There must be an easier way...

[luckykaa]

I was reading up on a body tracking algorithm. All was going well until I came across this lovely equation

k = (y-mk)^TK^-1(y-mk)  (

(y is a 5 value vector, m is a mean value for expected y and K is a 5x5 covariance matrix).

Most of this is fine.  The problem I have is K^-1.  Are we really trying to find the inverse of a 5x5 matrix?  I have no idea how to do that.  I'm only a simple computer scientist and I'm sure we can find an easier way to work out probabilities. 

I really need to read up on this stuff. 

Comments

[xenaclone.livejournal.com]

Xenaclone's hubby writes:

The inverted matrix multiplies a vector, so you don't have to do the full matrix inverse. I can't do your equation notation, so I'll improvise. If vector z denotes inverse K times (y-mk), then Kz = y-mk. This is a 5x5 set of simultaneous equations so you solve those for z with a standard library algorithm such as Gaussian elimination with interchanges. Then you multiply y-mk (transposed) by z (which is a scalar product).

Hope that helps. D.

[luckykaa.livejournal.com]

Great! Thanks. Thought there must be some sort of shortcut.

My maths is so rusty.

[squirrel-dreams.livejournal.com]

Anyone fancy a pint?.

[luckykaa.livejournal.com]

That would be a unique solution to the problem.