Bias and standard deviation mean and maximum Doppler frequency estimators

Abstract

The performance of four spectral techniques (FFT, AR Burg, ARMA and Arithmetic Fourier Transform AFT) for mean and maximum frequency estimation of the Doppler spectra is described. The mean frequency was computed as the first spectral moment of the spectrum with and without the noise subtraction. Different definitions of f_max were used: frequency at which spectral power decreases down to 0.1 of its maximum value, modified threshold crossing method [23] and novel geometrical method. "Goodness" and efficiency of estimators were determined calculating the bias and standard deviation of the estimated mean and maximum frequency of the computer simulated Doppler spectra. The power of analysed signals was assumed to have the exponential distribution function. The SNR ratios were changed over the range from 0 to 20 dB. The AR and ARMA models orders selections were done independently according to Akaike Information Criterion (AIC) and Singular Value Decomposition (SVD). It was found, that the ARMA model computed according to SVD criterion had the best overall performance and produced the results with the smallest bias and standard deviation. The preliminary studies of the AFT proved its attractiveness in real-time computation, but its statistical properties were worse than that of the other estimators. It was noticed that with noise subtraction the bias of f_mean decreased for all tested methods. The geometrical method of f_max estimation was found to be more accurate of other tested methods, especially for narrow band signals.