Boresight Sensor

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Description

This module aims to calculate the miss-angle between a boresight on a Spacecraft and a target object. This module is intended to provide a mechanism to extend the functionality of a generic instrument or simulation module that does not perform an internal field of view check.

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Example Use Cases

• Evaluate Pointing Constraint Violation: Sensors like Star Trackers may be damaged if pointed at the sun. This module can be used to add a pointing constraint check to a component that extends its functionality or adds an FOV safety margin that FSW could monitor.

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Module Implementation

The first step of this module is to calculate a pointing frame following an identical procedure to that described in the RelativePoint module, where a relative pointing vector is calculated between the parent spacecraft ${}^{\mathcal{N}}{\mathbf{r}}_p$ and target ${}^{\mathcal{N}}{\mathbf{r}}_t$:

$${}^{\mathcal{N}}\hat{\mathbf{r}}=\frac{{}^{\mathcal{N}}{\mathbf{r}}_p{-}^{\mathcal{N}}{\mathbf{r}}_t}{|{|}^{\mathcal{N}}{\mathbf{r}}_p{-}^{\mathcal{N}}{\mathbf{r}}_t||}$$

along with a relative velocity vector:

$${}^{\mathcal{N}}\hat{\mathbf{v}}=\frac{{}^{\mathcal{N}}{\mathbf{v}}_p{-}^{\mathcal{N}}{\mathbf{v}}_t}{|{|}^{\mathcal{N}}{\mathbf{v}}_p{-}^{\mathcal{N}}{\mathbf{v}}_t||}$$

A coordinate system about this principle axis is then built such that:

$$\begin{gathered} \hat{\mathbf{x}}=\hat{\mathbf{r}} \\ \hat{\mathbf{y}}=\hat{\mathbf{z}}\times \hat{\mathbf{r}} \\ \hat{\mathbf{z}}=\hat{\mathbf{r}}\times (\hat{\mathbf{r}}\times \hat{\mathbf{v}}) \end{gathered}$$

This gives us the rotation between our target frame $R$ and the inertial frame $N$ as $[RN]=[{\hat{\mathbf{x}}}^T,{\hat{\mathbf{y}}}^T,{\hat{\mathbf{z}}}^T]$. Next, we compute the rotation between the pointing frame and the body frame $\mathcal{B}$ as:

$$[BR]=[BN][RN{]}^T$$

The boresight pointing vector ${}^{\mathcal{B}}{\hat{\mathbf{p}}}_{\mathbf{b}}$ in the body frame, can then be expressed and projected into $R$,

$${}^{\mathcal{R}}{\hat{\mathbf{p}}}_b=[BR{]}^{\mathcal{B}}{\hat{\mathbf{p}}}_b$$

The miss-angle $M$ is then evaluated as the angle between the ${}^{\mathcal{R}}\hat{\mathbf{r}}{=}^{\mathcal{N}}\hat{\mathbf{r}}$:

$$M=\arccos {(}^{\mathcal{R}}{\hat{\mathbf{p}}}_b{\cdot }^{\mathcal{N}}\hat{\mathbf{r}})$$

The azimuth angle is then calculated by taking the arctan of the last components of the boresight vector in $R$.