Abstract
This paper is concerned with the influence of forgetting factors on the consistency of prediction error methods of identification. Based on the work of Ljung, a martingale approach is employed and it is shown that the incorporation of forgetting factors into standard on-line estimation algorithms can lead to a loss of system and parameter identifiability, unless the behaviour of the forgetting factors over time satisfies certain conditions. The main theorem covers the cases when the factors are deterministic functions of time or calculated via an adaptive mechanism.
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