Abstract
In recent years, there have been many studies on the system identification problem, which is that of estimating the parameter vector from noisy observations.
This paper deals with the synthesis of an input signal for identification. The system considered here is a scalar input and scalar output discrete linear system with Gaussian additive noise on the observations. The synthesis of the input signal is to determine the input sequence which minimizes the estimation error, subject to a given amplitude-constraint on the signal. It is assumed that the system is being operated off-line during the identification procedure, so that the input is open to choice.
In this paper, the input sequence is chosen to minimize the determinant of the covariance matrix in the least square estimation error. It follows from the above result that the input sequence is given by the repetition of the uncorrelated sequences which take the maximum values under a given amplitude-constraint.
Next the realization of the sequences which satisfy the condition is treated as a block problem in combinatorial analysis. The block design is settled according to the number of unknown parameters. Then the input sequence may be obtained and is called the Uncorrelated Minimum Length Sequence.
Finally in the case of the low order system, these input sequences are shown in the list. The example demonstrates that estimation error decreases rapidly by the use of the sequences proposed here, which makes them effective in the system identification.
