A recursive least-squares (RLS) algorithm for on-line parameter estimation is defined by the following set of equations:

(t) = y(t)x T (t)(t 1)

L(t) = P(t 1)x(t) / +x T (t)P(t 1)x(t)

(t) = (t 1) +L(t)(t)

P(t) = 1/ {P(t 1)L(t)[P(t 1)x(t)]T }

a) What is the variable in the algorithm called? Explain its effect in the algorithm and give typical values.

b) Sampled input/output data collected from a process is shown in the table below. The model to be estimated is of the form: Y(z) / U(z) = z 1b0 / 1+a1z1

i) Express the process model as a difference equation. Hence, define x T (t) and for use in the RLS algorithm.

ii) Use the data to compute the first recursion (at t=2) of the RLS algorithm. Start the algorithm with the initial conditions = 0.99, P(1) = 100I, (1) = 0.

sample no., t 1 2 3

input, u 1 -1 -1

output, y 0.17 -0.1 -0.