In the last step ofthe quality control algorithm, time differences of pseudorange and carrier-phase double-difference observations (triple-differences) are formed for each individual satellite. The absolute value of each triple-difference is then compared to a test thresh- old, and the observation is rejected if the threshold is exceeded. This editing procedure is possible due to the high data rate ofthe receivers and the low angular veloc- ity oftheCASSIOPEsatellite, which only causes a small effect in the triple-difference due to the geometric change in the baseline. In this editing step, pseudorange jumps and carrier-phase cycle-slips are detected. If cycle-slips are detected, the corresponding ambiguities are newly initialized as float values based on code-carrier differences. The next step is the measurement update. The Kalman- filter processes both pseudorange and carrier-phase observations. It can be configured to use single-frequency measurements from any number of signals. In the case ofCASSIOPE, it can process only L1 C/A, only L2 P(Y), or both signals together. No combination is formed when processing more than one frequency. Instead, mea- surements from the different frequencies are treated as independent and complementary observations. The ionospheric delay does not need to be estimated since it cancels out in the differencing over the short baselines. Using both L1 C/A and L2 P(Y) is a particularly interest- ing option, since observations on a second frequency with
L2, and combined L1/L2 observations are summarized in Table 4 based on 1-month data sets forthe three baselines. In addition, the rates of false-positive and false-negative decisions on the acceptance of estimated ambiguities are provided. Theresults are based on the epoch-wise estima- tion of relative antenna positions and double-difference phase ambiguities using only the pseudorange and carrier phase observations obtained at this epoch. The float-value ambiguities were subsequently used to estimate a set of integer values using the modified least-squares ambiguity decorrelation method (M-LAMBDA; Chang et al. 2005 ; Teunissen 1995 ). Based on the observed level of post-fit residuals, single-difference code and phase measurements forthe various baselines were weighted with standard deviations of 0.5 m and 10.0 mm, respectively, and obser- vations with inconsistencies ofthe more than 6 m in the L1 and L2 double-difference pseudoranges were rejected. A minimum ratio of 3 forthe squared residuals norm of best and second-best estimates was adopted as an acceptance threshold forthe estimated integer ambiguities in all cases to keep the number of false positive decisions at or below about 1%. For verification purposes, the actual ambiguities were independently derived from the double-difference carrier phase observations and the known baseline vec- tors and spacecraft attitude.
Based on the experiences with the SHEFEX II mission described above, an improvement ofthe GNC procedure for future missions was considered. This mainly consists of a new data fusion concept for drift correction ofthe sensors. To get a first idea how the new algorithm could work, a first test ofthe new system was performed by Inertial Science, using a van for transportation. The van transported a DMARS-R platform as well as a Novatel GNS. A test route with the van was driven to see how the drift correction would work. The test loop route had a length of 21.6 km, and included a local residential street and a freeway in Thousand Oaks, California. The route passed under four bridges which caused GNS signal blackouts for approximately 2 s. Additionally, the route included about 1 mile of heavily shaded area with trees. The starting point was the same as the end point. Before starting the trip, several self-alignments with the platform were made. During this trip, whenever GNS was available, the drift correction was made. After the trip theattitude was compared with pre- surveyed data just after the vehicle test. The graphs in Fig. 8 show the van tests results.
