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Concurrent Spacecraft Attitude and Orbit Estimation wip Attitude Control Based on Magnetometer Gyro and GPS Measurements prough Extended Kalman Filter.

Byline: Tamer Mekky Ahmed Habib

Abstract: pe main objective of pis research is to provide attitude estimation orbit estimation and attitude control algoripms suitable for application to pe next Egyptian scientific satellite. Concurrent spacecraft orbit and attitude estimates must be suitable for usage by pe attitude control algoripm. pe developed estimation algoripms are able to deal wip sever tumbling conditions characterized by large initial attitude angular velocity and position estimation errors. pe estimation algoripms could provide attitude estimates wipin 0.5o(3-o) and 60 m (3-o) for pe position estimation errors. pe attitude control algoripm developed is able to bring pe spacecraft from its initial tumbling conditions to nadir pointing wipin an error of only 0.5o (3-o).

Keywords: Attitude Orbit Control Estimation EKF GPS Gyro Magnetometer.

1. INTRODUCTION

When pe satellite leaves its launching vehicle it enters an operation mode called pe detumbling mode. pe detumbling mode is characterized by high angular velocities and large satellite attitude angles. pe task of pe attitude and orbit control system (AOCS) of an earp pointing satellite is to slow down pis angular motion and bring pe satellite to nadir pointing. To do so pe AOCS must implement suitable algoripms for attitude and orbit estimation wip attitude control. pese estimation algoripms should provide attitude and orbit estimates to pe attitude control algoripm. Bop estimation and control algoripms must be able to deal wip large initial attitude angles and angular rates [1] provided algoripms for spacecraft attitude estimation based on magnetometer measurements. But pe results obtained were valid only for small attitude angles [2] describes pe process of magnetic attitude estimation of a tumbling spacecraft.

pe process didn't include solutions neiper to pe problems of pe attitude control nor orbit estimation [3] deals wip pe problem of attitude and orbit determination and control for a small geostationary satellite. Orbit estimation process isn't included in pis study. In [4] pe problem of spacecraft attitude and orbit estimation wip attitude control is addressed but pe estimation process was basically dominated by magnetometer measurements. pe process of attitude estimation based on magnetometer measurements usually is characterized by slow convergence [5] described pe process of fast spacecraft orbit and attitude estimation but it didn't include pe process of attitude control [6] discussed pe process of spacecraft attitude estimation and control. But due to pe absence of orbit estimation process pe attitude angles converged slowly (typically after 3 orbits) [7] also didn't include pe process of orbit estimation.

In addition pe algoripms discussed were limited to coarse (not fine) attitude estimates (typically

wipin 6o) [8] discussed pe problem of attitude estimation but pe resulting attitude estimates hadn't been feedback to pe control algoripm. Furpermore pe problem of orbit estimation isn't discussed at all.

pe main objective of pis research is to provide high accuracy attitude estimation orbit estimation and attitude control algoripms suitable for application to pe next Egyptian scientific satellite during pe detumbling and attitude acquisition modes. pe estimation algoripms provided high accuracy estimates (typically wipin 0.5o 3-o for attitude estimates and 60 m 3-o for pe orbital estimates). To do so pe work done in [4 5] is extended to provide high accuracy fast converging attitude and orbit estimates needed by pe attitude control algoripm. pe provided algoripms are capable of dealing wip high angular velocities and large attitude errors usually characterizing pe detumbling and attitude acquisition modes. pe attitude control algoripm presented is capable of bringing pe satellite from pe detumbling mode to pe attitude acquisition mode wipin an error of only 0.5o (3-o).

pe measurement sensors utilized were GPS receiver magnetometer and gyro. GPS and magnetometer measurements are used to provide estimates of pe spacecraft orbital motion while as magnetometer and gyro measurements are used to provide estimates of spacecraft attitude.

2. MODELING SPACECRAFT ATTITUDE AND ORBITAL MOTION

pe first step to model pe spacecraft orbital and attitude motion is to select pe elements of pe state vector. pe state vector is selected to beEquation

EquationAre pe components of pe spacecraft velocity vector defined in pe Earp Centered Inertial Coordinate System.

Equation

pere exists a quternion error vector which expresses pe rotation from pe spacecraft attitude direction in space q Rc B and pe target attitude direction toward which pe satellite is oriented at pe end of pe attitude maneuver qT [9]. pe spacecraft attitude direction in space is parameterized by pe attitude quternion representing pe rotation from pe reference coordinate system to pe body coordinate system q Rc B . pe reference coordinate system has its x axis pointing in pe direction of pe spacecraft velocity in its orbit its z direction is nadir direction and its y direction completes a right hand rule orpogonal coordinate system. pe quaternion error vector is given by [9 10].Equation

EXTENDED KALMAN FILTER

GPS and magnetometer provide strong observability of pe spacecraft orbital states because GPS could measure directly pe spacecraft position vector and pe magnetometer measurements are also functions of spacecraft position. Information of spacecraft attitude is considered to be sufficient when pe attitude sensors could measures two or more vectors in pe spacecraft body frame of reference.

pus magnetometer and gyro measurements are used to provide pese two vectors (which are namely: pe earp's magnetic field vector and pe angular velocity vector) required by pe attitude estimation algoripm to solve pe attitude problem unambiguously. perefore magnetometer and gyro measurements assure full observability of pe spacecraft attitude states. In addition magnetometers and gyros are utilized as sensors because:

1. pey are commonly used devices onboard most spacecraft orbiting pe earp.

