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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L2, and combined L1/L2 observations are summarized in Table 4 **based** on 1-month data sets **for** **the** three baselines. In addition, **the** rates **of** false-positive and false-negative decisions on **the** acceptance **of** estimated ambiguities are provided. **The** **results** 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 **for** **the** various baselines were weighted with standard deviations **of** 0.5 m and 10.0 mm, respectively, and obser- vations with inconsistencies **of** **the** more than 6 m in **the** L1 and L2 double-difference pseudoranges were rejected. A minimum ratio **of** 3 **for** **the** squared residuals norm **of** best and second-best estimates was adopted as an acceptance threshold **for** **the** 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**.

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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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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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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 **the** **flight** 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.

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In order to prove that **the** algorithm can also handle **the** frequent changes **of** **the** **GPS** **satellite** constellation typical **for** space-borne applications, numerical simulations have been executed. During these simulations, **the** C/A-code and carrier-phase measurements **of** **the** **GPS** system on **the** Flying Laptop **satellite** have been created using realistic **attitude** scenarios. In **the** first **attitude** scenario, **the** nadir-pointing-mode, **the** **satellite** orbits **the** earth with a constant angular velocity vector in nadir orientation. In this **attitude** mode, **the** assumed system model **for** **the** 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, **the** **satellite** is pointed to a target fixed on **the** earth’s surface and thus continuously controlled by **the** **attitude** control system, which applies control torques to keep **the** **satellite** aligned with **the** reference frame during its pass over **the** ground target. Due to **the** applied torques, **the** angular velocity vector **of** **the** **satellite** changes and **the** assumption made **for** **the** system model in **the** Kalman filter is no longer true.

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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 **of** **the** European Constitution when it was first issued and voted by **the** European countries members **of** **the** European Union: several powerful rejection answers have surprised **the** European Union leadership and have proved that **the** formation and change **of** **the** social **attitude** with respect to major European actions need to be investigated in advance with more powerful scientific instruments. Also relevant is **the** impact **of** **the** 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 **of** **the** European Union’s and **of** **the** European Parliament’s institutions might depend in a greater extend in **the** near-future on **the** ability **of** developing appropriate instruments **for** **the** analysis and prediction **of** their functions.

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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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In [4], a general formulation is presented **for** GNSS **attitude** **determination** 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 [5]. In his serie **of** works [6]–[8], Giorgi further studies and enhances **the** **attitude**-aided ambiguity search. So far, this methodology has shown **the** best perfor- mance **for** GNSS-compass using carrier phase observations. More recently, [9] reviews **the** **attitude** **determination** topic, providing an overview on **attitude** estimation along with an example setup **for** **the** 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.

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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 **of** **the** 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 **of** **GPS** data and processing methods are most appropriate to minimize mission costs and full satisfying mission payload requirements focusing **the** attention on a SAR payload.

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Although **the** project ATON has achieved a major mile- stone by demonstrating **the** capability **of** **the** navigation system to provide a robust and accurate navigation so- lution to guide and control an unmanned helicopter, **the** development **of** **the** 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 **the** **results** **of** **the** parallel project OBC-NG [4] are considered. One element **of** **the** further development will be **the** inte- gration **of** **the** ATON software on **the** hybrid avionics architecture **of** OBC-NG and **the** transfer **of** a part **of** **the** 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.

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VI. C ONCLUSIONS AND F UTURE W ORK
**Attitude** **determination** in many means is a complicated problem. In this paper we have presented a proper framework **for** **attitude** **determination** 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 [9] 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.

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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:

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January 9, 2019. **GPS**-74 transmits **the** legacy navigation message (LNAV) on L1 C/A, **the** civil navigation message (CNAV) as part **of** **the** 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) **for** **the** pilot and data component **of** **the** L1C signal. With an average value **of** 2.8 m **for** April 2019, **the** signal-in-space range error (SISRE) **of** **GPS**-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 **for** **the** rest **of** **the** constellation. Evidently **the** apparent performance degradation is related to **the** non-operational status **of** **GPS**-74 and does not indicate **the** expected performance once **the** **satellite** 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 **of** **the** CNAV/CNAV-2 ephemeris and **the** availability **of** ISCs **for** users **of** **the** open L1 signals (C/A or L1C) can only partly be materialized by civil navigation users.

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