Flight Dynamics Operations solution for full-electric propulsion-based GEO missions

Transcription

1 SpaceOps Conferences 5-9 May 2014, Pasadena, CA SpaceOps 2014 Conference / Flight Dynamics Operations solution for full-electric propulsion-based GEO missions Felipe Jiménez 1, Javier Cuesta 2, Roberto Sánchez 3 and Raúl Núñez 4 GMV, Tres Cantos, Madrid, E-28760, Spain Manuel J. Sansegundo 5, Manuel Sánchez 6, Almudena Murillo 7 HISPASAT, Arganda del Rey, Madrid, E-28500, Spain E Electric propulsion satellites are being increasingly demanded by satellite agencies, operators and manufacturers due to their high efficiency in terms of mass consumption. This low consumption capabilities permits to design lighter satellite platforms, which lead into saving great launcher costs. As part of Hispasat s Hispasat AG1 (HAG1) mission, GMV has upgraded their focusgeo FDS solution which allows to flight an on station full-electric propulsion based satellite like HAG1 simplifying the complexity of operations for this kind of missions, which leads into increasing the safety and reliability of the computations performed. This new solution enhance most important challenges of this kind of missions such as Manoeuvre Optimization, collocation strategies, operations coordination with chemical propulsion satellites and Orbit Determination. I. Introduction lectric propulsion satellites are being increasingly demanded by satellite agencies, operators and manufacturers due to their high efficiency in terms of mass consumption. This feature permits to design lighter satellite platforms, which lead into launcher costs reduction. Commercial GEO satellite operators are starting to show a great interest in this kind of missions. Hispasat is one of the pioneers in the commercial market to use these technolgies, and plans to launch HAG1 satellite, a full electric propulsion (EP) based platform for all operations but LEOP which uses standard chemical propulsion. As part of the HAG1 mission activities, GMV has upgraded focusgeo FDS in order to implement an on station full-ep based satellite like HAG1 simplifying the complexity of operations for this kind of missions, which leads into increasing the safety and reliability of the computations performed. focusgeo is used by Hispasat to control all the satellite fleet at various orbital slots. This paper describes the main aspects of this state-of-the-art solution and how HAG1 satellite is intended to be operated by Hispasat. Aspects like manoeuvre Optimization, Orbit determination with large amount of manoeuvres, operations coordination with chemical propulsion satellites and automation of FDS operations are big challenges that demand efficient solutions. 1 Section Head of Western Commercial Programs, Flight Dynamics and Operations Unit, fjimenez@gmv.com 2 Division Head of Commercial Programs, Flight Dynamics and Operations Unit, jcuesta@gmv.com 3 Project Engineer, Flight Dynamics and Operations Unit, rosanchez@gmv.com 4 Project Engineer, Flight Dynamics and Operations Unit, rnunez@gmv.com 5 Head of Space Segment Engineering & Programs Development, mjsansegundo@hispasat.es. 6 Satellite Operations Engineer Manager, msanchez@hispasat.es 7 Satellite Operations Engineer Deputy Manager,, amurillo@hispasat.es 1 Copyright 2014 by GMV. Published by the, Inc., with permission.

