A Hybrid CPF-HAF Estimation of Polynomial-Phase Signals: Detailed Statistical Analysis

Abstract

In this paper, we consider parameter estimation of high-order polynomial-phase signals (PPSs). We propose an approach that combines the cubic phase function (CPF) and the highorder ambiguity function (HAF), and is referred to as the hybrid CPF-HAF method. In the proposed method, the phase differentiation is first applied on the observed PPS to produce a cubic phase signal, whose parameters are, in turn, estimated by the CPF. The performance analysis, carried out in the paper, considers up to the tenth-order PPSs, and is supported by numerical examples revealing that the proposed approach outperforms the HAF in terms of the accuracy and signal-to-noise-ratio threshold. Extensions to multicomponent and multidimensional PPSs are also considered, all supported by numerical examples. Specifically, when multicomponent PPSs are considered, the product version of the CPF-HAF outperforms the product HAF (PHAF) that fails to estimate parameters of components whose PPS order exceeds three.Index Terms-Polynomial-phase signals, high-order ambiguity function, cubic phase function, parameter estimation, multicomponent signals, multidimensional signals, non-Gaussian noise.

A Novel Parameter Estimation Method Based on LSU-EKF for Polynomial Phase Signal

“…In order to use the discrete-time state (21), the model (18) must be discretized somehow [27], and can be described in the form…”

“…Therefore, precise estimations of range, velocity, and acceleration obtained from the echoes of high-speed targets, such as rockets and missiles, are of great importance for radar detection and imaging [9,10]. In recent years, parameter estimation of PPS has attracted considerable attention and many methods have been proposed [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Among these methods, a typical estimator of the unknown coefficients is the least squares estimator [11,12], which is an effective approach, being both computationally efficient and statistically accurate when the noise is white and Gaussian.…”

A Hybrid Algorithm for Estimating the Parameters of Polynomial-Phase Signals

“…Above the threshold, the GCPF-HAF outperforms the HAF and CPF-HAF about 4dB and 2dB, respectively. For multicomponent analysis, the tested signals in this example are the same as the two-component PPS used in [7] except for the amplitudes which are different in [7] Fig. 2(a) and Fig.…”

“…Recently, a simple modification of HAF has been proposed [6,7]. When dealing with monocomponent PPS, this approach indeed outperforms the HAF in terms of the accuracy and signal-to-noise-ratio (SNR) threshold.…”

A Frequency Domain Extraction Based Adaptive Joint Time Frequency Decomposition Method of the Maneuvering Target Radar Echo

“…Compared with the PHAF, CPF uses a lower nonlinear transform and has better performance of the computation and the signal to noise ratio (SNR) threshold. To process higher-order PPS, a series of improved methods are proposed such as a hybrid HAD-CPF method [19] and other modifications [20]. Although the product form of CPF (PCPF) is proposed to reduce the cross terms [21], these CPF methods are also influenced by the cross terms of the mc-PPS as PHAF, especially when the numerous components are contained and the intensities of every component are similar.…”