VII. C ONCLUSION
In this paper, a calibration method of USBL installation error based on attitudedetermination is proposed to accurately estimate the installation error angle for USBL. The installation error angle of USBL and SINS is constant in application, so the calibration of installation error angle can be completed by attitudedetermination method. Firstly, the vector observation model based on the installation error angle matrix is established. The calibration method proposed in this paper can be obtained by constructing observation vectors and reference vectors. In order to correct the accumulated attitude errors of SINS, the SINS/GPS integrated navigation method is used to obtain more accurate attituderesults. The position of transponder needs to be calculated by LBL system in advance. The simulation experiment and field test are carried out, to verify the performance ofthe calibration method proposed in this paper. Theresultsof simulation and field experiments show that the performance ofthe proposed calibration method is the best among several calibration methods. More importantly, the proposed method can complete the real-time calibration technology of installation error angle, and has no specific requirement for calibration experiment route. Based on the experiment and analysis of this paper, we can draw a conclusion that the proposed method has high application value
The following diploma thesis is related to the AsteroidFinder/SSB project ofthe German Aerospace Center (DLR). AsteroidFinder/SSB is a compact satellite that will be used for detecting aster- oids with an optical payload (telescope). Especially the objects that are completely inside the Earth orbit are of interest. The task of detecting weak light sources like asteroids places chal- lenging requirements to theAttitude Control System (ACS). Therefore the AsteroidFinder/SSB needs to be stabilised and controlled by an active there axis ACS. A preliminary design was established during Phase 0/A ofthe project. Based on these resultsthe following diploma the- sis focus on the development oftheattitudedetermination and control algorithm. Therefore a simulation environment is programmed and two different KALMAN filters are investigated as attitudedetermination algorithms. These are the extended KALMAN filter and the unscented KALMAN filter. Afterwards a guidance strategy is derived to reach the main mission goals. It is followed by the development of an attitude control strategy which is based on linear quadric GAUSSIAN control. At the end the algorithm functionality is validated through simulation.
A very obvious and simple approach is the use of energy balance relations along the orbit. In this approach, the velocities derived by numerical differentiation from thesatellite positions along the orbits (as result of a geometric orbit determination) are used to compute the kinetic energy which balances the potential energy, modeled by the unknown gravity field parameters. The application ofthe energy integral for problems ofSatellite Geodesy has been proposed since its very beginning (e.g., O’Keefe 1960, Bjerhammar 1967, Reigber 1969, Ilk 1983a). But the applications did not lead to convincing results because ofthe type of observations and the poor coverage ofthesatellite orbits with observations available at that time. The situa- tion changed with the new type of homogeneous and dense data distributions as demonstrated e.g. by Jekeli (Jekeli 1999) or discussed in Visser (Visser et al. 2003). Two gravity field models based on the energy balance approach and kinematical CHAMP orbits, TUM-1s and TUM-2Sp, have been derived by Gerlach (Gerlach et al. 2003) and Földvary (Földvary et al. 2004), respectively. Both models come close to the GFZ (GeoForschungsZentrum) gravity field models EIGEN-1 (Reigber et al. 2003a), EIGEN-2 (Reigber et al. 2003b), EIGEN-CHAMP3Sp (Reigber et al. 2003c), derived by the classical perturbation approach. Another approach is based directly on Newton’s equation of motion, which balances the acceleration vector with respect to an inertial frame of reference and the gradient ofthe gravitational potential. By means of triple differences, based upon Newton’s interpolation formula, the local acceleration vector is estimated from relative GPS position time series (again as a result of a geometric orbit determination) as demonstrated by Reubelt (Reubelt et al. 2003). The analysis techniques, mentioned so far, are based on the numerical differentiation oftheGPS-derived ephemeris, in the latter case even twice. Numerical differentiation of noisy data sets is an improperly posed problem, in so far, as the result is not continuously dependent on the input data. Therefore, any sort of regularization is necessary to come up with a meaningful result. In general, filtering techniques or least squares interpolation or approximation procedures can be applied to overcome these stability problems. The respectable resultsofthe energy approach in a real application, demonstrated by Gerlach (Gerlach et al. 2003) and Földvary (Földvary et al. 2004). Nevertheless, numerical differ- entiation remains the most critical step in these gravity field analysis procedures. An advanced kinematical orbit determination procedure which delivers directly velocities and accelerations can help to overcome these intrinsic problems.
