Recent content by Ultimâ

Thanks for that. As ben mentions, I had a case of a rate of changes (sounds like a rare disease), where the chain rule needed to be applied, and I thought the outcome seemed a bit weird. Thanks tiny-tim for verifying my suspicions that the partial can be treated as an ordinary differential...

I think the heading says it all. What happens if we take the partial derivative of a rate for example? eg \frac{\delta}{\delta t}(\frac{dx}{dt}) If it was normal differentiation with respect to t we'd get acceleration, or \ddot{x}. I read somewhere that the partial can be treated as...

It would be nice to think it was that simple tiny-tim, but I fear \dot{\theta} is related to changes in \theta even for small variations. HallsofIvy, I'm not familiar with using the total variation approach, but it is part of a Jacobian so I would assume it was a derivative. I've just posted...

Well since I was asked for it, here's the full problem I have (see pdf),...Anything wrong with my reasoning here for the elements I have calculated for the Jacobian?

Thanks for the input, will give it a go

This is a bit weird, both are functions of theta (and time) ... so I assume the operator is on both ... is it a case of applying the product rule? \frac{\delta}{\delta \theta}(\dot{\theta} cos\theta)

z_1=x^2+x^3 \medskip z_2=y+sin(x) Jacobian is: J=\left[ \begin{array}{cc} \frac{dz_1}{dx} & \frac{dz_1}{dy} \\ \frac{dz_2}{dx} & \frac{dz_2}{dy} \end{array} \right] ...which is J=\left[ \begin{array}{cc} 2x & 3x^2 \\ cos(x) & 1 \end{array} \right] and...

tiny-tim - Sorry if I didn't make things very clear, but I was just hoping people could check what I had done seemed reasonable - that is simplifying the derivatives in 1.->4. These happen to be four of the elements of J (yes it is a Jacobian) that I'm inputting as a matrix for an Extended...

That is \frac{\Delta p }{\Delta t}}/\Delta p =\frac{\Delta \dot{\theta} }{\Delta t}}/\Delta \dot{\theta}

Sorry! I just jumped into a shorthand replace with the following: \frac{\Delta p }{\Delta t}}/\Delta p =\frac{\Delta \dot{\theta} }{\Delta t}}/\Delta \ddot{\theta} The context is trying to create a Jacobian matrix to estimate the covariance for angular rates. I don't really want to...

Just to clarify, 3. slightly, the dt is actually the sample period, so \dot{\theta}dt\approx \Delta\theta, but I'm unsure how this affects the derivative... Also, in 2. maybe I should use the product rule, but I think the term you are using for differentiating needs to be different...

Hello, I'm toying around with a Jacobian that has raised some interesting problems. It's a case of differentiating rates of some variable x, with respect to itself. First one I suspect the answer is zero, though perhaps my reasoning is a bit flawed. 1. \frac{d}{d\theta}(\dot{\theta})...

I know this is a tricky area, but I had kind of hoped for at least some light shed on my initial question. Cyrus, there are several good tutorials about the basic Kalman filter on the internet that provide the ground-work. It's easy to implement on simple, linear systems. The EKF is the...

Possibly try http://www.xs4all.nl/~rauw/fdcreport/FDC14_preview_007.pdf This has a fairly good coverage of aircraft modelling, I'm not sure if it's quite what you're looking for as I've not dealt with forces yet, but there is a section that discusses them...

Hi Rainman, Thanks for replying. I wasn't expecting such a quick response. You've certainly brought some things to my attention I was unaware of and given me some interesting things to think about. In actual fact, it's the states of an aircraft I'm looking at (about 12, including...