Star Tracker

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Description

The star tracker is crucial in generating sensed Euler parameters based on the actual simulated attitude. It takes the Spacecraft’s actual structure-to-inertial attitude in the form of Modified Rodriguez Parameters (MRPs) as input. It produces an output comprising Euler Parameters (EPs) and a corresponding timestamp. To incorporate measurement noise into the Euler parameter readings, a Gauss-Markov process model is applied.

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Example Use Cases

• Star Tracker: Outputs Euler parameters based on the state and dynamics of the spacecraft it’s attached to.

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Module Implementation

The Module implementation for the star tracker is a basic conversion of MRP parameters to the Euler parameters and errors added to it using the Gauss-Markov error models.

The conversion of an MRP to Euler parameters is as follows. The MRP is initially converted into a quaternion as follows.

$$Q=\left[\begin{array}{c}\frac{1-\mathrm{MRP}\cdot \mathrm{MRP}}{\overrightarrow{PS}}\\ 2\times \frac{{\mathrm{MRP}}_X}{\overrightarrow{PS}}\\ 2\times \frac{{\mathrm{MRP}}_Y}{\overrightarrow{PS}}\\ 2\times \frac{{\mathrm{MRP}}_Z}{\overrightarrow{PS}}\end{array}\right]$$

Where $PS=1+(\mathrm{MRP}\cdot \mathrm{MRP})$

The Quaternion is then converted to the Euler parameters as follows

$$e=\left[\begin{array}{c}{\tan }^{-1}(-2\frac{Q_2{Q}_3-Q_0{Q}_1}{Q_0^2-Q_1^2-Q_2^2+Q_3^2})\\ {\sin }^{-1}(Q_1{Q}_3+Q_0+Q_2)\\ {\tan }^{-1}(-2\frac{Q_1{Q}_2-Q_0{Q}_3}{Q_0^2+Q_1^2-Q_2^2-Q_3^2})\end{array}\right]$$