The Study On Novel Time Delay Estimation Methods Based On Stable Distribution

The Gaussian distribution plays a predominant role in signal processing. Its simple justification by the Central Limit Theorem and attractive analytic properties has made it the most important statistical distribution. However, there are many phenomena which are decidedly non-Gaussian and therefore are necessary to look beyond oversimplified Gaussian assumption and into more realistic non-Gaussian models. Any non-Gaussian assumption of signal or noise will inevitably introduce nonlinear and/or nonminimum phase problems, which result in complexity of signal processing algorithms, model construction and analytic computation.The estimation or tracking of the time delay between received signals impinging on two separated sensors is important in some fields, such as sonar, radar, biomedical application and position locating in wireless networks, etc. Although the work that deals with the problem of time delay estimation has already been presented in the literature, it has always assumed a Gaussian signal and noise model. A better model for the noise is the a stable distribution which can model, in addition to the Gaussian distribution, a wider and more impulsive range of phenomena. Based on this obersation, new methods for time delay estimation in impulsive noise environments are studied using theαstable distribution theory. And multipath time delay estimation problem is thrown into signal reconstruction to arise novel alogrithms. Main research and conclusions are summarized as:(1)New time delay estimation methods for impulsive noise environments are addressed. The impulsiveness ofαstable distributed noise can make the performance of conventional time delay estimation methods degrade even invalidate. Firstly, considering the effect of a stable distributed noises for the classical second order statistics, this dissertation combines covariation spectrum and chirp Z transformation (CZT) which is one of the most useful spectrum analysis methods, and consequently proposes a novel multi-source time delay estimation method in impulsive noise environment. Simulations show that the proposed algorithm is a high resolution method suited forαstable distributed noises condition and its performance is better than the common method named covariation method. Secondly, two roubst adaptive algorithms are proposed for fractional time delay estimation which define novel cost function and transfer the time delay estimation into the parameter estimation of FIR filter. Some conclusions are deduced in theory. (2) Taking into consideration the influence ofαstable distributed noise on second order cyclostationary statistics, fractional lower order cyclostationary statistics are developed, and then applied to time delay estimation problems. The trational cyclic correlation is just a correlation of two frequency shift signals and in nature cyclic spectrum is just power spectrum with two dimentions which represent time lag and cyclic frequency respectively. Therefore theαstable distributed noise has impact on them. Combinig with the theory of fractional lower order statistics theory, novel function are introduced and their properties are proven. Firstly, an approach for estimating time delay with signal selectivity in the presence of impulsive noise is developed. Simulations show that the performance of proposed algorithm is not only better than that based on second order cyclic correlation, but also the covariation algorithm. Secondly, considering such circumstance that relative motions can be discribed as a fixed time delay and Doppler shift, a new algorithm based on the propesed p th order cyclic ambiguity function is investigated.It is showed that time delay and Doppler shift can be jointly estimated in the presence of impulse noise. It has better estimation accuracy than second order, fractional lower order and cyclic ambiguity function. Finally, a new adaptive time delay estimation method is proposed for highly corruptive environments, which is based on the proposed robust cyclic correlation estimator. Simulations show that the performance of the proposed algorithm is superior to the LMP (Least Mean P-norm) time delay estimation method and adaptive time delay estimation method based on second order cyclic correlation in alpha-stable distributed noises.(3)According to Whittaker-Shannon theorem, this dissertation announces that the problem of multipath time delay estimation is equal to that of signal reconstruction problem. Firstly, the multi-dimention optimization is transfered into mulitiple one-dimention optimization, which simplize the process.Then by using the match pursuit and subspace pursuit algorithms in compressing sense theory, the amplitude and time difference of different paths are gained. At the same time, a proposed adaptive subspace pursuit algorithm is applied into multipath time delay estimation, which needs less prior knowledge with effective results.