2 II. Proposed FDS solution: Overall Design The solution for HAG1 on station full Electric Propulsion satellite combines platform specific modules specifically designed for this mission integrated in the focusgeo FDS suite with all mission independent modules, such as: Pre-processing of Tracking data (PREPRO), Orbit Determination and Maneuver Assessment (GORDAM), Orbit Propagation with either impulsive and Continuous maneuvers (as those of HAG1), Event and Ephemeris Generation (PRODGEN), Station Keeping and Maneuver Planning and Collocation and Proximity assessment specifically designed to cover any satellite cluster configuration required. These functionalities are extensively used by Hispasat to control all the satellites of the on orbit fleet. This paper does not intend to present in detail all the generic functions but to describe how the FDS is adapted to the HAG1 EP case. In Figure 1 it is presented the HAG1 FDS logical flowchart in which Mission Independent and HAG1 platform modules interact in the same focusgeo FDS framework: Figure 1: Overall Architecture of the HAG1 FDS Modules HAG1 platform specific modules are in charge of performing the computations required to determine the orbit and calculate maneuvers (plus all the ancillary functions). The main functionalities developed are described below: 1) IDEA-CTRL: In Figure 1 this module is placed embedded in the Mission independent functions but it is in fact platform specific for HAG1. This module is the core of the Station Keeping Planning and computes the required EP thruster firings required to control Inclination, Drift (in Longitude), Eccentricity and Angular Momentum of HAG1 satellite, 2) MASSEVO: is the mass evolution component of focusgeo. This component computes the satellite mass consumption (using the Book keeping Method) using telemetry information for the duration of each EP thruster actuation and other TM parameters information needed to estimate the mass consumed. MASSEVO also computes fuel mass consumed and remaining propellant on board the satellite to maintain fuel book-keeping records. MASSEVO also predicts the delta-v in (E, N, R) axis using the characteristic data for each thruster. Before running MASSEVO, the user must specify the manoeuvre time span, pressures (normally taken from TM), and the rest of inputs needed for the computations. The outputs of MASSEVO component are the mass consumption estimation on a tank basis, the new satellite mass and the prediction for delta-v in (E, N, and R) reference frame. 2

3 3) THRUST-CAL: Thruster calibration software is aimed to evaluate the actual thrusters performances in terms of thrust level and mass flow rate as function of discharge current and voltage for EP thrusters and pressure for Cold Gas Thrusters (CGT) and Chemical Propulsion (CP) Thrusters. The computed value is then used to estimate the fuel consumption in MASSEVO and will be updated on-board for dedicated AOCS processes. 4) AM.MONITORING: This module checks if the Angular Momentum (AM) build-up generated by the commanded orbital maneuvers behaves as predicted by the dedicated planning modules. The module has the following inputs: - Estimated S/C quaternion from telemetry - Estimated S/C total angular momentum from telemetry - Predicted angular momentum from Maneuver Planning process The module produces as output the Delta angular momentum (on-board estimated versus predicted). 5) ATT-PROP: This module is in charge of computing the attitude profile of the satellite during the following Mission operation phases: - The on station phase of the satellite (where the satellite is Nadir pointing) with possible offsets commanded by ground, in order to compare it with respect to the attitude profile coming from TM. - In case of contingency, this module will also have the possibility of computing satellite attitude profile for Sun Pointing Mode. - The module generates as well a set of Chebyshev polynomials in case it is required to be commanded for manual guidance - FDS generates plots in which the estimated and real evolution of the attitude can be compared. This module is only for trending and verification purposes. 6) COG-PREDICTOR: This module is in charge of the computation of the current Centre of Gravity of the satellite. 7) ORBIT-UP: Computation of orbital elements for the HAG1 satellite on-board propagator update procedure. In the following sections describe in detail the Maneuver Optimization and the Orbit Determination processes that are the keys for the control of HAG1. III. The Maneuver Optimization problem: IDEA-CTRL The IDEA-CTRL component calculates the combined North/South/East/West manoeuvres needed to control Inclination, Drift, Eccentricity and Angular momentum at the same time using EP thrusters. In addition to the aforementioned SK targets, a series of constraints shall be fulfilled and therefore this adds more complexity to the problem of computing the optimal manoeuvres to be performed. Finally it must be considered that the manoeuvres computed within a Station Keeping cycle shall minimize the propellant consumption. Station keeping for a satellite based on Electric Propulsion thrusters, as it is the case of HAG1, needs to be performed almost daily because of the inherently low thrust force of an EP system. For HAG1, a station keeping cycle of 7 days has been defined as nominal, but FDS is required to be flexible enough to plan different cycles as needed. In this nominal scenario, Station Keeping manoeuvres are performed during 6 consecutive days while the 7th day is reserved for orbit determination. The fact that the EP Thrusters are mounted at around 45 degrees to the Normal/Tangential directions means that there are no specific thrusters dedicated to Eccentricity/Drift control and Inclination. All thrusts contribute to the control of all the SK control parameters and therefore all of them shall be computed simultaneously as part of global optimization problem. A. Solver mathematics This Station Keeping optimization problem has been faced as a non linear programming (NLPQL) optimization problem in which mass propellant is intended to be minimized. In order to do so, Thrust time or equivalently Thrust arc shall be minimized. The algorithm used for this optimization is the sequential quadratic programming algorithm with distributed and non-monotone line search 1, 2. IDEA-CTRL uses this approach to optimize the EP firings that minimize an objective function that in this case will be the Thrust duration of the different thrust within a SK cycle. These thrusts shall fulfil the different SK targets (Inclination, Drift, Eccentricity and Angular Momentum) imposed to the Mission and the platform constraints required by the satellite platform. 3

