3 deleted 3 characters in body edited Mar 29 '16 at 16:58 holmeski 1,68788 silver badges1717 bronze badges 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 edited Mar 29 '16 at 12:51 holmeski 1,68788 silver badges1717 bronze badges 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 answered Mar 27 '16 at 20:13 holmeski 1,68788 silver badges1717 bronze badges 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.