User`s guide

7 Recursive Techniques for Model Identification

Algorithms for Recursive Estimation

In this section...

“Types of R ecu rsive Estimation Algorithm s” o n page 7-6

“General Form of Recursive Estimation Algorithm” on page 7-6

“Kalman Filter A lgorithm” on page 7-8

“Forgetting Factor Algorithm” on page 7-10

“Unnormalized and Normalized Gradient Algorithms” on page 7-11

Types of Recursive Estimation Algorithms

You can choose from the following four recursive e stimatio n algorithms:

• “Genera l Form of Recursive E stimation Algorith m ” on p ag e 7-6

• “Kalman Filter Algorithm” on page 7-8

• “Forgetting Factor Algorithm ” on page 7-10

• “Unnormalized and Normalized Gradient Algorithms” on page 7-11

Youspecifythetypeofrecursiveestimation algorithms as arguments

adm

and adg of the recursive estimation com m ands in “Commands for Recursive

Estimation” on page 7-3.

For detailed information about these algorithms, see the corresponding

chapter in System Identiﬁcation: Theory for the User by Lennart Ljung

(Prentice Hall PTR , U pp er Saddle River, NJ, 1999 ).

General Form of Recursive Estimation Algorithm

The general recursive identiﬁcation algorithm is given by the following

equation:

ˆˆ

θθt t Kt yt yt

()

=−

()

() ()

−

()

7-6