## Thursday, April 14, 2011

### Parallel Filters

First: Matrix multiplication is O(n^3), or more particularly O(mnp) when multiplying an mxn by an nxp matrix. This means that doubling the length of the state vector increases the amount of work for the filter by about 8 (a little less, as sometimes we have 1xm by mx1 and such). In any case, it is large. Maybe we don't have to.

The only reason I wanted to combine the filters in the first place is so that the rotation part of the filter can take advantage of the acceleration part. Since the acceleration part is not symmetrical (gravity is there also) I figured that the filter would use the acceleration to adjust the orientation, but as it turns out, it doesn't. The acceleration measurement has no effect whatsoever on the orientation. So, no point in keeping them in the same filter.

Actually the two filters do have an effect on each other, and it's not a good one. I put together the two filters into one 16-element superfilter at about 10x the cost of the old orientation-only filter. I didn't feed it any acceleration updates, and yet the acceleration did update. Based on no information whatsoever, the thing thought it was 100m away from the starting point after 1 minute. I have no idea how the gyro updated the acceleration

So, break the filter in half.