Rate-gyro and compass: Kalman filter

Tim Wescott ha scritto:


> Convenient, simple -- and damned subtle and hard to wrap your brain 
> around:
> 
> Use the fact that integers wrap to your advantage.  It's the only time 
> you'll be able to, so revel in it.
> 
> If you're programming in C, on a machine that uses 2's compliment 
> arithmetic, then INT_MAX will equal 2^(N-1) - 1, where N is the word 
> width in bits.  INT_MIN will equal exactly -2^(N-1).  So map your angles 
> into integers such that INT_MIN represents -180 degrees.  Then -- as if 
> by magic -- you'll find that +179 degrees + 1 degree = -180 degrees.


Tim,

I understand how much I have to learn!


> Now _carefully_ arrange your filter:
> 
> y_t = y_t + (x_t - y_t) / factor.
> 
> This is a first-order low-pass with a pole at 1 - 1/factor.  What's cool 
> about it is that (on all of the machines that I've encountered) the x_t - 
> y_t term wraps, so it always finds the shortest path between the state 
> and the target.


Very, very interesting.


> Try it,  You'll like it.  Hopefully this will get you started -- I'm sure 
> this can be extended to 2nd-order filters, but you'll have to use a more 
> state-space approach rather than looking up bilinear filters in a cook 
> book.


By the way, may you suggest me a good book about digital filters that 
presents both theory and C code?

Thanks
Marco