Online parameter estimation using matrix pseudoinverse

Online parameter estimation using matrix pseudoinverse

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
Proceedings of the Institution of Electrical Engineers — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

A method based on the matrix pseudoinverse is presented for the online identification of discrete-time systems of known order. Recursive algorithms are described which provide minimum-norm estimates of the parameter vector when insufficient data are available, and least-squares estimates with adequate data. These estimates can be updated easily with each pair of additional input-output data, as matrix inversion is not required. When the order of the system is not known, it may be determined offline using one of the two methods described. A recursive algorithm for calculating the residual error is also derived. A number of examples are given to illustrate the usefulness of the methods.


    1. 1)
      • Lee, R.C.K.: `Optimal estimation, identification and control', 28, Research monograph, 1964.
    2. 2)
      • A.I. Liff . System identification in the presence of noise by digital techniques. IEEE Internat. Conv. Rec. , 6 , 152 - 166
    3. 3)
      • R. JOHANSSON . (1993) , System modelling and identification.
    4. 4)
      • F.W. Smith . System Laplace-transform estimation from sampled data. IEEE Trans. , 37 - 44
    5. 5)
      • A.V. Balakrishnan , V. Peterka . Identification in automatic control systems. Automatica , 817 - 829
    6. 6)
      • R. Penrose . On best approximate solution of linear matrix equations. Proc. Cambridge Phil. Soc. , 17 - 19
    7. 7)
      • T.N.E. Greville . Some applications of the pseudoinverse of a matrix. SIAM Rev. , 15 - 22
    8. 8)
      • A. Albert , R.W. Sittler . A method for computing least square estimates that keep up with the data. SIAM J. Control , 384 - 417
    9. 9)
      • C.H. Wells . Minimum norm control of discrete systems. IEEE Internat. Conv. Rec. , 3 , 55 - 64

Related content

This is a required field
Please enter a valid email address