How many scalar equations for 4-state Kalman filter

Hi,
I read a paper it said that "For a 4-state Kalman filter, all the Kalman filter equations can be expressed as 30 scalar equations."

Because 30 is not an integer multiples of 4, I do not know how it get 30 scalar equations.

Could you help me on that?

Thanks,

On Fri, 01 Mar 2013 16:40:42 -0800, fl wrote:

> Hi,
> I read a paper it said that "For a 4-state Kalman filter, all the Kalman
> filter equations can be expressed as 30 scalar equations."
> 
> Because 30 is not an integer multiples of 4, I do not know how it get 30
> scalar equations.
> 
> Could you help me on that?
> 

The number of scalar equations you'll get from a Kalman filter is going 
to vary very strongly by the number of states, strongly by the number of 
inputs and the number of outputs, and to some extent by how you do your 
arithmetic.

Because you're just quoting a statement made for "a 4-state Kalman 
filter" I can't even assess its validity, much less give you detail.

Why don't you write out the matrix equations for the filter in question, 
then reduce them down to scalar equations?  The answer should be plain 
then, and you'll remember how and why in detail.

This would be a good homework problem, or possibly an in-class lecture 
example.  That's just the sort of thing that you should be doing on your 
own if you want to self-learn the subject.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com