Detection And Parameter Estimation Of Polynomial Phase Signal

Polynomial phase signals(PPSs) are found in numerous application fields including radar, sonar, radio communication and geophysics. Therefore there are important theoretical consequences and important application value for the detection and estimation of PPSs. In addition, noise is everywhere, and PPSs are submerged in noise. Many researches focus on the decrease of the signal-noise ratio(SNR) threshold for PPSs. The detection and estimation algorithms for PPSs can loosely be grouped into two classes: one is based on multi-linear transforms, such as the high order ambiguity function(HAF), and its product version(PHAF); Another is based on phase unwrapping, such as Kitchen's unwrapping estimator, the estimator of Djuric. There are their advantages and weaknesses for the two kinds of algorithms.Numerous theories and methods for the detection and parameter estimation of monocomponent PPSs have been proposed in the last decades. Unfortunately, they would be limited if they were used to treat the multicomponent PPSs(mc-PPSs), because the parameter estimation of mc-PPSs is more complex than that of monocomponent PPSs. Thus, according to the methods that have been used to treat PPSs, the study works for the detection and parameter estimation of PPSs are as followings.1.Use sparse representation to detect and estimate PPS in additive white Gaussian noise.The optimal detection for PPSs in additive white Gaussian noise is systematically studied based on sparse representation, and a fast sparse representation algorithm for PPSs is proposed by combining group testing algorithm and fast Fourier transformation(FFT). It can significantly low the SNR threshold.2.De-noise PPSs in additive white Gaussian noise by combining dictionary learning algorithm with sparse representation.A dictionary learning algorithm that can de-noise PPSs in additive white Gaussian noise by using sparse representation, and it can increase the SNR effectively.3.Analyze and solve the uncertain problem in estimating multicomponent polynomial phase signal by using PCPF-HAFTwo effective methods are presented to solve the uncertain problem, one is setting three time points, which is based on the frequencies at three time points are in the same straight line; Another is based on two time points. Firstly, polynomial phase signal is constituted by using the various possible two highest-order phase parameters of each component. Secondly, the polynomial signal is multiplied by the transformed signal, and the sum value is computed. Finally, find the maximum value, and its corresponding parameter estimations are correct.4.Present refined algorithm for estimating the parameters of mc-PPS based on PCPF-HAF.Nonuniformly spaced signal sample methods are presented in order to use FFT in PCPF-HAF, and multiple scaling factors are used to obtain the product in estimating multicomponent third-order polynomial phase signal. Since the amplitude parameters are not refined in filter/unwrapped phase estimates, study the refining polynomial phase signal parameter estimations by using singular value decomposition.