Attitude Determination using Infrared Earth Horizon Sensors

Transcription

1 Attitude Determination using Infrared Earth Horizon Sensors Tam N. T. Nguyen Department of Aeronautics and Astronautics Massachusetts Institute of Technology 28 th Annual AIAA/USU Conference on Small Satellites August 6, 2014

2 Problem Overview Many CubeSat science missions require attitude knowledge during eclipse Common attitude sensors have various limitations in meeting this requirement Sun sensors: inoperable during eclipse Magnetometers: inaccurate, not sufficient for full attitude determination Star trackers: more complex, expensive CubeSats often lose attitude knowledge during eclipse?? 8/5/2014 T. Nguyen 2

3 Motivation for IR Earth Horizon Sensors (EHS) Earth is a bright target in the long-wave infrared range EHS provide direct attitude knowledge relative to Earth Thermopiles are inexpensive and low in size, weight, power space horizon Earth Thermopile detector Image: Excelitas The horizon is detected when sensor s field of view is partially obstructed by Earth 8/5/2014 T. Nguyen (tamz@mit.edu) 3

4 Sensor configuration coarse sensor fine sensors 2-mount configuration in the satellite s body frame MIT s Micro-sized Microwave Atmospheric Satellite (MicroMAS) (MIT/LL - approved for public release) 8/5/2014 T. Nguyen (tamz@mit.edu) 4

5 Objectives Given 2 valid horizon sensor readings from distinct mount directions 1. Estimate a nadir vector in the satellite s frame with sub-degree accuracy 2. Validate estimation accuracy and sensitivity with mounting offset with simulation 8/5/2014 T. Nguyen (tamz@mit.edu) 5

6 Nadir vector estimation approach 1. Define an Earth-sensor model and solve for nadir angles Simple model Earth disk is circular Earth IR emission is constant within sensor s FOV Sensor responsivity is uniform within FOV Earth disk radius is constant 2. Solve for possible nadir vector solutions 3. Resolve ambiguity Advanced model Sensor responsivity is Gaussian within FOV Earth disk radius is updated in real time from ephemeris knowledge 8/5/2014 T. Nguyen (tamz@mit.edu) 6

7 Nadir angle - Simple model Sensor FOV ε Unit sphere around satellite S α ρ Earth Disk Spacecraft-centered celestial sphere with projections of sensor s FOV and Earth disk ε = sensor s FOV radius (constant) ρ = Earth disk radius (constant) α = angle between nadir and sensor boresight S = overlap area between sensor FOV and Earth disk Sensor reading S α = 2[π cos(ρ) acos cos(ε) acos (ρ+ ε < α < ρ+ ε) cos ρ cos ε cos α sin ε sin α acos cos ε cos ρ cos α sin ρ sin α cos α cos ε cos ρ sin ε sin ρ J. Wertz. Spacecraft Attitude Determination and Control (implemented with look-up tables in flight software) 8/5/2014 T. Nguyen (tamz@mit.edu) 7 ]

8 Nadir angle - Advanced model Sensor sensitivity Approximate sensor s Gaussian sensitivity with piece-wise constant function Sensor field can be divided into regions of constant sensitivity with corresponding weight factor Sensor reading S 1 G 1 + S 2 G 2 + S 3 G 3 S 1, S 2, S 3 : overlap area of Earth disk with each sensor region G 1, G 2, G 3 : Gaussian weighting factors 8/5/2014 T. Nguyen (tamz@mit.edu) 8

9 Nadir angle - Advanced model Earth disk size update Earth disk size can be updated in real-time from ephemeris knowledge Satellite position x ρ Earth disk radius: R E ( x) R( x) where: ρ sin 1 R E ( x) R ( x) R E ( x) R E ( x) = Earth radius from ellipsoid model R ( x) = Orbit radius (figure not drawn to scale) 8/5/2014 T. Nguyen (tamz@mit.edu) 9

10 Solving for nadir vector Geometric representation of the solutions Sensor boresights: S 1, S 2 Nadir angles: φ 1, φ 2 P S 1 = cos(φ 1 ) P S 2 = cos(φ 2 ) P =1 P x S 1x + P y S 1y + P z S 1z = cos(φ 1 ) P x S 2x + P y S 2y + P z S 2z = cos(φ 2 ) P x 2 + P y 2 +P z 2 = 1 Equations can be solved analytically (no iterations required) Possible nadir vector: P, P -> 2 possible solutions (ambiguity) 8/5/2014 T. Nguyen (tamz@mit.edu) 10

11 Resolve ambiguity P z x Initial selection can be done by comparing to estimate from another attitude sensor Sun sensor in daytime Magnetometer in eclipse P Nadir estimate from other y sensors (can be coarse) Earth A running estimate can be computed from previous sensor readings after initial selection 8/5/2014 T. Nguyen (tamz@mit.edu) 11

12 STK Simulation Scenario y y Spacecraft sensor model sensor FOV: 10 o mount directions: - x, + y horizon sensor dip angle: 20 o ISS orbit x Nadir z Attitude: Yaw with 4 o nutation (Satellite s z-axis oscillates around nadir vector with maximum offset of 4 o ) 8/5/2014 T. Nguyen (tamz@mit.edu) 12

13 Simulation results Simple model Advanced model 1-σ 1-σ Angular error: (1.23 +/- 0.43) o Angular error: (0.18 +/- 0.08) o 8/5/2014 T. Nguyen (tamz@mit.edu) 13

14 Mounting sensitivity analysis 1 o error 0.5 o error no mounting error y = 2.76x Error in x-y components of nadir vector Nadir estimation errors Nadir direction centered at (0,0,0) linear correlation 1 o boresight offset on each mount leads to an additional 2.8 o in attitude error 8/5/2014 T. Nguyen (tamz@mit.edu) 14

15 Summary and future work A nadir vector was computed from EHS readings with high accuracy Model Simple model Advanced model Advanced model with unknown mounting offset Nadir estimation error (1.23 +/- 0.43) o (0.18 +/- 0.08) o Increases linearly with 2.8 o nadir error for every degree of mounting offset Future/In-progress work: Model sensor noise and response dynamics Variations in IR spectrum and interference Verify attitude accuracy from on-orbit data 8/5/2014 T. Nguyen (tamz@mit.edu) 15

16 Acknowledgements Prof. Kerri Cahoy Micro-sized Microwave Atmospheric Satellite (MicroMAS) team at MIT and Lincoln Laboratory National Science Foundation Frank J. Redd Student Competition 8/5/2014 T. Nguyen 16