Development of Magnetometer and Sun Sensors Based Orbit and Attitude Determination for Cubesat

Transcription

1 Development of Magnetometer and Sun Sensors Based Orbit and Attitude Determination for Cubesat MTS-UFS-CONAE Maria Pereyra, Roberto Alonso and Jose Kuba 1st IAA Latin American Symposium on Small Satellites Advances Technologies and Distributed Systems March 7-10, Buenos Aires, Argentina

2 Agenda 1 Introduction Attitude Determination Orbit Determination

3 Introduction Motivation 2 Roles and Responsibilities. As part of the Maestría en Tecnología Satelital (Master on Satellite Technology) the students have to follow almost all of the typical steps to complete the design and analysis of a Cubesat 3U. The first author is the leader of the Attitude and Orbit Determination and Control for this project. The second and third author have had the role of counselors and reviewers of the work done. In this framework emerged the need to have a robust and simple system compatible with the resources aboard the Cubesat. This research is the answer for both function for this Cubesat.

4 Introduction Attitude Determination 3 COTS Accuracy Power(mW) Cost Notes Nano Star 6 arc sec Mass 350 g Tracker rad. (3 axes) Custom. Magnetometer 200 nt Mass 18 g (HMC 5883L) rad. (2 axes) Honeywell Inc. Sun Sensor rad Mass 5 g (Innovative 0.5 (2 axes) Only in Solution in Space) sunlight Sun Sensor rad Mass 110 g (Innovative 0.3 (2 axes) Horizon and Solution in Space) Sun sensors Rate rad/sec Mass < 5 g Gyroscope 0.02 deg/sec (1 axes) Drift: 18 /hr/hr

5 Attitude Determination Selected Method 4 Hardware i. Tri Axial Magnetometer. ii. Sun Sensor or Coarse Sun Sensor. iii. Gyroscope. Computation Methods. a. Quest or TRIAD. b. Linearized Kalman Filter.

6 Attitude Determination Filtering 5 Dynamics Equation q = 1 2 q ω ḃ = ξ b. Measurement 1. Angular velocity, ˆω = ω + b + u g 2. q using Sun and Magnetic Field vectors, (Quest or TRIAD). Needs orbital positioning during daylight. 3. Magnetic Field vector during eclipse (needs orbital positioning). Contributions i. Use of Linearized Kalman Filter instead of Extended or Particle Filter. ii. Method of Magnetic Field Calculation.

7 Orbit Determination. Approaches 6 Three approaches are available for small spacecrafts. The second scheme is not considered because it involves a GPS receiver which is not permitted in small satellites due the high consumption of energy.

8 Orbit Determination Initial State 7 To reduce the error given by the current TLE from NORAD, Angle and range are used to reduce the error given by the current TLE from NORAD.

9 Orbit Determination Filtering 8 For simplification, a two body problem is considered just as an example. a = G m earth r r 3 + a pert = µ r r 3 + a pert. H = F = f x = [ ] h = x x=x ref µ + 3µ x 2 r 3 1 3µ x 1 x 2 3µ x 1 x 3 r 5 r 5 r µ + 3µ x r 3 1 x 2 r µ 3µ x 2 5 r 3 2 3µ x 2 x 3 r 5 r µ x 1 x 3 3µ x 2 x 3 r 5 r µ 3µ x 2 5 r 3 3 r x ECI ρ y ECI ) y xeci( 2 2 ECI x ECF 2 +1 x ECI z ECI ρ 3 z2 ECI ρ 2 +1 y ECI ρ 1 ( y 2 x ECI ECI x ECI 2 +1 y ECI z ECI ρ 3 z2 ECI ρ 2 +1 ρ 2 z ECI. x ECI ρ ) ρ 3 z2 ECI ρ

10 Orbit Determination Observables 9 Magnitude of the Magnetic Field vector.

11 Orbit Determination Observables 10 Sun to Field vector angle.

12 Orbit Determination Approach Real Time Propagation 11 Where, ) f xy2 = 3 J 2 (5 R2 e 1 R 2 f xy4 = 3.75J 4 R 2 e a g = ( 21 R4 R 2 e R 4 ( 35 R3 e 30 Re R 3 R R f z3 = J e 3 R J 2 = x (f xy2 + f xy3 + f xy4 ) y (f xy2 + f xy3 + f xy4 ) z (f z2 + f z4 ) + f z3. ( R f xy3 = 5 J e 3 7 R3 e R R 3 ) 3 Re R ) ) 14 R2 e + 1 f R 2 z2 = 3 J 2 (5 R2 e 3 R ) 2 ( + 3 Re Re f R z4 = 1.25 J R4 R 2 e 70 R2 R 4 e J 3 = J 4 = R e = m. ) + 15 R 2

13 Orbit Determination Approach On Board Real Time Measurements 12 y 1 = B T meas B meas B mod B mod + n y1 y 2 = The new noise variables B T meas S meas BT mod S mod + n B T meas B meas B T mod B y2. mod E (n y1 ) = 0 E ( ) n y1 ny T 1 = σ 2 m E (n y2 ) = 0 E ( ) ( n y2 ny T 2 = σ 2 m + B T meas I Smeas Smeas) T Bmeas σs 2 h k1 = h k (x(t k )) x h k1 = h k (x(t k )) y h k1 = h k (x(t k )) z h k (x b + d x ) h x (x k ) d x h k (x b + d y ) h x (x k ) d y h k (x b + d z ) h x (x k ) d z

14 Orbit Determination Approach On Board Real Time Contributions Linearized Kalman Filtering. 2. Improving TLE. 3. Magnetic Field Calculation via table. 4. Numerical calculation of H. Results Error in attitude 0.5 degrees during dayligth and 1 degrees in eclipse. Error in orbit around 500 meters in magnitude.

15 Thank you for attending this presentation.