Study On Theory And Methods Of Time-delay Estimation Of Signal With Alpha Stable Noise

Gause signal model occupies a dominant position in traditional signal processing. In many cases, the hypothesis of signal Gause distribution is reasonable and can be proved by central limit theorem is proper. Although Gause model can depict many kinds of signal and noise well, in fact there are a lot of Non-Gause signal and noise. Such as underwater sound signal, voice signal, low frequency atmosphere noise, many biomedicine signals and many artificial signals and noises .These signals and noises belong to broad sense Gause distribution—αstable distribution.αstable distribution is a distribution which broaden the finite variance restrict in broad sense central limit theorem. This distribution has considerable meaning in actual application. The probability density function ofαvoice has more thick streak than Gause distribution ,so the voice owns very strong impulsive character. This kind of distribution has no close second moment, thus it is very difficult to analytical analysis which must be processed in Banach space instead of Hilbert spaceTime-delay is an important character feature of signals. Time-delay estimation has significant meaning and is a very active field in signal processing. It has significent sense in both practice and theoretics. When studying principle andmethods of time-delay estimation scholars using principle and methods of digital signal processing , signal detection and estimation , time sequence analysis and modeling and adaptive signal processing ,and then prove new power to these fields, advance the development of these fields. On the other side , the development of time-delay estimation are rapidly used in military field such as radar sonar and electroacoustic measuring, industrial fields such as oil exploration , seismic exploration ,allocation for leaking position of buried pipe line, and scientific fields such as ocean acoustic ,seismology and biomedicine.Traditional time-delay estimation methods are most based on seconds-order or high-order statistics that have gained very good effect when dealing with Gause signal and traditional Non-Gause signal. But work false when dealing withαstable noise because of lack of finite variance, even give wrong result. These years there appear some methods aimed at dealing withαstable noise .These methods are most based on fractional lower-order statistics, so couples of signal and noise are imported because of using of non-linear transformation.This thesis lists the traditional time-delay estimation methods. It is to emulate the traditional correlation method and point out the degeneration of these methods in time delay estimation withαstable noise signals.To evaluate the performance of different kind of methods, I bring forward two criterion named global peak degree and local peak degree. The two criterion are abroad used in the thesis. The thesis study methods appearing these years aimed atαstable noise, and especially study carefully methods based on fractional lower-order statistics, compare the performance with noise of different SNR andαvalue. I point out that the methods will work worse whenαvalue approach 2 and then prove it insimulations. I analyze the adaptive method based on least p norm, and discuss the iteration process based on grads and Newton methods.The thesis bring out two new methods for time-delay estimation : method base on limiting scope integrator and time-delay estimation method based on perfect delay filter. They show excellent performance in simulation.Because second-order moment ofαstable signal if infinite , traditional time-delay estimation method work badly when dealing with signal withαstable noise. So to use traditional method to estimate time-delay of signal with stable noise, we must modulate signal so that the second-order and high-order moment of signal modulated would be cut down to finite. Fractional lower-order statistics are such kinds of modulation method. But it bring in couple of signal and noise. For these reason ,we bring out the time-delay estimation method based limits scope integrator .Method base on limiting scope integrator can cut downαstable noise power with little couple of signal and noise. After modulated , any order moment of signal will be finite. The thesis study three kind integrators, and integrator 2 perform best for it remain signal's information farthest and doesn't introduce any impulsive noise.To use limiting scope integrator to estimate time-delay, one of the most important problem is to decide the scope limit. If we know the limit of signal amplitude, we can set scope limit to 3-5 times of toplimit of the signal amplitude. If we know the signal amplitude and the SNR between signal and Gause noise, then we can calculate scope limit by formula 4.2.2 . And if we know nothing about signal and noise, we can set scope limit to 2-4 time of standard deviation of the received signal.The thesis particular compare the performance of the time-delay estimation method based on limiting scope integrator when the SNR andαof the signal and noise change. We point out that the smallerαis ,the tolerant scope limit coefficient allowed. The thesis also compare the performance of the three integrator when using in time-delay estimation ,and point out that integrator 2 performs best. We also compare the performance of method based on limiting scope integrator and the existing method based on fractional lower-order statistics.The aim of the time-delay estimation if to get a serial of numbers that contains the only"1"at the time-delay position and"0"at all the other position. Adaptive methods were designed to get best filter performance. In traditional use of adaptive methods, our main purpose was to get the filter result. But in time-delay estimation, we don't care how the filter result is like. We give more attention to the final filter parameters.For the two reason mentioned above, we design the time-delay estimation method based on perfect delay filter. The method can get ideal result of time-delay estimation. In this thesis we particular analyze the performance of the method when SNR andαof signal and noise changed. We point out that the method tolerate lower SNR whenαbecome smaller. Whenα=0.4 the method give right result at even SNR=-60DB.The traditional time-delay estimation method, based on either correlation or adaptive method, is not sensitive to the signal attenuation which only influences the signal voice. These methods can do nothing with estimation of the signal attenuation. However, the time-delay estimation method which based on the ideal time-delay filter can get different results from different attenuation degree will be used to estimate the attenuation. In this thesis we deduce the formula to estimatethe signal attenuation inαvoice according to the time-delay estimate results that is unreachable by those traditional and based on the related or self-adaptation time-delay estimation numeration.