Study On Methods Of Parameter And Time Delay Estimation Of Chirp Signals In Colored Noise

Recently , we have made great progress in the estimation of weaksignal in noises . Such as spectral estimation applies cross-spectral theoryand high-order self-spectral theory up to now .So Cross-high-ordermoment(CHOM) method based high-order cumulant and cross-spectralestimation . The cross-high-order-moment such as the cross-fourth-ordermoment is firstly proposed to measure both the Chirp signal parameterestimation and the Chirp signal time delay estimation are affected in colorednoise .Chirp signal (linear modulated signal, LFM) is a very important signal indigital signal processing community. It is widely used in many systems, e.g.,communication, radar, sonar, seismography, geology and bioengineering.The research on Chirp signal is of significance in both signal processingtheory and its practice applications. However, the correlation function ofChirp signal contains time variable t, i.e. the Chirp signal is nonstationary.So it brings difficulty in our study.The work of this paper includes two primary questions: parameterestimation and time delay estimation of Chirp signals. Various techniqueshave been used to perform Chirp signals parameter estimations, but theyalmost have disadvantages of high complexity and huge computational cost.The other flaw is that the additive noise of these methods must be restrictedin Gaussian noise. In time delay estimation domain, the mature approachesare mostly based on assume of stationary model. The excellent methods ofChirp signal time delay estimation are even less. To solve these questions,here we propose a set of new Chirp signal processing methods based onthe cross-high-order-moment method .In parameter estimation domain , frequency modulation slope-m andinitialization frequency-f are estimated . Based on the analysis of Chirpsignals and the additive noise , four correlation Chirp signals are producedby estimation . Then , The cross-high-order moment matrix is gained and itssingular value decomposition characters are studied profoundly . Thirdly ,the cross-high-order moment Pisarenko method , the cross-high-ordermoment minimum norm-TLS method , the cross-high-order moment MUSICmethod and the cross-high-order moment ESPRIT method are proposed ,frequency modulation slope-m is gained by estimation . In order toinitialization frequency-f is gained by frequency modulation slope-mestimation value , the cross-high-order moment matrix is regained then thecross-high-order moment Pisarenko method , the cross-high-order momentminimum norm-TLS method , the cross-high-order moment MUSIC methodand the cross-high-order moment ESPRIT method are proposed . Chapterthree presents the emulation conclusion of the four methods and testify thecorrectness and the validity of the new approaches based on mulriple Chirpsignals are effective to estimation from colored noises . The newapproaches pssess high resolution and stability, computational costs arealso small .In time delay estimation domain , The cross-high-order moment matrixis gained and its singular value decomposition characters are studiedprofoundly , but the cross-high-order moment matrixes of time delayestimation and parameter estimation are ineqable . In the cross-high-ordermoment matrixe of time delay estimation , add the accessional phase inorder to avoid cross multiply .the cross-high-order moment matrix is gainedand its singular value decomposition characters are studied profoundly , buttime delay estimation is gained are multi-value . The cross correlationmethod is used to get a primary estimation value of Chirp signal delay time ,then the cross-high-order moment Pisarenko method , the cross-high-ordermoment minimum norm-TLS method , the cross-high-order moment MUSICmethod and the cross-high-order moment SVD method are proposed tomodify the primary value . Chapter four presents the emulation conclusion ofthe four methods to verify that they appropriate for practice . If the crosscorrelation method is get a primary accurate estimation value of Chirp signaldelay time , then the cross-high-order moment Pisarenko method , thecross-high-order moment minimum norm-TLS method , the cross-high-ordermoment MUSIC method and the cross-high-order moment SVD method canput into practice .The main tasks are generalized as:1. The structure of Chirp signal is analyzed and a set of new Chirpsignal processing methods are proposed: First, the nonstationary Chirpsignals are estimated by the cross-high-order moment method .2. Based on the analysis of Chirp signals and the additive noise,cross-high-order moment method suitable for Chirp signal parameterestimation is brought forward. Then cross-high-order moment function isdiscovered.3. The cross-high-order moment matrix is gained and its singular valuedecomposition characters are studied profoundly. Then the cross-high-ordermoment Pisarenko method , the cross-high-order moment minimumnorm-TLS method , the cross-high-order moment MUSIC method and thecross-high-order moment ESPRIT method are proposed. Chapter threepresents the emulation conclusion of the three methods and contrasts themto the famous Radon-Wigner transformation method to testify thecorrectness and the validity of the new approaches.4. In time delay estimation section, we first explain why thecross-high-order moment method suitable for parameter estimation doesn'tsuit time delay estimation any more. Then the cross-high-order momentmethod for time delay estimation is offered.5. Time delay estimation method is used to obtain the cross-high-ordermoment function . Through the analysis of the function, we find there is adifficulty that the period of 2π mτ i cannot be determined. So we put forwarda set of new approaches: the cross correlation method is used to get aprimary estimation value of Chirp signal delay time, then thecross-high-order moment Pisarenko method , the cross-high-order momentminimum norm-TLS method , the cross-high-order moment MUSIC methodand the cross-high-order moment SVDmethod are proposed to modify theprimary value. Chapter four presents the emulation conclusion of the fourmethods to verify that they appropriate for practice.Compared with general approaches, the methods in this paper havemany prominent virtues:1. They have low complexity. Here we estimate directly nonstationarysignal, which avoid the use of other complicated convert Chirp signals into akind of stable state by quadratic form transformation processing methods.2. They have good noise-restrain ability. Because of the introduction ofthe cross-high-order moment estimation methods, the approaches in thispaper can work in low SNR almost without any prior information aboutcolored noise3. They can get accurate estimation results even with short datasequences. It makes these methods more applicable to engineeringpractice.4. They all have high resolution and stability.Generalized speaking, we consider that both the Chirp signal parameterestimation methods and the Chirp signal time delay estimation methodsproposed in this paper have academic significance and engineeringapplicable value. They are effective and can put into practice.