Identification of processes in closed loop-identifiability and accuracy aspects
Automatica (Journal of IFAC)
Frequency-domain approach to the regulation of linear stochastic systems
Automatica (Journal of IFAC)
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We compare two methods of estimating transfer functions from observed records of input and output when the output contains an additive noise component of unknown statistical structure. The two methods correspond to (a) a ''weighted least-squares'' estimate (A@^"1) and (b) a ''simple least-squares'' estimate (A@^"2). The estimate A@^"1 is the more attractive theoretically, since it is equivalent to a maximum likelihood approach when the system is open-loop and the noise process is Gaussian, but it is difficult to compute numerically. On the other hand, A@^"2 is the much simpler estimate to compute and is the one most commonly used in practice, particularly as a first approximation in an iterative approach. It should be noted, however, that both A@^"1 and A@^"2 will, in general, be biased in the case of closed-loop systems. In this paper we determine conditions under which A@^"2 will be identical with, or close to, A@^"1 in the case of a closed-loop system in which the feedback is linear with an additive noise component.