Considering the experience of earlier activities with the ATON system, a position accuracy in the order of low one-digit percent of (camera) line-of-sight range was as- sumed as a likely upper bound. Given theflight trajectory followed (Fig. 14), this translates to a ground truth accu- racy requirement of centimeter level. Therefore, the he- licopter payload was equipped with a high-grade GNSS receiver NovAtel Propak6. It uses both L1 and L2 fre- quencies and the German precise satellite positioning service, SAPOS. This service relies on a network of ref- erence stations with precisely known positions to deter- mine corrective data for all visible GPS satellites. Fur- thermore, two GNSS antennas were used allowing the receiver to also determine heading and pitch angles in the North-East-Down reference system. The Propak6 output has the following 1σ accuracies: about 0.03 m in position, about 0.4 degrees in heading and pitch, and about 0.03 m/s in velocity.
In order to prove that the algorithm can also handle the frequent changes oftheGPSsatellite constellation typical for space-borne applications, numerical simulations have been executed. During these simulations, the C/A-code and carrier-phase measurements oftheGPS system on the Flying Laptop satellite have been created using realistic attitude scenarios. In the first attitude scenario, the nadir-pointing-mode, thesatellite orbits the earth with a constant angular velocity vector in nadir orientation. In this attitude mode, the assumed system model forthe Kalman Filter comes close to the real world dynamics, thus the filter does not suffer performance problems. The second attitude mode is the target pointing mode. During this mode, thesatellite is pointed to a target fixed on the earth’s surface and thus continuously controlled by theattitude control system, which applies control torques to keep thesatellite aligned with the reference frame during its pass over the ground target. Due to the applied torques, the angular velocity vector ofthesatellite changes and the assumption made forthe system model in the Kalman filter is no longer true.
Classical statistical measures of attitudes are already considered by the scientific community as insufficient and nearly powerless in building up global maps of attitudes evolution and change for large populations of subjects. For instance, no research community has tried so far to base the analysis of socio- economical and political attitudes in the case of a financial crisis (like the one which has recently affected the world) on agent-based simulations. No research community has ever reported research studies and predictions concerning a possible major social and political attitude change in the countries of North-Africa and Middle–East with respect to the political regimes and local governments as the current huge attitude change the news agencies are describing these days. Another example is the rejection ofthe European Constitution when it was first issued and voted by the European countries members ofthe European Union: several powerful rejection answers have surprised the European Union leadership and have proved that the formation and change ofthe social attitude with respect to major European actions need to be investigated in advance with more powerful scientific instruments. Also relevant is the impact ofthe attitudes modeling and simulation in the areas like institution building and institutional authority building: due to the complex functional and beaurocratic structure, the organization and efficiency ofthe European Union’s and ofthe European Parliament’s institutions might depend in a greater extend in the near-future on the ability of developing appropriate instruments forthe analysis and prediction of their functions.
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 ofthe spherical air bearing. An on-board-computer, an IMU, a battery and a power supply system are mounted on top oftheattitude platform, too. The on-board computer executes the control algorithms in real time. The different models forthe 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 theattitude platform are tracked by the laboratory’s position and attitude tracking system.
In , a general formulation is presented for GNSS attitudedetermination problems, showing the relation between carrier phase ambiguity resolution and solving the corresponding at- titude matrix. Moreover, Teunissen proposed the C-LAMBDA (Constrained Least-squares AMBiguity Decorrelation Adjust- ment) method, for which the problem of finding the carrier phase integer ambiguities is constrained adding the GNSS compass problem . In his serie of works –, Giorgi further studies and enhances theattitude-aided ambiguity search. So far, this methodology has shown the best perfor- mance for GNSS-compass using carrier phase observations. More recently,  reviews theattitudedetermination topic, providing an overview on attitude estimation along with an example setup forthe multi-antenna system on a vehicle. Nonetheless, an in-depth discussion on how to formulate a recursive Bayesian estimation of a rigid body attitude using multiple GNSS antennas is still missing.
Scientific small satellite missions for remote sensing with Synthetic Aperture Radar (SAR) payloads or high accuracy optical sensors, pose very strict requirements on the accuracy ofthe reconstructed satellite positions, velocities and accelerations. Today usual GPS receivers can fulfill the accuracy requirements of this missions in most cases, but for low-cost- missions the decision for a appropriate satellite hardware has to take into account not only the reachable quality of data but also the costs. An analysis is carried out in order to assess which on board and ground equipment, which type ofGPS data and processing methods are most appropriate to minimize mission costs and full satisfying mission payload requirements focusing the attention on a SAR payload.
