The verification and performance evaluation of theattitudedetermination algorithm has been accomplished with test data, collected during a field experiment. For this exper- iment, three GPS antennas have been mounted to an aluminum rack in a comparable arrangement to the antenna system on theFlyingLaptopsatellite. The two baseline vec- tors had a lengths of 0.4 m and 0.6 m. The aluminum rack has been placed on a turntable in order to simulate the rotation of thesatellite. The turntable allows a rotation of the antenna array around the vertical axis with a constant rate. The antennas were connected to three Phoenix GPS receivers. The plots in Fig. 6 show the Euler angles yaw, pitch and roll over time for measurements taken over an interval of one hour with a rotation rate of 1 ◦ /s. The angles describe the rotation of the antenna array with respect to the local horizontal coordinate system. The upper plot forthe yaw angle clearly shows the rotation rate of the platform. The plots forthe roll and pitch angle in the lower plot represent the tilt of the platform with respect to the local horizon. Ideally, both angles should be zero at all times. Instead, both pitch and roll angle show variations with a standard deviation of about 1 ◦ . The maximum variations are in the order of 2 ◦ . The deviations of the roll and pitch angle are caused by errors in the horizontal components of the differential antenna positions. These positioning errors can be of different origin. The dominating error source are multipath errors on the carrier phase measurements, which are caused by multiple signal receptions at the antenna due to reflections of the electromagnetic wave at objects in the vicinity of the antenna array. During the field experiments, the carrier phase multipath errors of low elevation satellites reached mag- nitudes of up to 2.5 cm , which corresponds to the observed deviations of the Euler angles. In contrast to the measurement errors causes by the receiver noise, the assumption of a Gaussian distribution does not hold for multipath errors. Therefore these errors are more difficult to be filtered out using a Kalman Filter. Additionally, systematic errors like antenna phase center variations and mounting offsets introduce errors in the solution forthe Euler angles. A rigor assessment of the magnitude of the different error sources cannot be provided forthe experiment, since no reference attitude from a more accurate sensor is available.
As part of e-POP, theGPSAttitude, Positioning, and Profiling experiment (GAP) provides GPS-based orbit and attitude information of CASSIOPE as well as total electron content and electron density measurements of the ionosphere (Kim and Langley 2010 ). GAP is made up of commercial off-the-shelf (COTS) components including five NovAtel OEM4-G2L miniature GPS receivers. Four of these (GPS-0 to GPS-3) are connected to patch antennas on the zenith facing (z) panel of the CASSIOPE spacecraft. The respec- tive code and carrier phase measurements can be used for precise orbit determination, while differential measurements between pairs of antennas provide information on the space- craft attitude (Kim and Langley 2007 ). In addition to this GAP-A (“attitude”) subsystem, a single GPS-O (“occulta- tion”) receiver (GPS-4) is connected to a NovAtel pinwheel antenna with an anti-velocity pointing boresight direction to collect high-rate ionospheric radio occultation (RO) meas- urements. GAP was conceived and developed by the Univer- sity of New Brunswick in partnership with the University of Calgary and Bristol (now Magellan) Aerospace. RO process- ing and data analysis have been undertaken by colleagues at various institutes (Shume et al. 2015 , 2017 ; Watson et al. 2018 ; Perry et al. 2019 ).
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 of the energy integral for problems of Satellite 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 of the type of observations and the poor coverage of thesatellite 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 of the 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 of theGPS-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 results of the 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.
One of the main challenges of the PRISMA formation flying is the realization of an on-board navigation system for all mission phases which is robust and accurate even for various spacecraft orientations and frequent thruster firing for orbit control. The requirements fortheGPS-based PRISMA real-time navigation software are outlined in  and represent the key drivers forthe design of the system addressed in this paper. Goal of the absolute and relative orbit determination is to achieve an accuracy of 2 m and 0.1 m, respectively (3D, rms) and provide continuous position and velocity data of the participating spacecraft at a 1 Hz rate for guidance and control purposes as well as forthe PRISMA payload. As detailed below, this is achieved by two software cores residing in the MAIN on-board computer. The two cores are executed at 30 s and 1 s sample times to separate the computational intensive orbit determination task from orbit prediction functions with low computational burden. An extended Kalman filter has been developed which processes pseudorange and carrier-phase measurement data issued by the local Phoenix GPS receiver on MAIN and sent via an Inter Satellite Link (ISL) from the remote Phoenix GPS receiver on TARGET.
The following diploma thesis is related to the AsteroidFinder/SSB project of the 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 of the project. Based on these results the following diploma the- sis focus on the development of theattitudedetermination 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.
