3 deleted 3 characters in body
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gyroscopes do not measure [dRoll ,...] they measure angularbody rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angularbody rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

-- relation --

this is the relation between the measured body rates from the imu and the euler rates.

\begin{equation} \label{eq:euler_rates} \begin{bmatrix} \dot \phi \\ \dot \theta \\ \dot \psi \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi \tan\theta & \cos\phi \tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \end{equation}

where $\left[ p, q, r \right] ^T$ are the body rates measured from the imu.

gyroscopes do not measure [dRoll ,...] they measure angular rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angular rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

-- relation --

this is the relation between the measured body rates from the imu and the euler rates.

\begin{equation} \label{eq:euler_rates} \begin{bmatrix} \dot \phi \\ \dot \theta \\ \dot \psi \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi \tan\theta & \cos\phi \tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \end{equation}

where $\left[ p, q, r \right] ^T$ are the body rates measured from the imu.

gyroscopes do not measure [dRoll ,...] they measure body rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates body rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

-- relation --

this is the relation between the measured body rates from the imu and the euler rates.

\begin{equation} \label{eq:euler_rates} \begin{bmatrix} \dot \phi \\ \dot \theta \\ \dot \psi \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi \tan\theta & \cos\phi \tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \end{equation}

where $\left[ p, q, r \right] ^T$ are the body rates measured from the imu.

2 added 448 characters in body
source | link

gyroscopes do not measure [dRoll ,...] they measure angular rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angular rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

-- relation --

this is the relation between the measured body rates from the imu and the euler rates.

\begin{equation} \label{eq:euler_rates} \begin{bmatrix} \dot \phi \\ \dot \theta \\ \dot \psi \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi \tan\theta & \cos\phi \tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \end{equation}

where $\left[ p, q, r \right] ^T$ are the body rates measured from the imu.

gyroscopes do not measure [dRoll ,...] they measure angular rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angular rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

gyroscopes do not measure [dRoll ,...] they measure angular rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angular rates to euler rates. The euler rates are then integrated to get the short term change in orientation.

-- relation --

this is the relation between the measured body rates from the imu and the euler rates.

\begin{equation} \label{eq:euler_rates} \begin{bmatrix} \dot \phi \\ \dot \theta \\ \dot \psi \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi \tan\theta & \cos\phi \tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \end{equation}

where $\left[ p, q, r \right] ^T$ are the body rates measured from the imu.

1
source | link

gyroscopes do not measure [dRoll ,...] they measure angular rates. These are not the same things. There is a transformation matrix ( that I do not have on hand) that relates angular rates to euler rates. The euler rates are then integrated to get the short term change in orientation.