Study On Parameter Estimation Of Chirp Signal

Linear frequency modulation signal (Chirp) as a kind of typical non-stationarysignals, are widely used in communications, radar, sonar, medicine, seismicexploration, and many other signal processing fields. In many cases, somenon-stationary signals with complex time-varying frequency can be approximated asmultiple chirp signal components. Therefore the study of chirp signal has boththeoretical significance and practical value.Time-frequency analysis method can express time-varying frequency intwo-dimensional time-frequency plane, so it is very suitable for non-stationary signalprocessing. For the most existing time-frequency distributions, or resolution is nothigh, or have serious cross-term interference, this paper mainly studied the twoTime-frequency transforms which are suitable for the chirp signal processing, localpolynomial Fourier transform (LPFT) and fractional Fourier transform (FRFT).This paper mainly includes the following contents:1、Local polynomial Fourier transform are studied, and the properties and idealtime-frequency performance of LPFT are analyzed. The cross-terms in the energydistribution of multi-component chirp signals based on LPFT transform are discussedin detail, and points out that the cross terms of local polynomial periodogram can benegligible under certain conditions. Comparing the LPFT with short time Fouriertransform (STFT) and Wigner-Ville distribution (WVD), and the simulation resultsshow that the LPFT owns better time-frequency resolution than STFT, can providemore ideal time-frequency distribution than WVD and is almost free from thecross-term interference when processing the multi-component chirp signal.2、The theory that LPFT can estimate the instantaneous frequency of polynomialphase signal is analyzed. For a single component of the chirp signal, a hierarchicalsearch method is proposed based on LPFT to achieve the fast chirp rate estimation ofChirp signal, and then the initial frequency is estimated by dechirping method, thismethod ensure the estimation accuracy and reduce the computation at the same time.The simulation results show that this method is effective. LPFT under low SNR canstill provide good time-frequency distribution, so a method combining LPFT withHough transform is put forward to achieve detection and parameter estimation ofmulti-component chirp signal in the strong noise background. To compare the methodin this paper with Wigner-Hough Transform method in the simulation experiments,the results show that the method in this paper can still realize the detection andparameter estimation of Chirp signal and achieve good estimation precision in verylow SNR environment, whose anti-noise performance is superior to WHT. In addition, an improved algorithm based on time-frequency filtering is put forward to solve thelarge computation complexity, and an improved algorithm based on thresholdselection is put forward to solve the problem that strong signals shield week signals.3、 Several kinds of definitions and basic properties of fractional Fouriertransform are studied, the theory that FRFT can detect and estimate the chirp signalare analyzed, because the FRFT uses linear frequency modulation base function, it isespecially suitable for processing chirp signal. In view of the problem that traditionalbidimensional peak search method based on FRFT need to scan the angle of rotationand search the peak, and high estimation precision need multiple computationalcomplexity, a detection and estimation method based on time delay multiplicationcombined with FRFT is put forward, and the optimum seeking method is used ininterval searching, this method ensures the accuracy of estimation and reduces thecomputation complexity at the same time. In the process of multi-component chirpsignal, due to the problem that strong signal "submerged" weak signals, the "CLEAN"algorithm is used to achieve detection and estimation of multi-component signalsfrom strong components to weak components.