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Correcred typos and added pseudo measurement explanation.
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iandareid committed Jun 20, 2024
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15 changes: 10 additions & 5 deletions docs/developer-guide/rosplane/estimator/estimator-example.md
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Expand Up @@ -13,13 +13,16 @@ The other states are then estimated as a all at once.
This is called the position estimation step, though more than just position is estimated during this step.
The estimator runs on a set timer with a configurable frequency (see Parameters section for details).

<!-- TODO: add full vector of states and explain them (especially the psuedo measurements) -->
The estimator makes large use of something called a pseudo-measurements.
These measures assume that the side slip angle is zero and the corresponding wind triangle solution.
This allows us to take these measures and then find the wind in the north and east directions along with the yaw of the aircraft.
They are more fully explored in section 8.11.4 of the UAV book.

## Nomenclature

| Symbol | Meaning | Range |
|:------:|:-------:| :---: |
|$\large{\chi}$| Course/Heading | $[-\pi,\pi)$ |
|$\large{\chi}$| Course | $[-\pi,\pi)$ |
|$\large{\phi}$| Roll | $[-\pi,\pi)$ |
|$\large{\theta}$| Theta | $[-\pi,\pi)$ |
|$\large{\psi}$| Yaw | $[-\pi,\pi)$ |
Expand All @@ -28,6 +31,8 @@ The estimator runs on a set timer with a configurable frequency (see Parameters
|$\large{q}$| Pitch Rate | - |
|$\large{r}$| Yaw Rate | - |
|$\large{V_a}$| Airspeed | $\geq 0$ |
|$\large{w_n}$| Wind North | - |
|$\large{w_e}$| Wind East | - |

## Sensor Model Inversion

Expand Down Expand Up @@ -287,9 +292,9 @@ The measurement noise matrix, $R_{position}$, is defined as:
0 & \sigma_{gps, e}^2 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & \sigma_{gps, V_g}^2 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & \sigma_{gps, \chi}^2 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & \sigma_{psuedo, w_n}^2 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & \sigma_{psuedo, w_n}^2 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & \sigma_{psuedo, \psi}^2 \\
0 & 0 & 0 & 0 & \sigma_{pseudo, w_n}^2 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & \sigma_{pseudo, w_n}^2 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & \sigma_{pseudo, \psi}^2 \\
\end{bmatrix}
\end{equation}

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