Least squares for dynamic models

2 LEAST SQUARES AND ORTHOGONAL DECOMPOSITION 3.2.1 Least squares for dynamic models 

The lecist squares method for parameter estimation is a central technique in the area of process identification. The method itself is particularly simple to apply if the selected model structure has the property of being linear-in-the-parameters. In this case, the least squau es parameter estimates can be found suicilytically. For example, consider a model of the following form 

For a dynamic system, we assume that the discrete-time process input sequence u(A ) and the discrete-time measured process output sequence y(ft) ) where /s = 1,2. M enumerates the sampling intervals, are related by the linear regression model given by 

If the matrix is invertible, the minimum of the least squares error is unique, with the estimated parameters given by 

The matrix is called the correlation matrix and the invertibility condition on this matrix is sometimes called the sufl cient excitation condition for parameter estimation. 

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