TIME DELAY ESTIMATION OF SIGNALS USING WIGNER-VILLE DISTRIBUTION

The conventional representation of signals in the time domain or frequency domain are inadequate for analysis of signals, the obvious solution was to seek an alternative way to represent the signal as a two-variable function whose domain was two-dimensional space. An effective method based on correlation was proposed in this research work for the estimation time-delay of a signal which is corrupted by the non-stationary random noise. The time delay estimation was converted into parameter estimation. The research shows that the concept of reducing cross-terms with the help of using appropriate parameter values, which are unfortunate mathematical artifacts in determination of Wigner-Ville Distribution (WVD) of a multi-component chirp signal. The research was carried out using Linear Frequency Modulated (LFM) (chirp) signal based on quadratic time-frequency domain. From the derivation as well as simulation result of WVD of a multi-component chirp signal, it was clearly shown that cross-term appears in the middle of the signals. Quadratic TFD (QTFD) is able to provide high time and frequency resolutions but suffer heavily from the cross-terms which cause inaccurate signal interpretation. If the signal characteristics are known, a kernel can be designed that can suppress the cross-terms while preserving the auto-terms which is very important in generating accurate TFD. However, this is not practical in a non-cooperative environment where the exact signal characteristics are unknown. Thus, a new adaptive directional ambiguity function Wigner-Ville distribution (ADAF-WVD) was developed that adaptively estimate the kernel parameters in the ambiguity domain based on the signal characteristics. Accurate TFRs are produced for all signals with IF estimation performance verified using Monte Carlo simulation meeting the requirements of the Cramer-Rao Lower Bound (CRLB) at SNR > 8dB. A time delay estimation of chirp signal based on correlation method is presented which is converted to parameter estimation with less computational complexity and is suitable for chirp signal analysis. The statistical analysis in terms of signal-to-noise-ratio (SNR) and the estimation accuracy was also studied. The proposed method based on correlation, approximates the Cramer-Rao Lower Bound (CRLB) in terms of the inverse mean square errors (MSEs) for different signal-to-noise ratios (SNRs). The method was tested by simulations to show the efficacy which yield result of variance which is theoretically equated to Cramer-Rao Lower Bound (CRLB). The result of the estimation was obtained with the help of construction of appropriate MATLAB code and valid when compared with other simulation results and related theory.