A generalized change detection problem

Igor V. Nikiforov (1, 2)

1 ICS - Institute of Control Sciences [Moscou]
2 Université de Lille, Sciences et Technologies

The purpose of this paper is to give a new statistical approach to the change diagnosis (detection/isolation) problem. The change detection problem has received extensive research attention; however, the change isolation problem has, for the most part, been ignored. We consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of Lorden's (1971) results. We introduce a joint criterion of optimality for the detection/isolation problem and then design a change detection/isolation algorithm. We also investigate the statistical properties of this algorithm. We prove a lower bound for the criterion in a class of sequential change detection/isolation algorithms. It is shown that the proposed algorithm is asymptotically optimal in this class. The theoretical results are applied to the case of additive changes in linear stochastic models.

Domains: Engineering Sciences [physics]

Igor V. Nikiforov. A generalized change detection problem. IEEE Transactions on Information Theory, 1995, 41 (1), pp.171-187. ⟨10.1109/18.370109⟩. ⟨hal-02881347⟩