4 The general optimization problem to minimize an objective function f under nonlinear equality and inequality constraints can be defined as: (1) Where the objective functions to be minimized is the summation of the individual Thrust arcs of each individual thruster (which is equivalent to the duration of the thrusts and thus to the Mass propellant consumed): (2) Weight factors can be used in order to promote certain thrusters with respect to others. By default all thrusters should be weighted equally to one. B. Station Keeping Targets and Platform Constraints Once defined the objective function to be minimized it shall be defined the equality and inequality constraints that shall be accomplished. These constraints will be parameterized as function of the thrust arcs (duration) and also the thrust centroid position within the orbit. Here below it is defined the main targets and constraints that have been defined for the HAG1 Mission. It is important to consider that the formulae defined within this section are particular for each orbit revolution. This means that the algorithm tries to minimize the objective function of minimum consumption in each single orbit, but certain targets only make sense to be defined for a complete SK cycle of seven days. 1. Inclination Target Inclination target is defined for a SK cycle period of 14 days. Once this target in inclination is computed, it is equally divided among the SK days of manoeuvres (6 out of 7). IDEA-CTRL module allows selecting among different target control strategies for the inclination: - Fixed target Inclination (defined by either the Inclination module and Ascending Node or by the Inclination vector components )). - Move Orbit pole to target inclination: The target inclination modulus i T is specified by the user. There are two possibilities for inclination pole correction direction: o o It can be a value manually entered by the user (D). It can be automatically computed according to a long-term strategy to be the optimum direction in terms of fuel consumption, replacing the input parameter D. The calculation is made by means of a numerical integration of an approximate pole drift model for a time span of Y years. This model is based on the perturbations due to the Sun, Moon and the J2 tesseral term of the Earth - Move Orbit pole symmetrically: The target pole is calculated by the program such the maximum value of the inclination, for a given length of time after the manoeuvre, is minimized. Same possibilities as in previous mode for direction to move pole are available. - Symmetric Evolution with respect to the target circle: The target pole is calculated by the program such the maximum value of the inclination y-component (following CNES criterion), for a given length of time after the manoeuvre, is minimized. Same possibilities as in previous two modes for direction to move pole are available. 2. Eccentricity target Eccentricity target is defined for a SK cycle period of 7 days. IDEA-CTRL module allows selecting among different target control strategies for the eccentricity: - Sun Pointing Perigee 3 : This strategy is based in choosing the more optimal time for the burn, minimizing the radius of the motion of the eccentricity by an optimal use of the drift correction burns. The goal of this strategy is to point the eccentricity vector, i.e. the perigee to the Sun in the forthcoming station keeping cycle at the middle of the Station Keeping cycle. - Sun Pointing Apogee: This strategy is completely analogous to the Sun Pointing Perigee but in this case is the satellite Apogee which shall point the Sun position at the middle of the SK cycle. - Fixed target Eccentricity, defined by either the Eccentricity vector components ) 4

