As part of e-POP, **the** **GPS** **Attitude**, 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 ).

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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 **the** **satellite** 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 **the** **satellite** 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 **the** **GPS**-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.

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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 **for** **the** **GPS**-**based** PRISMA real-time navigation software are outlined in [2] and represent **the** key drivers **for** **the** 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 **for** **the** 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.

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VII. C ONCLUSION
In this paper, a calibration method of USBL installation error **based** on **attitude** **determination** 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 **attitude** **determination** 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

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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 2.2.5.1. 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**.

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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.

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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

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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 **the** **satellite** 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. **The** **Flying** **Laptop** 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.

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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 [1].

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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 [13] 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 **the** **Satellite** 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.

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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.

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