overall three-steps AD procedure (float estimation, ambiguity resolution and solution fixing ) is presented. The method performance is assessed on a Monte Carlo simulation, where different noise levels, number of satellites and baseline lengths are tested. The results show that the inertial aiding, along with a constrained attitude model for the float estimation, significantly improve the performance of attitude determination compared to classical unaided baseline tracking.
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Instantaneous estimation of attitude from GNSS

Instantaneous estimation of attitude from GNSS

An optimal integer ambiguity estimation problem is still a challenging topic that can be explored from mathematical stability, precision and cost, while at the same time the fixed integer ambiguity must be the corrected one. In case of moving platform applications, where the antenna arrays are rigidly mounted and no fixed coordinate information of the master antenna is given, it is difficult to fulfill the reliable ambiguity of carrier phase observation. This complication is added by the absence of the fixed reference station. The algorithm is then developed by utilising prior information about the fixed baseline vectors, hence the precise and reliable integer ambiguity set can be estimated. The problem occurs whenever the demand about the attitude determination becomes higher. It is actually not an easy job to solve the reliable integer ambiguities in short time span (or even high data rate) applications due to slightly changing in satellite geometry. This problem can be solved by loosening the data rate of observation up to one Hertz, where the gap of information from GNSS can be predicted by using KF algorithm. This method has also another advantage in providing attitude information in case of GNSS signal absence.
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GNSS Satellite Orbit Validation Using Satellite Laser Ranging

GNSS Satellite Orbit Validation Using Satellite Laser Ranging

launched first satellites or even started an operational service, the GNSS landscape has experienced major changes in recent years. As part of the Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS), a global network of multi-GNSS monitoring stations has been established and various analysis centers have started to determine orbits of selected GNSSs on a routine basis. As a key feature, all satellites of the new constellations (i.e. Galileo, BeiDou, QZSS and IRNSS) are equipped with laser ranging reflector arrays enabling high-precision two way ranging measurements. The paper illustrates the use of SLR observations collected by the ILRS for validation of precise and broadcast ephemerides of the new constellations. As an independent and unambiguous tracking system, SLR helps to gain a better understanding of the new satellites, which still lack a thorough characterization of their orbit and attitude dynamics. SLR tracking is thus considered an essential contribution for a future use of the new GNSSs in space geodesy. The paper also addresses operational aspects of SLR tracking of the new navigation satellites related to their specific orbits, regional distribution and continuously increasing number.
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Green attitude and economic growth

Green attitude and economic growth

(b) large impact of wealth: ξ k = −0.7 Figure 4: Transitional dynamics: evolution of the growth rate; solid red line: ˆk (δ(k)) from (21), dashed green line: ˆk ∗ from (18), solid green line: ˆk (¯δ) from (16); parameters: ε = 0.05, ρ = 0.05, A = 1.5, γ = 2 Figure 4 displays the evolution of capital growth. First, capital growth is unambiguously reduced if green attitude is fostered by capital accumulation. During the growth process green attitude evolves, hence the parameter δ decreases and the negative environmental externality diminishes. Capital growth decreases in time, as abatement activity increases, this case is shown in figure 4(a). Nevertheless, figure 4(b) shows that the growth reduction induced by the impact of wealth on green attitude may even overcompensate the negative externality with respect to capital accumulation. During the transition process, capital growth may result suboptimally low, if wealth has a large impact on green attitude. The growth reduction implied by the continuous decrease in future capital return due to the perpetually enhancing green attitude is larger than the overaccumulation implied by the environmental externality. However, the more realistic parameter setting is an only small impact of wealth on green attitude, corresponding to figure 4(a).
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Green attitude and economic growth

Green attitude and economic growth

1 Introduction Recent research in various disciplines identifies an increased sensitivity of individuals as re- gards environmental problems such as pollution, loss of biodiversity, global warming, ozone depletion or tropical deforestation. Summarizing this, the European Commission (2008, p. 3) states within the Special Eurobarometer 295 entitled ’Attitudes of European Citizens towards the Environment’ that: ". . . citizens are becoming more aware of both the potential effects of these problems in their daily lives and the role they could play in protecting their environment." Follow-up studies confirm these preoccupations (see e. g. European Commission, 2014). Bretschger and Smulders (2007, p. 1) already emphasize the importance of social dynamics in the context of environmental quality evolution because of learning behaviour or changing per- ception. In industrialized economies, perception of environmental issues strengthens over time, e. g. by increasing pollution, environmental education or increasing income. Hence, individual awareness of environmental degradation is endogenous and as a consequence, pollution and accumulation dynamics become considerably more complex. We focus on the determinants of environmental externalities as well as on their evolution on the growth path. We show that the properties of dynamic market equilibrium depend crucially on whether and in which way indi- vidual attitude towards the environment is influenced by economic development. The relevance of pollution perception for the resulting time path of environmental quality was also discussed by Schumacher and Zou (2008) who show that pollution perception may change the dynamics qualitatively and lead to intergenerational inequity.
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Risk Attitude and Nonmarital Birth