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 attitude results. 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 of the calibration method proposed in this paper. The results of simulation and field experiments show that the performance of the 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
There are many formation control architectures that could be implemented which lie between the extremes of centralised and decentralised control. For example, the reference satellite could be allowed to fly freely, with only absolute position being of importance for orbit maintenance. The follower satellites could then use a decentralised control approach to maintain their own position relative to the leader (and each other for collision avoidance). Alternatively, a reference satellite in a widely dispersed formation with a centralised control architecture could determine where individual satellites in the formation needed to be to complete a particular task, and the low-level control system onboard each individual satellite would determine the optimal collision-free trajectory to achieve the desired position. Individual satellites could determine their own position via a decentralised architecture, and control this to within an error box, without further reference to the location of the other satellites. Larger formations could be grouped into smaller clusters, each with a mid-level ‘leader’ that reports to an overall formation reference satellite, creating a true hierarchy. Ultimately, however, the most appropriate architecture is dependent on the mission, the number of satellites and their proximity within the formation, and the manoeuvres they are likely to perform. There are a number of references which describe the results of studies into satellite formation flying control topology, autonomy and communications protocols. Examples include Mandutianu, Hadaegh et al. (2001), Smith and Hadaegh (2002), and Mueller (2004). A selection of classical orbit determination techniques which use various combinations of Earth-based observations to calculate a satellite orbit are described by Curtis (2005). However, the differencing of satellite absolute position data measured from the ground (usually by radar, telemetry, or optical telescopes) will not provide sufficiently accurate relative position information for formation flying, and it is therefore necessary to make on-orbit relative position measurements using the systems introduced in section 18.104.22.168. This more accurate data can be used to actively control the formation to a higher precision from onboard the spacecraft than if the data is to be relayed to Earth (although the necessary control reactions can be planned quite accurately using orbit propagators). This ability to respond to position errors with basic actuation requires a minimum level of autonomy for each spacecraft in a formation, and will be greatly facilitated by accurate on-board real time orbit determination.
It is a great accomplishment of the GRACE mission operations team to have kept the GRACE mission nominally operating despite several defunct components for more than 8 years after the planned mission termination. The very good performance of the twins is a result of continuous optimization, parameter adjustment, adaptations, software update, satellite maneuvers, etc. The current greatest challenges are to keep the energy budget stable and to optimize the propellant consumption. Demanding spacecraft maneuvers and handling are necessary to optimize the battery performance after 2 solar cells failed on each spacecraft and the battery capacity decreased from nominal 16 Ah to 3 Ah (Herman et al., 2012). In order to minimize the propellant consumption, several approaches have been tested and implemented on GRACE, cf. Section 6.3. Also the health of the scientific instruments such as the K-band ranging assembly, accelerometer, GPS receiver and the star cameras is under critical observation. Although the nominal limit of 10 6 thruster activation cycles has been exceeded by some of the 12 attitude control thrusters (see Table 3.2), so far they continue to work nominally.
The GHOST “GPS High precision Orbit determination Software Tools” are specifically designed forGPSbased orbit determination of 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 of the 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.
Theattitudedetermination and control system of FlyingLaptop uses four reaction wheels as actuators and three internal redundant magnetorquer for desaturation. Thedetermination is achieved by four fiber optic gyros and two star cameras. The system supports different pointing modes. The target pointing mode is used forthe OSIRIS overflights. In this mode thesatellite orients itself to a target position in the WGS84 system. As the target passes underneath thesatellitethe target rotation of thesatellite increases and it decreases after the point of maximum elevation over the target. Thesatellite is required to stay below 150 arcseconds of misalignment between the pointed axis and the target system. Because the beam divergence of OSIRIS is 1.2 mrad (approx. 247 arcseconds) a margin of 1.6 should allow thesatellite to establish a stable link. However the uncertainty in the alignment error of OSIRIS w.r.t. to thesatellite body system is still larger than 40 arcseonds. Additionally, at the begin of the mission thesatellite was not able to fulfill its pointing requirement. Therefore, an update of the flight software in July 2018 included an extended kalman filter fortheattitude sensor data fusion and propagation. This allows FLP to reach the required pointing performance.
The latest generation of GPS satellites, termed IIF for “follow-on” is built by Boeing. Between 2010 and spring 2015, a total of nine Block IIF satellites has been added to theGPS constellation. The orientation of the spacecraft coordinate system is shown in Fig. 4 based on design draw- ings contained in Fisher and Ghassemi (1999) and Dorsey et al. (2006) . The direction of the positive x-axis can most easily be identiﬁed from the placement of the large auxil- iary payload receive antenna, which extends from the x-face. Furthermore, a þx-oﬀset of the navigation antenna relative to the center of the Earth-facing þz-panel may be recognized. The manufacturer-speciﬁc axis designa- tion is compatible with the IGS convention, as indicated by the (positive) x-oﬀset of the antenna derived by Dilssner (2010) , who adopted an IGS-style yaw-steering attitudeforthe PCO and PCV estimation of the IIF spacecraft. Speciﬁc aspects of the IIF attitude control law during the eclipse season are likewise discussed in Dilssner (2010) .
