Experiments with maximum entropy and maximum likelihood spectra of VHF radar signals

Abstract

Maximum entropy and maximum likelihood methods (MEM, MLM) are applied to estimate wind‐induced Doppler shifts of VHF radar signals and to compare the accuracies of both methods with the accuracy of the periodogram method used with the SOUSY VHF Radar. At large signal‐to‐noise ratios (S/N ≳ 100), differences between the three Doppler shift estimates are one order of magnitude smaller than the frequency resolution of the periodogram. At moderate signal‐to‐noise ratios (0.3 ≤ S/N ≤ 10), MEM and MLM estimates have significantly higher accuracies than the periodogram estimates with the largest differences in accuracy occurring just above S/N = 0.3; MLM tends to be slightly more accurate than MEM. In contrast to the periodogram method, MEM and MLM clearly indicate a limiting signal‐to‐noise ratio (S/N ≈ 0.3) below which the Doppler shift estimates are dominated by noise rather than radar signals. For any routine application it is of basic importance that there are stochastic relationships between signal‐to‐noise ratio and the prediction error filter lengths of MEM and MLM that yield optimum Doppler shift estimates. Since the accuracy of Doppler shifts obtained by MEM and MLM increases with decreasing spectral width, both methods have their greatest potentials when they are applied to radar signals measured with small antenna beam widths, small pulse lengths and short coherent integration times.