5 3. Drift target This target is defined so that the satellite reaches a given target for its Mean Longitude at the end of the 7 day Station Keeping cycle. Figure 2: Angular Momentum Database 4. Angular Momentum Constraints The total Angular Momentum produced by each of the EP firings shall be below the maximum value allowed. In order to always fulfill this constraint, IDEA-CTRL has a dedicated database where the target of the Angular Momentum after each firing is configurable. 5. Thruster Sequence As part of the optimization process, one of the variables that are likely to be optimized in order to improve the cost function is the set of thrusters to be used and its order. The thruster s selection in each cycle shall be defined by the set to be used (nominal or redundant). Therefore, in each cycle the same set of four thrusters will be used. Nominally, there can be up to six firings per orbit. Therefore, two out of the four thrusters are allowed to thrust twice in a given orbit. In order to not degrade certain thrusters, the selection of the extra thrust pair to be used shall be alternated among Station Keeping sequences. In order to perform the selection of the thrusters order, IDEA- CTRL module contains a set of inputs in order to either manually configure the set of thrusters to be used in each of the days of the SK cycle, or automatically compute the thrusters order. In the latter case, all the feasible combinations of thrusters orders are analyzed. Then, among those for which all the targets and constraints are fulfilled, IDEA-CTRL selects the combination which minimizes the objective function. Figure 3: Thruster Sequence tab of IDEACTRL -Main Options 5

6 C. IDEA-CTRL User Interface One of the Main advantages of the IDEA-CTRL module is its user friendly MMI that allows and flexible configuration of the inputs required for the complex optimization problem that is being performed by the Software. For instance, main Input of IDEA-CTRL allows configuring which Targets are to be fulfilled (Inclination, Drift, Eccentricity, and Angular Momentum) and the strategy to be used for each of themy to follow. (e,g,: eccentricity can be selected to follow a Sun Pointing Perigee strategy or a fixed predefined target). It is also possible to configure in each execution the Manoeuvre Cycle scheduled, indicating the days within the cycle where there are EP burns planned. This is used to to perform Orbit Determination. In the next figure it is shown some of the inputs that can be configured: Figure 4: IDEA-CTRL Main Input Options Besides the Main Input panel that will be configured at the beginning of each SK cycle, IDEA-CTRL has additional Inputs required as part of the process implemented in this module: - Thruster Constraints File: This database defines thrusters constraints such as minimum and maximum thrust duration, minimum separation time between thrusts and constraints in certain thrust positions if needed. - Station Keeping Database: This database defines the Station Keeping control parameters, such as Longitude window, and Inclination and eccentricity control circle (which are used for Symmetric and Sun Pointing Perigee strategies respectively) - Thruster Database: defines the orientation, thrust and Isp for each of the thrusters - Orbit File: The orbit file is used to know the evolution of the orbit before the manoeuvre optimization for next cycle. This orbit is previously generated by the Orbit Propagation module SORBAM. - Power Database: This database defines the Power evolution models of the satellite batteries. These parameters are used by IDEA-CTRL to compute which is the minimum time between thrusts so that there is always energy available in the satellite batteries. - Angular Momentum Database: This database contains: Thruster Calibration Parameters: This is the Angular Momentum variation calibrated for a given satellite mass and for a given thrust duration. In order to know the prediction of the Angular momentum variation for a given thrust firing, IDEA-CTRL multiplies the values in this table by the ratio between the thrust duration and the reference duration and also the ratio between current reference Mass and actual Mass. 6

