Parameters Estimation And Time-frequency Analysis Of Chirp Signal

In the field of radar, sonar, vibration measurement, oceanography, seismology, EEG analysis, etc, the signal which is to be processed is time-variational and highly non-stationary, here we need use polynomial phase signal to found up the model. The phase function of the polynomial phase signal is quadratic or high-order function of time. Chirp signal, which is the base of the research of polynomial phase signal, has quadratic polynomial phase. Parameter estimation and the research of time-frequency analysis of chirp signal are not only common problem in the signal processing domain but also part of the research of signal processing theoretic and methods. As the great accomplishment has been achieved in the one-dimensional chirp signal parameter estimation in recent years, the research interest has been naturally turned to the research of parameter estimation of two-dimensional chirp signal. It is not only a necessity to continue the research, but also the needs of practice. Two-dimensional chirp signal can describe the process and the essence more sufficiently, and so it is more valuable in practice. In addition, two-dimensional chirp signal is the basic and representative problem in the multi-dimensional non-stationary signal processing field. So the two-dimensional chirp signal parameter estimation research can benefit the study of relevant field a lot.At present, the time-frequency analysis is the mostly widely used method when we analyzing the chirp signal. Along with the development of the research, the time-frequency analysis method continuously develops. The development of the time-frequency analysis method promotes the analysis and explanation of the chirp signal.After carefully reading a lot of papers on the chirp signal parameter estimation and time-frequency analysis methods, we give a comprehensive sum-up of existing methods, and find that there are three main problems in this field:(1) There is no method of parameter estimation of chirp signal in the non-Gaussian noise.(2) The parameter estimation method is not robustness.(3) Either the time-frequency resolution of the time-frequency analysis is not high or it is serious affected by the cross-terms.Based on the former research, the main innovation of this paper represents in the following three aspects.(1) The problem of parameter estimation of two-dimensional chirp signal in Gaussian MA noise is studied. And a new cross-spectral method based on mutual two-dimensional polynomial transform is proposed. The proposed method can well estimate the parameter of chirp signal in Gaussian MA noise, the estimation precision of the instantaneous frequency rate is high and estimation precision of the initial frequency is able to satisfy the need of project. In order to restrain the Gaussian MA noise, construct different time delay sequences of the received signal, and group the sequences into two teams, do polynomial phase transform to transform the two-dimensional chirp signal into two-dimensional harmonic signal, do cross- correlation to the two harmonic signal and use MUSIC method to estimate the instantaneous frequency rate, after demodulation, still use the former method to estimate the initial frequency.(2) The problem of the instantaneous frequency rate estimation of chirp signal in additive and zero or nonzero mean multiplicative noise is studied, and a new method based on one-dimensional or two-dimensional phase function and one-dimensional or two-dimensional product phase function is proposed. The precision of the proposed is high, and the quantum of calculation is relative small. The one-dimensional and two-dimensional phase function is defined, and the cross terms when the multi-component signal is analyzed using phase function is analyzed, and then the product phase function is defined to estimate the instantaneous frequency rate.(3) The problem of the application of high order statistics in the parameter estimation of chirp signal in colored Gaussian noise is studied, and a method of parameter estimation of chirp signal based on fourth-order cumulates is proposed. Because of the use of high order statistics, the Gaussian noise is well restrained, high precision estimation can be gotten and the calculation quantum is relative small. 1-D and 2-D fourth order cumulant of chirp signal is defined; using ML method to the cumulant, theparameter of the signal can be estimated.(4) The problem of the time-frequency analysis method of single or multi-component chirp signal is researched, and a new time-frequency representation, the SA-PWD, is proposed. The PWD proposed can well restrain the cross-terms and the noise while keeping high time-frequency resolution. By searching the extremum points of the two-order FRFT center momenter, the number of the signal components and the instantaneous frequency rate of each component can be gotten. Then a special window function that is used in the calculation of STFT is constructed. Then the SA-PWD can be calculated.At the same time, this paper has some groping effects to the following three problems.(1) Robustness parameter estimation of chirp signal.(2) Instantaneous frequency rate estimation of chirp signal in complicated noise background.(3) Consummating and developing of the time-frequency analysis method of multi-component chirp signal.