Two Dimensional Harmonic Parameters Estimation And Instantaneous Frequency Analysis Of Chirp Signal

Two-dimensional harmonic parameter estimation is a common problem in the signal processing field, while it is also a very important part in the research of signal processing theory and methods. Two-dimensional harmonic parameter estimation is widely used especially in the field of radar, sonar, vibration measurement, oceanography, seismology, EEG analysis, etc. As the great accomplishment has been achieved in the one-dimensional harmonic parameter estimation in recent years, the research interest has been naturally set in the research of two-dimensional parameter estimation. It is not only a necessity to continue the research, but also the needs of practice. For example, in the field of radar, sonar and oceanography, if the two-dimensional signal is modeled as the one-dimensional signal, then many valuable information will be lost. Two-dimensional harmonic can describe the process and the essence more sufficiently, and so it is more valuable in practice. In addition, two-dimensional harmonic parameter estimation is the basic and representative problem in the multi-dimensional signal processing field. The similar model exists in the problem of T&A (delay of the time and direction of arrival) problem and the 2-D DOA problem. So the two-dimensional harmonic parameter estimation research can benefit the study of relevant field a lot. However, in many practical cases, the signal is time varying and non-stationary, where the simple harmonic model can not describe the time varying information exactly any more. In these cases, the polynomial phase signal—PPS model ought to be used. The phase function of PPS is no longer the linear function of time, but the nonlinear polynomial function. Chirp signal is the PPS with quadratic polynomial phase function, and is the basic model of PPS. For example, radar return echoes from a maneuvering target have nonlinear phase characteristics, depending on the target maneuvers. Constant radial velocity will produce a linear phase term, constant radial acceleration –a quadratic phase term, etc. So the study of PPS, especially the instantaneous frequency of Chirp signal, is of great importance in the effort of making signal processing more reasonable, and will definitely be another hotspot in the signal processing research. The main works in this paper are summed up as follows. After carefully reading a lot of papers on the two-dimensional parameter estimation and Chirp signal instantaneous frequency research, we gave a comprehensive sum-up of existing methods, and found that there are three main problems in this field: (1) The simplification of the noise background, which lead to the failure in practical cases. (2) The limited resolution of existing frequency estimation methods, and most of them can not be used to estimate closely spaced frequencies. (3) The simplification of signal model, and the poor adaptability of the estimation methods. Based on the former research, the main innovation of this paper represent in the following three aspects. (1) This paper presents a new method to estimate frequencies of two-dimensional signal in colored noise, for example the additional non-Gaussian ARMA modeled noise. The main idea of this method is the observation that harmonics in colored noise show themselves as outliers in frequency domain. By using the capability of running median filters to remove outliers from data, we can get the power spectral of colored noise and get rid of the effect of the colored noise from observations. Then we use the two dimensional matrix pencil method or Esprit method to get the high resolution estimation of the frequencies. The outstanding advantage of this method is the strong adaptability to colored noise without known any of its statistical characteristics. The estimation result is of high resolution and the method is easy to realize. The performance of the proposed method is also illustrated by Monte-Carlo simulations. (2) Based on the two dimensional harmonic model, this paper studies the problem of estimating the frequencies of closely spaced complex exponentials in the presence of colored noise, and presents a new estimation approach using the two dimensional decimation technique. By using the capability of decimation in the time domain to increase the frequency intervals, the proposed method first separates the frequencies in the frequency domain, and then gives the exact frequency estimations by using the improved two dimensional matrix pencil method. The proposed method is easy to realize and has successfully improved the...