7 Maximum Angular Momentum Build after 1 st, 5 th and 6 th Thrust: These inputs define the different Angular Momentum target to be achieved after EP thrust in order to ensure that satellite is never above the maximum Angular Momentum value. - EP Profile File: This database stores the historical of computed EP firings, including Station Keeping cycle information (Cycle number, orbit number inside the cycle and Thrust number for each orbit), EP thrusters identifier of the thruster used in the firing, Start of the burn, Centroid of the manoeuvre, and the Angular Momentum achieved after the firing. - Bias Database: S/C bias to take into account for the manoeuvre computation process. - Satellite Database: Satellite name is read from this database in order to print it into the program s Standard Output. The outputs of IDEA-CTRL module are: - Standard Output: This is the main output of the module containing the computation results. Among others, this output displays for each of the days of the Station Keeping cycle, which combination of thrusters are feasible in the sense that all the targets can be achieved. Then among all these feasible combinations, IDEA-CTRL select the on each minimizes the objective function (i.e. lest consuming). At the end of each SK cycle day, the achieved Angular Momentum is displayed in order to check this constraint is not violated. Here below it is displayed a part of the IDEA-CTRL Standard Output: Figure 5: IDEA-CTRL Stdout - Orbit Plots: IDEA-CTRL generates plots of the evolution of the main relevant orbital parameters and also the Evolution of the Angular Momentum Components, as can be seen in the simulation described in next section. - Continuous Maneuver File: This file contains the information of the maneuver information that is required for the propagation of the orbit: - Execution Start Time - Maneuver Duration - Predicted East/North/Radial Acceleration: This is the three components of the acceleration as computed by IDEA-CTRL in the maneuver optimization process. - Estimated East/North/Radial Acceleration: This is the three components of the acceleration as estimated by the Orbit Determination module (GORDAM/SEGORD). - EP Profile File: This file contains additional information of the thrusters firings such as: - Cycle/Orbit/Thrust Number Id: These identifiers define the Station Keeping Cycle, The Orbit Number within the Cycle and the Thrust firing in each orbit respectively. 7

8 D. IDEA-CTRL Simulation Results In this section it is shown the results of a long term simulation performed with IDEA-CTRL module for the planning of the Station Keeping maneuvers for HAG1 satellite. The simulation has been performed for a period of one year in which inclination, eccentricity and Longitude drift targets, together with Angular Momentum constraints have been imposed to be accomplished. In order to demonstrate the flexibility of this Maneuver Planning SW, after nine months satellite starts to operate in inclined orbit and therefore IDEA-CTRL has been configured to let the inclination free after that period. It is noticed that, for the whole simulation period, IDEA-CTRL has always reached convergence for the solutions analyzed and optimization problem has always successfully finished. In the following figures it is shown the evolution of the main orbital parameters of HAG1 when performing the Station Keeping maneuvers planned with the IDEA-CTRL module. Eccentricity control strategy used in this simulation is Sun Pointing Perigee and Inclination Control is based on a fixed target close to the Inclination Control Centre (except when inclined orbit begins): : Figure 6: Mean Eccentricity evolution for a one-year period As seen in Figure 6, the eccentricity vector evolution is controlled with sufficient accuracy. The fact that eccentricity circle is followed so tightly improves the capacity of collocated the satellite in crowded clusters. When following inclination-eccentricity separation strategies, inter-satellite distances are completely ensured if satellite is able to control its eccentricity as per Figure 6. Inclination control is achieved within the specified targets. Inclination evolution is kept very close to the inclination centre. In this way collocation with other satellites is favorable: eccentricity-inclination separation strategy can be performed satisfactorily and therefore minimum inter-satellite distances can be maximized. After nine months of 8

9 inclination control it can be seen how inclination free drift begins. This strategy aims at simulating end of life operations to extend satellite lifetime: Figure 7: Inclination and Eccentricity evolution for a one year period Longitude control is shown in Figure 8 and is meeting as well the expected requirements. It can be observed that Longitude evolution just represents about ¼ of a standard Longitude window of ±0.1 degree. This feature helps different collocation configurations (e.g.: several longitude sub-windows can be defined, then several satellites can be controlled by means of eccentricity-inclination separation strategies, one pre sub-window). Figure 8: Longitude Evolution for a one-year period Angular Momentum evolution is also another constraint that must be fulfilled during the satellite lifetime. After each maneuver angular momentum increases and therefore thruster firings shall be selected in a way that Angular 9

