This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., $$ a_{P} $$ a P and $$ a_{P - 1} $$ a P - 1 of each component), all possible $$ a_{P} $$ a P and $$ a_{P - 1} $$ a P - 1 must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible $$ a_{P} $$ a P and $$ a_{P - 1} $$ a P - 1 . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomial-phase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims.

中文翻译：

---

一种用于估计多分量多项式相位信号参数的改进 PCPF 算法

本文考虑了阶数大于二的多分量多项式相位信号 (mc-PPSs) 的参数估计。当 mc-PPS 阶数超过三个时，所提出的方法结合了乘积三次相位函数 (PCPF) 和高阶模糊函数 (HAF)。在所提出的方法中，首先将 HAF 应用于观察到的 mc-PPS 以产生立方相位信号。其次，修改算法以使用 CPF 估计 mc-PPS 的参数。为了获得两个最高阶参数（即每个分量的 $$ a_{P} $$ a P 和 $$ a_{P - 1} $$ a P - 1）的准确估计，所有可能的 $$ a_{ P} $$ a P 和 $$ a_{P - 1} $$ a P - 1 在这一步中必须在所有瞬时频率组合中获得；然后，所有和值的最大绝对值必须通过对所有可能的 $$ a_{P} $$ a P 和 $$ a_{P - 1} $$ a P - 1 进行解密来识别。此外，非均匀间隔信号采样方法用于在 CPF 中采用快速傅立叶变换。所提出的方法不同于其他研究人员提出的PCPF-HAF方法；它被称为改进的 PCPF-HAF 方法，可以弥补传统方法在估计 mc-PPS 参数时的缺点。此外，PCPF-HAF 方法不能用于处理多分量三阶多项式相位信号，但所提出的方法可以使用非均匀间隔信号采样方法处理它们。与 CPF 相比，还可以更有效地抑制交叉项，导致估计参数的更高准确性和更低的信噪比阈值。提出了理论分析和模拟来支持这些主张。