2. peir ability to work during spacecraft detumbling attitude acquisition standby and high accuracy modes. And pe problem at hand requires sensors such as magnetometer and gyro pose are able to operate at pese conditions

3. Commonly used attitude sensors could not be used at pe problem at hand. For example pe sun sensor provides intermittent information only due to shadow over pe sensor. pe star sensor also could not be used because pe spacecraft is detumbling and using of such sensor requires high accuracy modes only.

Finally pis set of sensors could sufficiently provide full observability of pe spacecraft orbital and attitude states so as to provide high rate of convergence. pe same structure of pe extended Kalman filter found in [5] is utilized. pe only difference exists in pe measurement vector and its corresponding measure- ment matrix. pe measurement vector is given byEquation

5. OBSERVABILITY AND CONTROLLABILITY ANALYSIS

Check of pe observability and controllability matrices could be done prough pe computation of pe observability and controllability matrices. pe observability matrix OB is given byEquation

6. BLOCK DIAGRAMS AND FLOW CHARTS

To clarify pe relation between pe estimation and control algoripms a block diagram is given below in Figure 1.

To summarize pe solution procedure A flow chart is given in Figure 2.

7. A SIMULATION CASE STUDY

In order to verify pe developed mepodologies a case study spacecraft is utilized. pe spacecraft initial conditions are: a (semi major axis) = 7189200 m e (orbit eccentricity) = 0.01 i (orbit inclination) = 100.585o fi (right ascension of ascending node) = 339.5o 9 (argument of perigee) = 69 o and u (true

Table 1: A Comparison between pe Algoripms Developed in Reference [5] and Current Research Algoripm

Position###H NMR###C NMR###been deposited in the herbarium (voucher No. 86443)

###1###4.47 (dd J=3.5 3.3)###70.9###3.3. Extraction and Isolation

###2###4.67 (d J=3.6)###72.0

###The aerial parts (10 kg) of C. bonduc were soaked

###3###3.15 (s)###83.8###in ethanol for the period of 4 weeks and fruit (2 kg)

###4###4.35(d J=3.4)###70.1

###were soaked in ethanol for the period of 6 weeks.

###5###3.61 (s)###118.8###Vacuum liquid chromatography was performed on

###silica gel (Si 60 70-230 mesh E.Merk). The ehanolic

###6###3.61 (s)###118.8

8. CONCLUSION

pe mepods of spacecraft orbit and attitude estimation during pe detumbling and attitude acquisition modes had worked effectively wip each oper despite of large initial attitude and orbit estimation errors. pe estimation error was about 0.5o (3- o ) for pe attitude angles and 60 m (3- o ) for pe position estimation error. Bop estimates of spacecraft attitude and orbit are fed successfully to pe attitude control algoripm. pe attitude control algoripm was able to bring pe satellite from pe detumbling mode to nadir pointing during less pan half of an orbit wipin accuracy of 0.5o (3- o ). pe rank of pe observability and controllability matrices was pirteen which is indicating a full rank so pe plant is considered to be fully observable and controllable.

9. FUTURE STUDY

Note pat it is assumed pat pe only source of errors is zero mean Gaussian white noise as clarified by equations (2) and (7). pere are also several sources of errors which could affect pe overall suggested algoripm performance and robustness. pese sources could be due to one of pe following reasons:

1- Sensor bias offset.

2- Sensor bias drift rate.

3- Sensor colored noise.

4- Scale factor stability and dependence on pe operating temperature.

5- Sensor and actuator dynamics.

6- Axes non-orpogonality

complete solution of pese problems a multi-disciplinary team work should be formed to study and model pe effects of pese highly complicated factors over pe algoripm performance.

REFERENCES

[1] pomas B. Spacecraft Attitude Determination- a Magnetometer Approach. PhD pesis Aalborg University 1999.

[2] Erick JS. Magnetic Attitude Estimation of a Tumbling Spacecraft. MSc pesis California Polytechnic State University 2005.

[3] popil GA. An Attitude and Orbit Determination and Control System for a Small Geostationary Satellite. MSc pesis Stellenbosch 2006.

[4] Tamer M. New Algoripms of Nonlinear Spacecraft Attitude Control via Attitude Angular velocity and Orbit Estimation Based on pe Earp's Magnetic Field. PhD pesis Cairo University 2009.

[5] Tamer M. Fast Converging wip High Accuracy Estimates of Satellite Attitude and Orbit Based on Magnetometer Augmented wip Gyro Star Sensor and GPS via Extended Kalman Filter. EJRS 2011; 14(2): 61-57.

[6] Mohammad A Sang-Young P. Integrated attitude determination and control system via magnetic measurements and actuation. Act Ast 2011; 69: 185-168.

[7] Tian X Tao M Hao W Ke H Zhong J. Design and on-orbit performance of pe attitude determination and control system for p eZDPS-1A pico-satellite. Act Astr 2012; 77: 196-182.

[8]Xiaojun T Zhenbao L Jiasheng Z. Square-root quaternion cubature Kalman filtering for spacecraft attitude estimation. Act Astr 2012; 76: 84-9. http://dx.doi.org/10.1016/j.actaastro.2012.02.009

[9] Marcel JS. Spacecraft Dynamics and Control a Practical Engineering Approach. 1 1997. ed. Cambridge University Press

[10] Hinagawa H Yamaoka H Hanada T. Orbit determination by genetic algoripm and application to GEO observation. Adv in SpcRsrch 2014; 53: 542-532.

[11] Tamer M. pe Global Positioning System Application to Satellite Position and Attitude Determination. MSc pesis Aerospace Department Cairo University 2003
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Publication:Journal of Basic & Applied Sciences
Date:Dec 31, 2014
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