10 Momentum is always below its maximum value. Here below it can be seen how the angular Momentum constraint is accomplished in the present simulation: Figure 9: Angular Momentum evolution IV. The Orbit Determination Process Orbit determination is one of the most important processes within the FDS for any kind of commercial satellite missions and especially for GEO satellites. In the case of HAG1 mission, Orbit Determination process is specially important due to the fact that SK maneuvers are performed using full-ep and therefore an important number of maneuvers are performed every day of the cycle devoted to orbital corrections (six out of seven). This number of manoeuvres requires to almost continuously tracking them by the Orbit Determination process, which may detect any undesirable under or over performing effect on the manoeuvre execution. In such scenario is essential to determine the best Station Keeping cycle that allows a proper Orbit Determination process. The SK cycle shall accomplish the orbit determination accuracy requirements of the Mission and at the same time, shall allow tracing the evolution of the different thruster performances along the satellite lifetime. Also it is important that the selected scenario could be flexible enough to permit at any time to re-plan the maneuver cycles, following the needs of the FDS engineers. A. Station Keeping Cycle Definition Even if the assumed default scenario for the satellite station keeping maneuvers is based on a scheme (6 days for maneuver execution and the 7 th day devoted for both Orbit Determination and maneuver planning of the next SK cycle) there are back-up alternatives that shall be considered and analyzed: 1) 6 +1 scenario: 6 consecutive days of maneuvering and the 7th day devoted to orbit determination and planning of the next cycle. 2) scenario: This scenario will concentrate maneuvers in 5 days, permitting a larger margin for the orbit determination process and also for the planning of next SK cycle maneuvers. 3) scenario: In this scenario, maneuvers will be performed on the first 5 days and also in the 7 th one of the SK cycle. The 6 th day will be dedicated to collect ranging data and orbit determination could be performed in the 6 th or even the 7 th day of the cycle. The key point to analyze in this strategy is to compute the degradation on the orbit estimation because of the fact that the maneuver on the 7 th day is not estimated in the orbit determination but just considered in the orbit propagation. B. Ranging Measurements: Maximum time gap feasible without ranging The foreseen nominal Ranging measurements scenario defined for the mission is as follows: 1) Two Ground Stations available placed in Arganda del Rey and Canary Islands 2) Simple ranging measurements will be available from each of the stations. 3) Noise: Each station will have a ranging noise that will be around 5 meters. 4) Ranging Frequency: preferred option for the orbit determination process is to have continuous tracking during the whole satellite lifetime of the spacecraft. The definition of continuous tracking for the mission is 10

11 to have one Ranging measurement per hour and per Ground Station. This means that on average there will be one measurement available every 30 minutes. This solution is the baseline, but other alternatives maybe implemented if deemed feasible. It is important to remark that the fact that continuous tracking is preferred does not mean that is strictly necessary to ensure the safety of the mission. If there is a gap in the continuous ranging measurements from one of the two stations foreseen, operations will not be jeopardized and accurate enough orbit determination could still be performed, as it is presented in a study case here below. For a period of seven days, measurements from one of the two Ground Stations have been removed starting with a gap of one complete day during the last ranging day available. Then the gap has being increased to a 2, 3, 4 and more days period and up to reaching a gap for which orbit determination is not feasible anymore. Evolution of the orbit determination accuracy as function of the ranging gap has been analyzed. The efficiency estimation of the different maneuvers inside the orbit determination interval is no longer possible due to the ranging gaps. Nevertheless, it has been analyzed if orbit determination itself could be still accurate enough not to jeopardize the mission operations. Here below, it can be seen which the differences were between the estimated state vector and the propagated one for different Ranging gaps (in days) in one of the two Ground Stations: Orbit Determination differences at EPOCH 2024/02/27-00:00:00 Ranging GAP 6d gap 5d gap 4d gap 3d gap 2d gap 1d gap 0d gap A (km) e 6.1E E E E E E E-07 i (deg) Ω (deg) ω (deg) Long (deg) E-07 Cp S/M (m 2 /kg) Table 1: Orbit Determination errors for different Ranging Gaps It can be seen that results are really accurate in all cases, and the orbit determination accuracy is not significantly affected by the lack of measurements. The limit for these gaps is just one complete day of ranging data. Below that limit (7 day gap case), the orbit determination convergence process is not ensured. C. Manoeuvre Assessment 1.10 The analysis and simulations of the HAG1 orbit determination scenario reflects the difficulty to calibrate the manoeuvres individually with the accuracy required. The 1.05 small size of the manoeuvres and their proximity introduce correlations between manoeuvres difficult to discriminate Additionally the absence of tracking between some manoeuvres does not allow to generate separate calibration estimation of the individual manoeuvres By introducing an initial covariance in the orbit determination process, it is possible to control the generation of the orbit determination solution as well as improving the estimation of the individual manoeuvres; Figure 10: Thruster Efficiency module estimation but the estimation of the efficiency of the individual manoeuvres is not sufficiently accurate. However, it is possible to implement a statistical process consistent with the orbit determination process implemented in focusgeo (also a statistical process) that provides a stable estimation of the manoeuvre calibration factors. 11

