Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we have developed theoretical properties of the least squares estimators (LSEs) of the parameters of multi-component chirp model with equal chirp rates, where the model is contaminated with linear stationary errors. We also propose two computationally efficient estimators as alternative to LSEs, namely sequential combined estimators and sequential plugin estimators. Strong consistency and asymptotic normality of these estimators have been derived. Interestingly, it is observed that sequential combined estimator of the chirp rate parameter is asymptotically efficient. Extensive numerical simulations have been performed, which validate satisfactory computational and theoretical performance of all three estimators. {We have also analysed a simulated radar data with the help of our proposed estimators of multi-component chirp model with equal chirp rates, which performs efficiently in recovery of inverse synthetic aperture radar (ISAR) image of a target from a noisy data.

翻译：具有相等调频率的多分量Chirp信号模型出现在多种雷达应用中，例如合成孔径雷达、快速移动目标的回波信号等。针对此类模型，已有多种次优估计器被提出，但这些方法存在可识别性问题或误差传播效应。本文推导了在模型受线性平稳误差污染条件下，具有相等调频率的多分量Chirp模型参数的最小二乘估计量的理论性质。同时，我们提出了两种作为最小二乘估计替代方案的高效计算估计量，即序贯组合估计量和序贯插件估计量，并建立了这些估计量的强相合性和渐近正态性。有趣的是，研究发现调频率参数的序贯组合估计量具有渐近有效性。通过大量数值仿真验证了三种估计量在计算和理论性能上的优越性。此外，我们利用所提出的相等调频率多分量Chirp模型估计量分析了模拟雷达数据，该方法能从含噪数据中高效恢复目标的逆合成孔径雷达图像。