Based on the experiences with the SHEFEX II mission described above, an improvement of the GNC procedure for future missions was considered. This mainly consists of a new data fusion concept for drift correction of the sensors. To get a first idea how the new algorithm could work, a first test of the 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.
In the last step of the 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 of the receivers and the low angular veloc- ity of the CASSIOPE satellite, 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 of CASSIOPE, 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
Removing redundancies can be performed by vari- ous types of compression. As this is the only way to preserve all the raw sensor data, its implementation is self-evident especially if the data volume is large, stor- age capacity is tight and computational capabilities are at hand. Analyzing the data directly on thesatellite not only requires high computational performance and long implementation time, but also takes the risk of losing important information because the raw data cannot be restored, while it decreases the needed storage capacity decisively. Moreover, the application of the analysis has to be very specific so a wide usage of the data is not feasible. The last possibility to reduce data volume is to screen the incoming data and select only valuable infor- mation for further processing, storage and down-link. A relatively simple image screener could be a cloud de- tection algorithm which marks all incoming images as non-valuable when they exceed certain cloud coverage. TheFlyingLaptop shall be able to perform continuous nadir observations where all incoming images are pre- processed, evaluated in regard to their relevance, and afterwards either stored or discarded.
AttitudeDetermination (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 theattitudebased 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 forthe float estimation, significantly improve the performance of attitudedetermination compared to classical unaided baseline tracking.
The OSIRIS-FLP features transmitter optics of 1mrad beam divergence and one laser source based on a high power directly modulated semiconductor laser diode of 100mW mean power, and also an EDFA-amplified source with up to 1W mean transmit power. The downlink scenario of On/Off-modulated optical DTE data transmission is described in  , the OSIRIS transmission experiment from FLP follows the upcoming CCSDS-standard (Consultative Committee for Space Data Systems) for Optical On-Off Keying (O3K) in regard to the physical layer parameters, i.e. carrier wavelength, data rates, and modulation format .
An increasing number of space missions nowadays require a synergic cooperation among multiple spacecraft. In some cases, payload and mission requirements impose constraints on relative distances and configurations, so that the spacecraft have to orbit in close formation. The usefulness of this architecture often lies in the spacecraft capability of maintaining defined orbital configurations for short or longer periods within a certain accuracy. In these cases, relative navigation plays a key role in the overall system performance as the knowledge of the relative kinematic states, i.e., relative positions and attitudes, of each formation member is a fundamental prerequisite for planning formation acquisition, formation reconfiguration, formation keeping or collision avoidance maneuvers .
Forthe short baselines foreseen for most of the 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 of the 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 of the 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 of the dual-frequency solution.
In this study, the linearised system dynamics are evaluated at each point on a reference orbit described by the Richardson third-order analytical solution for a periodic halo orbit around L2. This continues previous LEO formation flying work where the relative motion was governed by force gradients. The analytical approach also enables expressions for initial formation conditions, to which relative motion is so sensitive, to be derived. Segerman and Zedd  evaluate the modelling error with one example of model verification, and the other references discussed above do not evaluate or specify clearly the modelling error associated with linearisation. In order to design controllers using this formation flying tool, it is necessary to firstly evaluate the modelling error against a suitable numerical orbit propagator. In future, the controllers designed will be flown in theSatellite Tool Kit (STK) Astrogator software, and this was therefore used for model comparison. The gravity gradient model solution in terms of linear distance from L2 (quadratic was also implemented) is compared to similar scenarios in STK, and also the solution of Segerman and Zedd.
Once the nutation angle could be reduced better than 0.1 deg, further procedure conducted on the operation of LAPAN-A satellite series was observing the growth of nutation. Figure 6.10 displays the measurement of nutation growth for almost one day observation. In this observation period, the spacecraft performed a momentum bias attitude control through single pitch wheel operation. This observation result confirms that once the nutation has been damped, the nutation angle will remain low for a long period with the growth around 0.17 deg/day. Thus, the procedure of nutation damping can then be done once per day or another convenient interval. Even though a nutation damping using an angle mode of reaction wheel or a magnetic coil gives better result, they could not be well applied when the nutation angle is still high. When the spacecraft just wakes up from hibernation or in the post of attitude maneuver, the angular momentum is distributed on all three axes. The effective way to establish momentum bias attitude control is run up the pitch wheel (y wheel) to absorb the most of the momentum and activate the x wheel to damp the nutation in the angular velocity mode by setting a command of 0 deg/s. Generally, this procedure takes 5 to 20 minutes until steady condition has been reached. Once the spacecraft is in a steady condition within a nutation angle lower than 0.5 deg, the operator could switch the nutation damping to the other method to achieve pointing stability better than 0.1 deg. The nutation damping technique using an angle mode of wheel or a magnetic coil normally runs in a short time to get desired pointing stability and can then let the spacecraft to continue the most of its cycle in a single pitch wheel operation.