MODIFIED METHOD FOR SIGNAL DELAY ESTIMATION USING ROBUST DFT

Abstract

Modified method for estimating delay and direction of arrival for random wideband signals received by two displaced sensors and corrupted by non-Gaussian noise is designed. The method and corresponding algorithms are based on robust discrete Fourier transform (RDFT) applied in both reception channels instead of standard discrete or fast Fourier transform. The reason for applying the RDFT is to remove impulsive noise component from data. For the proposed modifications, Hodges-Lehman estimate and one simple adaptive estimate are used as robust estimates to determine spectra in both reception channels and, then, to obtain robust estimate of cross-spectrum. After this, cross-correlation function is obtained as inverse DFT from cross-spectrum estimate. Efficiency comparison is carried out for the proposed modifications and approaches designed earlier based on non-adaptive robust estimates as median and alpha-trimmed forms of DFT as well as classic approach. It is assumed that informative process can be modelled as Gaussian process with cut-off frequency smaller than for additive noise. Processes with symmetric alpha-stable distributions are employed as models of non-Gaussian noise where parameter α that relates to tail heaviness is varied in rather wide limits to simulate possible practical situations of different impulsivity of non-Gaussian noise. Noise intensity is varied by changing the parameter γ of symmetric α-stable process. The main attention in accuracy analysis is paid to probability of abnormal estimates of delay which is desired to be minimized. It is shown that the proposed modifications provide better estimation of time delay and direction of signal arrival in terms of abnormal error probability for practical situations when noise has heavy tail distribution and signal-to-noise ratio is low. Whilst for Gaussian noise with α=2 the classic method of signal processing is still the best, the proposed modifications perform considerably better for α=1.8, α=1.6, and α=1.4 the results for which are presented in plots. The proposed modifications, in general, also perform better than processing based on median and alpha-trimmed forms of RDFT.

Keywords

• оцінка затримки
• робастне дпф
• рознесені сенсори
• негаусові завади