Chirp signal (linear modulated signal, LFM) is a very important signal in digital 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 processing theory and its practice applications. However, the correlation function of Chirp signal contains time variable , i.e. the Chirp signal is nonstationary. So it brings difficulty in our study.The work of this paper includes two primary questions: parameter estimation and time delay estimation of Chirp signals. Various techniques have been used to perform Chirp signals parameter estimations, but they almost have disadvantages of high complexity and huge computational cost. The other shortcoming is that the additive noise of these methods must be restricted in Gaussian noise. In time delay estimation domain, the mature approaches are mostly based on assume of stationary model. The excellent methods of Chirp signal time delay estimation are even less. To solve these questions, here we propose a set of new Chirp signal processing methods based on quadratic form transformation. The main tasks are generalized as:1. The structure of Chirp signal is analyzed and a set of new Chirp signal processing methods are proposed: First, the nonstationary Chirp signals are converted into a kind of stable state by quadratic form transformation. Then the cross-spectral method is used in the later signal processing.2. Based on the analysis of Chirp signals and the additive noise, the quadratic form transformation method suitable for Chirp signal parameter estimation is brought forward. Through it Chirp signal is converted into stationary signal and the correlation function of the stationary signal is discovered.3. The correlation function matrix is gained and its singular value decomposition characters are studied profoundly. Then the cross-spectral MUSIC method, the cross-spectral SVD method and the cross-spectral ESPRIT method are proposed. Chapter three presents the emulation conclusion of the three methods and contrasts them to the famous Radon-Wigner transformation method to testify the correctness and the validity of the new approaches.4. In time delay estimation section, we first explain why the quadratic form transformation suitable for parameter estimation doesn't suit time delay estimation any more. Then the quadratic form transformation method for time delay estimation is offered.5. Time delay method is used to obtain the correlation function of the stationary signal derived from time delay estimation quadratic form transformation. Through the analysis of the correlation function, we find there is a difficulty that the period of cannot be determined. So we put forward a set of new approaches: the cross correlation method is used to get a primary estimation value of Chirp signal delay time, then the cross-spectral MUSIC method and the cross-spectral SVD method are proposed to modify the primary value. Chapter four presents the emulation conclusion of the two methods to verify that they appropriate for practice. Compared with general approaches, the methods in this paper have many prominent virtues:1. They have low complexity. Here we convert Chirp signals into a kind of stable state by quadratic form transformation, which avoid the use of other complicated nonstationary processing methods.2. They have good noise-restrain ability. Because of the introduction of the modern cross-spectral estimation methods, the approaches in this paper can work in low SNR almost without any prior information about colored noise3. Their computational costs are small. The cross-spectral MUSIC method and the cross-spectral SVD method only need one-dimension spectral peak searches, and the cross-spectral ESPRIT method doesn't need any spectral peak search.4. They can get accurate estimation results even with short data sequences. It makes these methods more applicable to engineering practice.5. They all have high resolution a... |