Inhomogeneous quadratic tests in transient signal detection: Closed-form upper bounds and application in GNSS

This paper focuses on transient signal detection based on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. These tests arise in many signal processing-related problems in biomedicine, finance or engineering, where sudden changes in the magnitude under analysis need to be promptly detected. Unfortunately, no closed-form expression is available for the density of inhomogeneous quadratic tests, which poses some concerns and limitations in their practical implementation. In particular, when trying to assess their detection performance in terms of probability of detection and probability of false alarm. In order to circumvent this limitation, two closed-form approximations based on results from Edgeworth series expansions and Extreme Value Theory (EVT) are proposed in this work. The use of these approximations is shown through a specific case of study in the context of transient detection for signal quality monitoring in Global Navigation Satellite Systems (GNSS). Numerical results are provided to assess the goodness of the proposed approximations, and to highlight their interest in real life applications.