Hi Doug Gray,

The format of discussions has forced me to reply to you here. I hope you see this.

The answer to your first question about the slip ball is easy. You don't need the DCM algorithm or a Kalman filter to simulate a slip ball. The 3 axis accelerometer IS the slip ball, since it is mounted in the plane. It represents the direction a plumb bob would point. You can figure it out from there.

Regarding your second question about the direction to the horizon, I am going to let ou figure it out. But here is a clue: the bottom row of the direction cosine matrix is the projection of the Z axis of the earth into the plane's coordinate system. In other words, the elements of the bottom row of the DCM are the X, Y, and Z components of a unit vector pointing down, as seen in the plane's coordinates. In the earth frame of reference, the accepted positive direction is down. So, I think all you have to do is take the bottom row of the DCM, treat it as a vector, flip its sign, and you will have a vector pointing up. If you throw away the coordinate along the fuselage, the two remaining coordinates will form a 2D vector that will point toward the horizon, possibly. Or something along those lines.

Best regards,
Bill

Doug,

What you did was fine, replying to the discussion. What happens is as people reply to replies, it keeps indenting to the right, and eventually it will not let you reply. So, I was not able to reply to your reply.

You will see a lot of noise in the raw accelerometer data, but on average, it will give you the same result as a slip ball. If you think about it, a slip ball is a damped "plumb bob". As I recall, the motion of a slip ball is damped by putting it in some liquid. Otherwise it would be bouncing all around the place. All that the slip ball is doing is measuring the direction of the forces on the plane, which is what the accelerometer actually does. In fact, the accelerometer, the slip ball, and a plumb bob, are all equivalent.

So, all you really need to do is to filter it a little bit.

Any thoughts on the direction to the horizon? The bottom row of the DCM is the indicator for that.

Bill