The validation ofthe combined GPS+Galileo RTK position approach presented in study was validated with real GNSS data recorded in a measurement campaign conducted in Koblenz, Germany in 2019 (DOYs 133 and 134). The data was collected on board ofthe vessel MS Bingen at 1 Hz. The equipment consisted of a navXperience GNSS antenna connected to a geodetic Javad DELTA Receiver and a TRIMBLE receiver for RTCM3 messages corrections from the reference station with a ground truth known coordinates in Koblenz, Germany. Static data of DOY 133 (UTC 20:00 - 08:00) was used forthe IAR analysis and the impact ofthe elevation mask ofthe combined GPS+Galileo RTK position solution approach studied in this work. The validation was made with the comparative with single frequency GPS-only System versus a Combined GPS+Galileo systems in dual frequency L1+L5 respectively.The analysis in the performance ofthe RTK positioning algorithm in loose combination approach proposed in this study was conducted for elevation masks of 10 ◦ , 15 ◦ , 25 ◦ , 35 ◦ and 45 ◦ respectively using the GNSS measurement data of DOY 133. In order to track accurately the position ofthe vessel independently on the GNSS information, a geodetic total station was placed on the shores ofthe river (see Figure 10) to ensure the availability ofthe reference information even in areas where the GNSS performance was poor, as elaborated in .
Although the project ATON has achieved a major mile- stone by demonstrating the capability ofthe navigation system to provide a robust and accurate navigation so- lution to guide and control an unmanned helicopter, the development ofthe system and its core software is continuing. Currently the focus is set on optimizing the software to make it more efficient and robust to run it on space-qualified hardware with limited computa- tional resources. As a reference architecture theresultsofthe parallel project OBC-NG  are considered. One element ofthe further development will be the inte- gration ofthe ATON software on the hybrid avionics architecture of OBC-NG and the transfer of a part ofthe image processing to FPGAs. In parallel, the work is going on to adapt the system and its elements to dif- ferent mission scenarios. They include asteroid orbiters and landers as well as landings on larger solar system bodies.
VI. C ONCLUSIONS AND F UTURE W ORK
Attitudedetermination in many means is a complicated problem. In this paper we have presented a proper framework forattitudedetermination from single camera vector observations in a known environment. The Gauss Newton method and the Davenport q-method were put on the test. The simulation results show that the Davenport q-method is a preferred choice. Based on the Davenport q-method many algorithms such as the QUEST algorithm  provide less “intensive” way to estimate the solution to the eigenproblem and will be included in the future research. Also in our future work we look for a way how to determine attitude from single camera vector observations when the environment is unknown. The SLAM theory in particular BOSLAM has taken our attention.
The early 1980s ushered in the beginning ofthe era ofthe new generation small satellite. Physically small satellites by themselves were nothing new; many ofthe early U.S. and Soviet satellites and later experimental satellites from other nations would fall into small satellite classification so that, over the last 60 years, some 1500 satellites under ~100 kg have been launched worldwide. However, what differentiates the later generation of small satellites was the combination of a different management approach with the use of commercially available microelectronics devices to create reprogrammable, reconfigurable satellites capable of sophisticated functions with high utility in a fraction ofthe volume, mass, cost, and timescales. In the earlier emerging of new generation small satellite, within limitation of its mass, weight and space, most ofthe missions using passive attitude stabilization. However, as small satellite technical capabilities gradually developed throughout the 1990s, interest grew in their use for technology demonstration and verification. A series of microsatellites demonstrated steadily improved EO capabilities so one of small satellite built by Surrey Satellite Technology Ltd. (SSTL), TMSat (ThaiPhutt) launched in 1997, became the first multispectral imaging microsatellite to achieve 300-m GSD (NIR, red, green, blue). It was achieved by using three- axis momentum bias approach in combination with the implementation of 6 m gravity gradient boom. The success of TMSat mission has been the baseline forthe next subsequent SSTL's small satellite product such as TiungSat-1, UoSat-12, Alsat-1 and so on –.
