I am having some trouble deriving the a posteriori estimate covariance matrix for the linear Kalman filter. Below I have shown my workings for two methods. Method one is fine and gives the expected result. Method two is the way I tried to derive it initially before further expanding out terms to...
This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation:
\left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T}
Where:
* ##R## is a DCM (Direction Cosine Matrix)
* ##\vec{v}## is the angular...
I am performing a Monte Carlo simulation of a weapon system to determine the effect of variations in weapon characterisitics on the accuracy of the weapon. For example, I might vary the muzzle velocity of the weapon and measure the angles between the aim point and the impact point (i.e. miss...
Hi,
I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following:
V = \frac{GM}{r}\left [ 1 +...
Ok, so how do I know whether a quaternion I define is a right of left quaternion?
For example, as I said in an earlier post:
Is this an example of a right or left quaternion?
Thanks,
Ryan
As further clarification of my earlier post, please consider the following diagram:
http://img171.imageshack.us/img171/2594/vec1a.png
This shows the following vector:
v=\begin{bmatrix}0\\1\\0\\0\end{bmatrix}
If I want to perform a right handed rotation of 90° around the z axis of the...
In this book:
http://books.google.co.uk/books?id=GtzzpUN8VEoC&pg=PP1&lpg=PP1&dq= spacecraft +attitude+determination+and+control&source=bl&ots=6Zv_jlYSPf&sig=cDohT-8MSwbNi2IKImeuXX17boI&hl=en&sa=X&ei=BxsIUNCGOYa90QWbxqz_BA&ved=0CFYQ6AEwAw
Unfortunately the page in question is not part of the...
If I have a vector like so:
v=\begin{bmatrix}
0\\
1\\
0\\
0
\end{bmatrix}
and the following quaternion which should perform a 90° rotation about the z axis:
v=\begin{bmatrix}
0.7071\\
0\\
0\\
0.7071
\end{bmatrix}
I would expect to obtain the following vector...
Hi,
I have been looking at quaternions to perform rotations, however I have come across two slightly different equations to do this:
v' = q^{-1}vq
v' = qvq^{-1}
What is the difference between these two?
Thanks,
Ryan
After taking a closer look at the post I linked to, I have another question. I thought that the time derivative of a rotation matrix was given by:
\frac{\mathrm{d}R}{\mathrm{d}t} = \tilde{\omega}R
However, in his post, D H states:
\mathbf T'_{R\to I} = \mathbf T_{R\to I}\mathbf X(\mathbf...
Ok, after posting this I found the following post in the 'Similar Threads' section at the bottom of the page:
https://www.physicsforums.com/showpost.php?p=1650790&postcount=3
It gives a very unambiguous derivation of the equation that I posted earlier.
Hi,
I have a couple of questions about velocities in inertial and rotating frames of reference, related by the following equation:
\mathbf{v_i} \ \stackrel{\mathrm{def}}{=}\ \frac{d\mathbf{r}}{dt} =
\left( \frac{d\mathbf{r}}{dt} \right)_{\mathrm{r}} +
\boldsymbol\Omega \times...