Study On Method Of Harmonic Parameter Estimation In Chaotic Noise Background

Chaotic signal is come from a determinate system which looks like ruleless andseemingly stochastic behavior , it is a ubiquitous complicated dynamics and naturalphenomena. the determinate system mean the chaotic function is known and unchanged.The stochastic character of chaos is that the evolvement of chaos function depend oninitial conditions sensitively and is unpredictable for long time . Chaos theory mainlystudy on nonlinear dynamics system , the purpose of chaotic theory is discovering pos-sible basic rules which hide in the seemingly random phenomena .In fact ,many naturephenomena is nonlinear and traditional linear theory can not explain the phenomena.Chaotic theory study has achieve many fruits since 1970's,including mechanism researchof chaos ,how to produce chaos ,the judgement of chaos and phase space reconstruc-tion etc. Today ,the new trend of chaotic research is change from abstract mathematicsproblem to engineering field.Chaotic signal processing is a fire-new branch of non-linear signal processing. It hasabundant research tasks in natural and engineering field,such as ocean, geology ,biologyand chemistry etc, it also can be used in chaotic secure communication , digital water-mark and electronic warfare. At present, chaotic signal processing becomes a popularscience research field. As an important branch of chaotic signal processing, harmonicsignal parameter estimation from chaotic background has important theory and appli-cation value. For example, the target signal character parameter estimation from seaclutter(which has been proved to be chaotic),fetal electrocardiogram extracted from ma-trix in biomedicine ,weak signal extracted from visual evoked potential and resistingchaotic interference all belong to signal extraction character parameter from chaoticbackground. The theory of harmonic parameter estimation in the chaotic noise back-ground is a new research field in recent ten years ,thus it has no systemic theory. Themethod of harmonic parameter estimation in chaotic background must closely dependon the character and attribute of chaotic signal which is different from other signal pro-cess method .The attribute of chaotic signal including predictable for short time, phase space reconstruction, controllable, fraction etc. Now, most of chaotic signal processingtheory are based on predictable for short time and phase space reconstruction, a fewresearcher use chaotic fraction to study signal detection. While the paper put forwarda new method to chaotic signal processing based on chaotic controllable character (infact , chaotic synchronization belong to chaotic control theory ). In this thesis , manynew theoretical methods ,which are used to harmonic parameter estimation from chaoticbackground under different conditions such as signal to noise , frequency ranges ,havebeen put forward by application of chaotic synchronization and modern signals pro-cessing theories ( cross power spectrum dense analysis , cross-higher-order cumulant ).Imitations by computer have proved effectiveness , robustness and usefulness of thesemethods.The following are the creative works of this thesis:1. This paper presents a frequency parameter estimation method for weak harmonicsignal embedded in chaotic'noise'based on chaotic synchronization. First of all ,wechanged the chaotic synchronization problem to stabilization of chaotic synchronizationerror system .second , we consider the chaotic synchronization driving by mixed signals(chaotic signal ,harmonic signal and other noise) as the stabilization of interfered system,and give some proof of the theory. Last, when chaotic synchronization occurred , theerror data series between drive and response signal have the harmonic signal , using signalprocessing method ,it's easy to estimate the harmonic frequency. The main characteristicof the method can be generalized as: (1) the method is mix of controlling theory andsignal processing theory , because chaotic synchronization actually belongs to chaoticcontrol theory. (2)the method only study the chaotic synchronization driving by onevariable.(3) three methods are presented to analyzing the synchronization error whichare cross spectrum ,MUSIC and SV D ff MN. simulation results show that the twoalgorithms can realize higher accurate and higher reliable frequency parameter estimationthan power spectrum used by other chaotic signal processing method ,another meritof these methods is that they can process more background noise such as Gaussiancolor noise and non-gaussian color noise.(4) The method is suit for the situation wherebackground interference signals is mixture of strong chaotic signal and strong other kindof noise, which is advantage of other kind of chaotic signal methods .2. the thesis present harmonic parameter estimation methods by using chaotic syn-chronization which the model and parameter of chaotic system are known ,in this part,the estimation of chaotic attractor of unification chaos is also given . The main researchcontent are: (1) we proved the relationship between chaotic synchronization error and interference which proof the method of this paper. Simulations show the method is notsensitively to the initial conditions. (2) designing the chaotic synchronization controllerof linear feedback by using estimation of chaotic attractor, emulation show it is betterthan variable substitute chaotic synchronization method.(3) we adopt nonlinear feedbackcontroller to synchronize chaotic system which need not estimation of chaotic attractorand can get a more exact feedback gain.(4) feedback gain adaptive control chaotic syn-chronization is a robust method, which can be used in strong chaotic noise and otherstrong noise.(5)using part of spectrum of chaotic signal ,the response chaotic system canalso synchronize the driving chaotic system, in this section, the filtered driving signaland the filtered error signal are both used to chaotic synchronization , the two methodsare suit for case that background noise is mixture of chaotic noise and wideband noise,and they can detect lower SNR harmonic signal.3. In practice engineering ,chaotic parameters will vary slightly because of compo-nents aging or changing of environment ,so we present a chaotic synchronization methodof parameters variable .In order to design controller ,we estimate the attractor of chaoticsystem with parameters vary. Base on theorem of chaotic synchronization with parame-ter vary, both the linear feedback and nonlinear feedback chaotic synchronization methodare used to estimation harmonic parameter .Since the parameters of driving and responsesystem are different ,the SNR is higher than the case parameter are known. In the end,a ffexible feedback idea is present to compensate the drawback of parameter vary.4. we present a harmonic parameter estimation method based on chaotic synchro-nization with chaotic system parameter fully unknown .In fact , most of application inengineering has no idea of parameter . A technique is introduced for estimating unknownparameters when a time series of only one variable from a multivariate nonlinear dynam-ical system is given. The technique is based on dynamic minimization of synchronizationerror and it loosen conditions of harmonic parameter estimation . In this section twodifferent control methods, linear feedback and adaptive control for synchronizing systemvariables are employed .Though the noise effect the estimation of parameter and syn-chronization ,the adaptive control gain method still work will on estimation parameterfrom chaos interference and other noise.5.In the natural science research ,some chaotic models are so complicated that it ishard to say the two system are same or almost same, such as laser array and life sciences.The research on harmonic parameter estimation by using chaotic synchronization withdifferent models has important value. The controller of chaotic synchronization consti-tute two part: one part is used to compensate the effect of response system variables which are the production of difference of driving-response system ,another is feedbackof error . The thesis only research some representative chaotic system because of thecomplication of chaotic synchronization between different system. Simulation show themethod is also effective.Summarily, in this paper the harmonic signal parameter estimation based on chaoticsynchronization approaches in different conditions is proposed . The method not only canestimation parameters in chaotic noise , but also do in mix noise (chaotic noise and otherkind of noise which can be correlated Gaussian noise and all kinds of uncorrelated noise) .It have many prominent virtues such as strong noise suppression ability, high estimationaccuracy and low computational cost. Both theoretical analysis and simulation resultsdemonstrate the effectiveness of the new methods. Keywords: chaotic noise background, harmonic signal, parameter estimation, chaotic synchronization , cross-higher-ordercumulant.