Specification for StarSensor class

1. Overview

1. functions

  • StarSensor class simulates a star sensor.
  • The StarSensor class calculates and returns the observed quaternions and error flags.

2. files

  • star_sensor.cpp, star_sensor.hpp : Definitions and declarations of the class
  • star_sensor.ini : Initialization file
  • plot_star_sensor.py: An example of a Python script to plot star sensor output

3. how to use

  • Set the parameters in star_sensor.ini.
  • Create an instance by using the initialization function InitStarSensor
  • Use Get* function to get quaternion information.

2. Explanation of Algorithm

1. Update

  • TBW

2. Judgement

1. EarthJudgement

  • Calculate the angle $\theta_{ce}$ between the earth's center direction $\boldsymbol{r_{sc}}$ and the earth's edge direction $\boldsymbol{r_{se}}$. $R_e$ is the earth's radius.
  • Calculate the angle $\theta_{es}$ between the sight direction $\boldsymbol{r_{sight}}$ and the earth's edge direction $\boldsymbol{r_{se}}$.
  • Judge the STT error flag by comparing $\theta_{es}$ with the earth forbidden angle $\theta_{efa}$. If $\theta_{es} > \theta_{efa}$, the earth is completely outside the earth forbidden angle.

\[ \begin{align} \theta_{ce} = \arctan{\left(\frac{|\boldsymbol{r_{se}}|}{R_e}\right)}\\ \theta_{cs} = \arccos{(\boldsymbol{r_{se}}*\boldsymbol{r_{sight}})}\\ \theta_{es} = \theta_{ce} - \theta_{cs} \tag{1} \end{align} \]

3. Results of verifications

1. verification of Earth judgement

1. overview

  • Check that Earth judgement is performed correctly

2. conditions for the verification

  • PropStepSec: 0.001
  • StepTimeSec: 0.1
  • EndTimeSec: 200
  • Initial position [m] : [4.2164140100E+07,0,0]
  • Initial velocity [m/s] : [0,3.074661E+03,0]
  • ControlledAttitude
    • main mode = EARTH_CENTER_POINTING: the pointing direction is determined by each case
    • sub mode = SUN_POINTING: [0,0,1]
  • STT quaternion from body frame to component frame: [0,0,0,1]
  • Earth forbidden half-angle: 10deg
  • The angle between the earth's center and edge direction: 8.6deg

3. results

  • The angle between pointing direction and earth center = 15deg
    • STT flag is always 1, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 15 - 8.6 = 6.4deg < 10deg.

  • The angle between pointing direction and earth center = 20deg
    • STT flag is always 0, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 20 - 8.6 = 11.4deg > 10deg.

  • The angle between pointing direction and earth center = 30deg
    • STT flag is always 0, since the angle $\theta_{es}$ between the sight direction and the earth's edge direction is 30 - 8.6 = 21.4deg > 10deg.

  • The output result obtained by the default initial settings.
    • The figure is generated by the Python script.