The marginalized likelihood ratio test for detecting abrupt changes

The generalized likelihood ratio (GLR) test is a widely used method for detecting abrupt changes in linear systems and signals. In this paper the marginalized likelihood ratio (MLR) test is introduced for eliminating three shortcomings of GLR while preserving its applicability and generality. First, the need for a user-chosen threshold is eliminated in MLR. Second, the noise levels need not be known exactly and may even change over time, which means that MLR is robust. Finally, a very efficient exact implementation with linear in time complexity for batch-wise data processing is developed. This should be compared to the quadratic in time complexity of the exact GLR.