It has to be stressed here that, in an analysis finalized to estimate whether the choice of a certain navigation system can fulfill requirements (3) or not, it has to be clear that there is an evident but not obvious distinction between what does happen in the reality and what one can measure and with which accuracy. In fact considering for example the simple case of a satellite flying in a LEO circular polar orbit at an altitude of 500 km, a preliminary analysis leads to the following order of magnitude assessments:
The GHOST “GPS High precision Orbit determination Software Tools” are specifically designed forGPSbased orbit determinationof LEO (low Earth orbit) satellites and can furthermore process satellite laser ranging measurements for orbit validation purposes. Orbit solutions are based on a dynamical force model comprising Earth gravity, solid-Earth, polar and ocean tides, luni-solar perturbations, atmospheric drag and solar radiation pressure as well as relativistic effects. Remaining imperfections ofthe force models are compensated by empirical accelerations, which are adjusted along with other parameters in the orbit determination. Both least-squares estimation and Kalman-filtering are supported by dedicated GHOST programs. In addition purely kinematic solutions can also be computed. The GHOST package comprises tools forthe analysis of raw GPS observations as well. This allows a detailed performance analysis of spaceborne GPS receivers. The software tools are demonstrated using examples from the TerraSAR-X and TanDEM-X missions.
Forthe short baselines foreseen for most ofthe TanDEM-X mission, the differential path delays are expected to remain less than a few centimeters or, equivalently, a tenth of a cycle. Thus, even a single-frequency differential GPS solution can be expected to deliver relative positions with a centimeter-level accuracy. As shown in Fig. This in fact the case forthe GRACE proximity as illustrated in Fig. 8. Here, single- and dual-frequency kine- matic relative navigation solutions are against the dynamically filtered relative navigation solution. Similar to the long-baseline cases discussed in , the kinematic dual-frequency exhibits an rms uncertainty of roughly 8 mm, which reflects the average position dilution of position (roughly 3) and the noise ofthe ionosphere-free L1/L2 carrier phase combina- tion of about 3 mm. Due to the elimination of ionospheric errors, the rms error is essen- tially constant over the entire day and does not exhibit a dependence on the relative dis- tance ofthe two satellites. A rather different behavior may, be observed forthe kinematic single-frequency solution. While a degradation due the impact of differential path delays is clearly obvious at separations above 10 km, the error at small baselines is roughly 3 times smaller than that ofthe dual-frequency solution.
January 9, 2019. GPS-74 transmits the legacy navigation message (LNAV) on L1 C/A, the civil navigation message (CNAV) as part ofthe L2C and L5 signals, and the 2nd generation CNAV-2 on the L1C signal. During the ﬁrst six months of operation, the CNAV-2 messages provided essentially the same parameter set as CNAV on L2 and L5, but added distinct inter-signal corrections (ISCs) forthe pilot and data component ofthe L1C signal. With an average value of 2.8 m for April 2019, the signal-in-space range error (SISRE) ofGPS-74 is worse by a factor of up to ﬁve compared to IIF satellites with Rubidium clocks. This can mainly be related to an extended upload interval of typically four days as opposed to one day forthe rest ofthe constellation. Evidently the apparent performance degradation is related to the non-operational status ofGPS-74 and does not indicate the expected performance once thesatellite is declared healthy. Only negligible diﬀer- ences may be noted between SISRE values for LNAV, CNAV, and CNAV-2, since all messages are presently derived from the same source of orbit and clock prediction and uploaded only once per day. As such, the improved smoothness ofthe CNAV/CNAV-2 ephemeris and the availability of ISCs for users ofthe open L1 signals (C/A or L1C) can only partly be materialized by civil navigation users.