12 The theory resides in the estimation of a calibration factor per thruster rather than per manoeuvre. In each orbit determination execution the parameter that is estimated is an efficiency factor (calibration factor) that applies to all manoeuvres that are executed with the same set of thrusters. The efficiency factor for each manoeuvre is defined by the equation: The hypothesis is that the efficiency factor for all manoeuvres executed with the same thruster is the same. For the purpose of estimating an unique efficiency it is necessary to generate a parameter that is common for all manoeuvres executed with the same thruster. Hence: (being n the number of thrusters). The estimation of manoeuvres is then reduced in the number of parameters from manoeuvres to efficiency factors being. As an example, the figure 10 shows the estimation ( ) of the individual manoeuvres as part of the orbit determination process where the correlation and lack of tracking between manoeuvres produces a high scatter in the estimated values. The right dashed points correspond to the estimation using the process described above. The simulated tracking data corresponds to calibration factors equal to 1.0. It can be noticed that computed efficiency factors are not exactly equal to 1.0 as they should theoretically be, but they are within a 2% error limit which is the range of the uncertainties of the ranging scenario defined for HAG1. D. The Sequential Orbit Determination Approach Taking into account the great number of measurements and maneuvers present in the orbit determination process of an EP satellite such as HAG1, the traditional batch process is not the most optimal method. In order to increase the accuracy of the orbit determination and maneuver assessment, state-of-the-art dynamical models and tracking measurements reconstruction patterns must be followed. The regular update is achieved through the use of sequential parameter estimation methods instead of the classical batch estimation techniques (normally based in the Bayesian least squares algorithm). Among the available sequential methods it is worth mentioning, besides the socalled sequential batch, the Kalman filter and the Square Root Information Filter (SRIF). The latter is implemented in SEGORD module to perform near real-time orbit determination updating the state almost as soon as new Figure 11: SEGORD Convergence plots tracking data arrive from the data retrieval system. The convergence achieved by the orbit determination sequential process performed by SEGORD has been analyzed paying special attention to the transient state duration. As can be seen in Figure 11 depicting the differences between the propagated and the estimated position and velocity in each processing interval, the convergence is rapidly achieved after one single geostationary orbit. It is also observed the stability of the orbital solution once the convergence has been reached. Nevertheless, it is not possible to observe (and, therefore, neither to estimate with a high level of certainty) the solar radiation pressure coefficients (Cp scale factor) for arcs shorter than 48 hours (two revolutions) 12

13 V. Conclusion Flight Dynamics operations for HAG1 on station full-ep station keeping will be covered by means of the upgrade of focusgeo. The complexity of this kind of mission have been analyzed in their different aspects such as orbit determination, manoeuvre optimization and scheduling activities and all of them will ensure the safety of the Flight Dynamics operations, including possible collocation in the cluster. References 1 Schittkowski K. (1985/86): NLPQL: A Fortran subroutine solving constrained nonlinear programming problems, Annals of Operations Research, Vol. 5, Schittkowski K. (2006): NLPQLP: A Fortran implementation of a sequential quadratic programming algorithm with distributed and non-monotone line search - user s guide, version 2.2, Report, Department of Computer Science, University of Bayreuth, Germany 3 Soop E. Mattias (2006): Introduction to geostationary Orbits,