A suboptimal quadratic change detection scheme

We address the problem of detecting changes in multivariate Gaussian random signals with an unknown mean after the change. The window-limited generalized-likelihood ratio (GLR) scheme is a well-known approach to solve this problem. However, this algorithm involves at least (log γ)/ρ likelihood-ratio computations at each stage, where γ(γ→∞) is the mean time before a false alarm and ρ is the Kullback-Leibler information. We establish a new suboptimal recursive approach which is based on a collection of L parallel recursive χ² tests instead of the window-limited GLR scheme. This new approach involves only a fixed number L of likelihood-ratio computations at each stage for any combinations of γ and ρ. By choosing an acceptable value of nonoptimality, the designer can easily find a tradeoff between the complexity of the quadratic change detection algorithm and its efficiency