[From Rick Marken (930330.1500)]

Bill Powers (930330.1330 MST) --

Thanks for the diagrams. I still have no response from Allan to

my questions about his experiment; but your diagram's will help

me describe what I think he's proposing.

My understanding was that he would do a simulation run with the

standard control system as below:

> ref sig (constant)

>

p ----- comp ---- e = error

> >

inp funct integrator

>

(i) (o)

+| |+ |

> ---------------

>

d

The disturbance would be, say, 1000 samples of filtered random

noise. Allan would then save the 1000 values of d, i and o

resulting from the run.

Now, in order to measure H(D) he injects a vector of i values

(the length of the vector going from 0 to 1000) in a run consisting

of 1000 iterations -- and computes the resulting 1000 outputs from

each run in an open loop preparation as below:

> ref sig (constant)

>

p ----- comp ---- e = error

> >

inp funct integrator

> >

(a) (o)

The candidate i vectors enter through (a) and Allan compares

each resulting set of 1000 o values to the actual disturbance

vector. The length of the first candidate i vector that produces

o values that match d perfectly is H(D) (There is a problem here;

What if you don't get any perfect matches to d, Allan?.Nothing

but an infinite loop gain system could produce outputs that

match d perfectly anyway: how about doing this just until a

candidate i vector produces o values that match the disturbance

to the same degree as did the o values generated in the closed loop

case. So, if the closed loop correlation between disturbance and

output was .99967, pick the first i vector that produces o values

that correlate .99967 with the disturbance).

Assuming you can find H(D) using this decidedly peculiar technique

(why not just measure the variance of d?) the next step is to

find H(D|P). My understanding is that Allan would "play" the

original i vector (from the actual tracking run) into the open

loop system (injected at point a) ALONG WITH the candidate i

vectors that were used in the determination of H(D). Since

the shortest candidate i vectors are added in first, Allan is

assuming that the output resulting from the original i vector

along with the "null" (0 length) candidate i vector will produce an

output that perfectly matches the disturbance (or, at least, matches

the disturbance as well as the output did in the original run).

Is this a correct description of the experiment Allan?

Best

Rick