Risk Attitude and Nonmarital Birth

study examines the influence of risk attitudes on out-of-partnership births and cohabiting births. We hypothesize that risk tolerance should be particularly associated with a higher probability of out-of-partnership birth. On the one hand, risk tolerance can involve a higher willingness to take the risk of an unwanted pregnancy. Even if a single woman has no wish to have children, a high degree of risk tolerance may induce her to contracept less effectively when engaging in casual sex. On the one hand, risk tolerance can increase a single woman’s propensity for a planned pregnancy. If the woman has a wish for a child and does not find a suitable partner, a high degree of risk tolerance may increase her willingness to take the risks associated with single motherhood. These risks involve financial insecurity, future disadvantages in the marriage market, and potentially adverse consequences for the child’s health status and school achievement.
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Green attitude and economic growth

Green attitude and economic growth

could also be explained by a more robust market for ideas in wealthier countries, in that their citizens feel free to express thoughts and debate issues without fear of repercussions from the government" (see Glaeser 2005, p. 210). Another essential factor of individual environmental perception is environmental quality on its own. As long as the pollution level is low, individuals do not care about the impact of their actions on environmental quality but only consider their impact on the resulting consumption path. As pollution increases, the negative impact of capital accumulation on environmental quality becomes visible and thus fosters environmental awareness of the individuals. For example, the survey underlying the Eurobarometer 365, (European Commission 2011) was carried out in april and may 2011, in direct succession of the Gulf of Mexico oil spill and the Fukushima nuclear accident. As a consequence, man-made disasters followed by water pollution were mentioned most freqently in 2011 to provoke the biggest effects of environmental change (see European Commission (2011, p. 14)). As also described by Schumacher (2009) green attitude will be the more likely if the pollution level is high. The environmental consequences of economic decisions are more obvious, hence green attitude will enhance.
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Building change detection based on satellite stereo imagery and digital surface models

Building change detection based on satellite stereo imagery and digital surface models

In binary change detection, a very important final step is to separate the relevant changes associated with buildings from other changes (noise and other areas which might contain irrelevant change, here e.g., no-buildings). Vegetation growth can also create a height change, and if these areas are located around buildings, it will largely influence the building change detection result. To alleviate this effect, we use normalized dif- ference vegetation index to indicate vegetation cover. Another important effect is shadowing which can significantly influence the quality of the DSMs. It has been shown in our previous paper [17] that shadow areas usually result in relatively bad matching results. Matching failures in shadow areas, which often represent ground level, are displayed in the original gener- ated DSMs partly as holes, and through interpolation methods, they often get higher height values than the ground level. If this kind of error exists only in data of one epoch, building change alarms are produced. Here, the shadow mask is extracted with the method introduced by Marchant and Onyango [28] in which the relationship of red/blue channel and green/blue channel can be used to extract the shadow class.
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Flight Results of GPS-Based Attitude Determination for the
Canadian CASSIOPE Satellite

Flight Results of GPS-Based Attitude Determination for the Canadian CASSIOPE Satellite

Differences between the a-priori differential antenna coordinates and the calibrated coordinates result from the fact that the electrical antenna phase center does not nec- essarily coincide with the mechanical center of the patch antenna and its exact location is affected by the material in its vicinity. Even if all antennas were mounted with the same orientation, different mounting geometries will cause different shifts in the antenna phase center. It should also be noted that the average effect of multipath errors will affect the estimated baseline vector. In the case of CAS- SIOPE, the antennas are mounted on fixtures that keep the solar array at an offset from the top panel of the main satel- lite body structure. Two patch antennas are embedded into the solar panel array; the other two protrude to the side. As a result, a different mean effect of multipath reflections can be expected for each antenna.
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Computational Modeling and Simulation of Attitude Change. Part 1, Connectionist Models and Simulations of Cognitive Dissonance: an Overview

Computational Modeling and Simulation of Attitude Change. Part 1, Connectionist Models and Simulations of Cognitive Dissonance: an Overview

For cognitive structures, in particular, this kind of distributed system provided the means to create an overall semantics by combining the meanings conveyed by several cognitive units. The procedure is quite simple: each node provides a piece of information which is propagated as a level of activation to all neighboring nodes. The spreading of activations makes that each node is dependent on all the other nodes directly or remotely linked to it, stimulating or constraining therefore the activations of all neighboring nodes Nodes’ mutual interdependency is controlled by the weights associated to each connection, such that each piece of information will get a particular degree of relevance in the overall output of the system. For cognitive consistency and consonance achieving tasks, this means that each unit in a conceptual structure will contribute to the overall consistency of the cognitive structure. As a constraint satisfaction algorithm is used, the contribution of each node to the global output will be accordingly adjusted so as the conceptual structure could achieve consistency (Read and Miller, 1994).
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