Research Of Signal Representation And Signal Detection Based On Geometry Information Theory

Information geometry is based on the differential geometric method;it is a set of innovation theory system that discusses the statistical and information theory on Riemann mannifold.And it is called the second generation of Information Theory.With advanced methematical tools and innovative ideas as the support,information geometry provides many scientific issues a new theoretical basis?thinking and methods to solve the problems.Breakthrough results have been achieved in various fields.In this paper,the two basic problems signal representation and signal detection are studied based on the theory of information geometry.In the part of signal representation:1? In order to exploit the signal intrinsic geometric structure,this paper discussed the representation method in a geometric view.At first,by analyzing the structural features of smooth signal,the signal could be mapped to the two-dimensional geometry in space.Then,form the sinusoidal signal,a detailed analysis of the geometrical characteristics and properties of the different signals is made under the representation methods.At last,the corresponding relationship between the geometric quantities and the signal information is studied.2? ccroding to the randomness of the signals contaminated by various of noises,we regarded the signals as a probability density function and represented them by using the Gaussian mixture model(GMM),so that the signal data is maped to the statistical manifold and then the signal can be analyzed by the correlation theory of geometry information.In the part of signal detection,based on the signal representation method,this paper mainly diucusses the following three aspects:1?Sinusoidal signal fault detection: in accordance with the need of sensible and reliable incipient fault detection methods,a fault detection method based on geometry signal represention is proposed.Firstly,the signals are represented by the geometry method.By observing the geometry quantities of the signals which are estmated by the least square ellipse fitting,we can detect the incipient fault such as parameters change,the unknown noise emergence,the deformation and so on.Simulation verifies the validity of the method.2?Signal detection in the Non-Gaussian background: Detection of weak stochastic signal under non-Gaussian background is a difficult problem,especially when the prior knowledge of the background as well as the signal is lacking,in accordance with this problem,this paper proposed an unknown stochastic signal detection algorithm using information geometry tools.Firstly we use Gaussian Mixture Model(GMM)to model the signals under detected.Secondly,the Kullbakc-Leibler divergence(KLD)between the GMMs of signal and noise is calculated to measure the difference between the signal and noise.Thirdly,the signal is detected by comparing the KLD with the threshold.Simulation results are presented to show the effectiveness and detection performance of the proposed algorithm under such situation.3?Radar signal CFAR detection: in accordance with the problems that traditional CFAR detection methods,this paper proposed a method processing the detection problem on the statistical manifold under the guiding of the framework of information theory.The correlation data of the detecting unit data are considered.Firstly,we use GMM to represent the detection unit data instead of regarding it just as algebra.Secondly,the Total Bregman Divergence(TBD)is used to calculate the GMM centers of the data replacing the former power average method which is considered in the Euclidean space.Thirdly,we distinguish the two hypotheses by the measurement of the Bregman divergence.Finally,the improve method is verified by simulation.