Automated Mode Separation In Oblique Ionograms

x-mode traces is then one of deconvolution. . A convolution may be written y = Hx + e, where x is the signal to be estimated, y is the measured or convolved signal and e is white Gaussian noise. Least squares estimation of x gives x = (H H) -1 H y, but the calculation of the inverse can be numerically unstable. . The LMS algorithm [3] estimates x recursively, taking the (k+1)th estimate of the signal, x k+1 , to be x k+1 = x k + H T (y - Hx k ), where m is a parameter chosen to make the solution stable. Variations of LMS can incorporate the fact that x is positive. . The convolution kernel is not know in advance so a range of kernels are tried, and only the best result kept. . The convolution kernel may vary with group range so each row of the ionogram is deconvolved separately. 4 DECONVOLUTION: PREPROCESSING The ionogram contains noise, overlapping parts of traces and traces which are not part of the F-layer. These can be partially removed through preprocessing. 5 Th