GLRT Detectors for Aircraft Wake Vortices in Clear Air

In this article, radar echoes of aircraft wake vortices are modeled as weighted sums of the frequency components of the echoes with a special covariance matrix for the weighted coefficients. With a proposed detection scheme, two generalized likelihood ratio test (GLRT) detectors are derived respectively for aircraft wake vortices with time-varying and time-invariant Doppler spectra. Then the analytical expressions for detection and false alarm probabilities of the detectors are derived and three factors are investigated which mainly influence the detection performance, i.e., the Doppler extension and uncertainty of the aircraft wake vortex, and the number of the detection cells. The results indicate that, the signal-to-noise ratio (SNR) loss induced by Doppler extension is generally several decibels. The SNR loss due to Doppler uncertainty is approximately proportional to the logarithm of the number of spectrum lines in the uncertain Doppler spectrum intervals. For a large number of detection cells, the SNR gain is approximately proportional to the square root of the number of the detection cells.