On-Orbit Calibration of Photodiodes for Attitude Determination

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1 On-Orbit Calibration of Photodiodes for Attitude Determination John C. Springmann University of Michigan, Ann Arbor, MI Adviser: James W. Cutler August 14, 2013 AIAA/USU Small Satellite Conference

Photodiode background and motivation Sun sensors are the most widely-used attitude determination sensor [1]. Photodiodes can be used for sun sensing.

2 Photodiode background and motivation Sun sensors are the most widely-used attitude determination sensor [1]. Photodiodes can be used for sun sensing. Most basic type of sun sensor Common on small spacecraft due to simplicity and low cost Generate current as a function of incoming light (normal to the photosensitive plane) (sun vector) photodiode [1] Lerner, G. M., Spacecraft Attitude Determination and Control, chap. 6.1: Sun Sensors, Kluwer Academic Publishers, 1978, pp

3 Example configurations (1 of 2) Photodiodes are mounted on each satellite surface. RAX-1 satellite 3

4 Example configurations (2 of 2) RAX-2 satellite Photodiodes are angled from the satellite surfaces. 4

5 Photodiode measurement model Single photodiode in low-earth orbit [2]: Scaling parameters Sensor noise Earth albedo (attitude- and position-dependent) Sun vector component, Irradiance in LEO Re-written with a dimensional scale factor C: [2] Bhanderi, D. D. V., Spacecraft Attitude Determination with Earth Albedo Corrected Sun Sensor Measurements, Ph.D. thesis, Aalborg University, Aalborg, Denmark, August

6 The measurements are subject to uncertainty in the photodiode model parameters Dimensional scale factor C Maps the incoming irradiance to sensor output Dependent on the specific photodiode and surrounding circuitry Measure pre-flight and assume constant? Photodiode orientation n High-tolerance integration? Measure after integration? Estimate both via on-orbit calibration. 6

7 On-Orbit calibration overview Goal: Estimate the calibration parameters (scale factor and orientation) using only on-orbit data. No pre-flight calibration required Accounts for any parameter changes due to launch or orbit environment Approach: Simultaneous estimation of spacecraft attitude and the calibration parameters. Nonlinear recursive estimation, extended Kalman filter is used Measurements include rate gyroscope, magnetometer, any number of photodiodes in any configuration An attitude- and position-dependent model is used to compensate for Earth albedo [2] [2] Bhanderi, D. D. V., Spacecraft Attitude Determination with Earth Albedo Corrected Sun Sensor Measurements, Ph.D. thesis, Aalborg University, Aalborg, Denmark, August

8 Example application: RAX-2 flight data Sensors: Three-axis gyroscope Three-axis magnetometer Photodiodes mounted in 14 different orientations Measurement frequency: 1 Hz 8

9 Resulting parameter estimates Scale factor C Improvements in scale factor range from % Azimuth of n Improvements in orientation range from 0-9 Elevation of n 9

10 Impact on Sun Vector Angular Accuracy Histogram of the angular difference between sun vector measurements pre- and post-calibration: Mean improvement:

11 Resulting Attitude Determination Accuracy 1-σ Uncertainty Bounds 11

12 The on-orbit calibration enables accurate, low-cost, attitude determination. 1-σ Uncertainty Bounds Sensor Price Photodiodes (SFH2430) (x17) $1.82 Magnetometer (PNI Micromag3) $49.95 MEMs Gyroscope (ADIS16405) $810* Total $891 *Cheaper equivalent-performance gyros are available 12

13 Summary Developed a method to calibrate photodiodes using only on-orbit data 9ᵒ improvement in sun vector measurement demonstrated Better than 0.5ᵒ 1-σ attitude accuracy demonstrated with a magnetometer/photodiode/gyro system This method replaces pre-flight calibration, saving time and cost In example application, the calibration was applied off-line, but it can be extended for real-time use EKF is well-suited for real-time implementation. Albedo model should be simplified or tabulated for real-time use. Can also upload parameters for real-time correction following offline calibration In addition to attitude determination, this method can also be used to track the orientation of actuated/deployed surfaces 13

14 Questions? 14

Attitude-Independent Magnetometer Calibration with Time-Varying Bias

Attitude-Independent Magnetometer Calibration with Time-Varying Bias John C. Springmann University of Michigan, Ann Arbor, MI Adviser: James W. Cutler August 10, 2011 AIAA/USU Small Satellite Conference